ludwig wittgenstein (auth.), jaakko hintikka (eds.)-wittgenstein in florida_ proceedings of the...

WITTGENSTEIN INFLORIDA

Proceedings of the Colloquium on the Philosophy of Ludwig Wittgenstein,

Florida State University, 7-8 August 1989

Editedby

JAAKKO HINTIKKA

Reprinted from

Synthese Volume 87, Nos. 1-2, 1991

SPRINGER SCIENCE+BUSINESS MEDIA, B.V.

ISBN 978-94-010-5573-4 ISBN 978-94-011-3552-8 (eBook)

DOI 10.1007/978-94-011-3552-8

Printed on acid-free paper

AlI Rights Reserved © 1991 Springer Science+Business Media Dordrecht

Originally published by Kluwer Academic Publishers in 1991 Softcover reprint ofthe hardcover 1st edition 1991

No part of the material protected by this copyright notice may be reproduced or utilized in any form or by any means, electronic or mechanical,

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SYNTHESE / Volume 87 Nos.1-2 May 1991

SPECIAL ISSUE ON WITIGENSTEIN

Part I

Preface 1

LUDWIG WITIGENSTEIN (HEIKKI NYMAN, editor; C. G. LUCKHARDT and M. A. E. AUE, translators) / Philosophy: Sections 86-93 (pp. 405-35) of the so-called "Big Typescript" (Catalog Number 213) 3

BURTON DREBEN and JULIET FLOYD / Tautology: How not to Use a Word 23

DAVID CHARLES McCARTY / The Philosophy of Logical Wholism 51

STEVE GERRARD / Wittgenstein's Philosophies of Mathematics 125

JULIET FLOYD / Wittgenstein on 2, 2, 2 ... : The Opening of Remarks on the Foundations of Mathematics 143

Partll

JAAKKO HINTIKKA / An Impatient Man and his Papers 183

DA VID STERN / The "Middle Wittgenstein": From Logical Atomism to Practical Holism 203

M. R. M. TER HARK / The Development of Wittgenstein's Views about the Other Minds Problem 227

C. GRANT LUCKHARDT / Philosophy in the Big Typescript: Philosophy as Trivial 255

DA VID PEARS / Wittgenstein' s Account of Rule-Following 273

MICHAEL LEE KELLY / Wittgenstein and "Mad Pain" 285

KENT LINVILLE and MERRILL RING / Moore's Paradox Revisited 295

THEODORE R. SCHATZKl / Elements of a Wittgensteinian Philoso-phy of the Human Sciences 311

PREFACE

Most of the papers appearing in volume 87 numbers, 1-2 are based on papers presented at the Colloquium on the Philosophy of Ludwig Wittgenstein held at the Department of Philosophy at Florida State University on 7-8 April 1989. We owe warm thanks to Florida State University for generously supporting this colloquium. The English translation of the chapter entitled 'Philosophie', from Wittgenstein's typescript number 213 (von Wright), appears here with permission of Wittgenstein's literary heirs, without affecting existing copyrights. The original German version of this chapter was edited by Heikki Nyman and appeared in Revue Internationale de Philosophie 43 (1989), pp. 175-203. Jaakko Hintikka's article (87, No.2) first appeared in a shorter form in The Times Literary Supplement No. 4565 (28 September to 4 October 1990, p. 1030). The present version appears with the permission of The Times Literary Supplement, which is gratefully acknowledged. Our thanks are due to all the participants of the colloquium and the contributors to these special numbers.

JAAKKO HINTIKKA

Synthese 87: 1, 1991.

LUDWIG WITTGENSTEIN

PHILOSOPHY

SECTIONS 86-93 (pp. 405-35) OF THE SO-CALLED "BIG TYPESCRIPT" (CATALOG NUMBER 213)

Edited by HEIKKI NYMAN

Translated by c. G. LUCKHARDT AND M. A. E. AUE

EDITORIAL NOTE

One of the most interesting writings by Wittgenstein is the typescript no. 213 in von Wright's catalogue (see G. H. von Wright, Wittgenstein, Basil Blackwell, Oxford, 1982, pp. 43-57). This work is colloquially known as The Big Typescript. It is unlike Wittgenstein's other writings in that it is organized in an almost conventional way into chapters and sections. Parts of The Big Typescript were included by Rush Rhees in the volume called Philosophical Grammar, but much of the text has so far remained unpublished.

What appears here (in the original German) is the chapter entitled 'Philosophie' (pp. 405-35 of the original). This chapter is Wittgenstein's most extensive statement of his conception of philosophy. Even if we make due allowance for the development of Wittgenstein's views, this chapter is of great importance for the understanding of Wittgenstein's entire philosophy. It appears here with the kind permission of Professor G. E. M. Anscombe and Professor G. H. von Wright.

The typescript form of TS 213 suggests that Wittgenstein might have considered it for publication. If so, he quickly changed his mind, and began to make handwritten changes in the typescript. They have been indicated here as fully as possible. The actual editing has been carried out by Heikki Nyman.

I hope that the publication of this important chapter helps our readers to appreciate more and more the scope and subtlety of Wittgenstein's thought.

JAAKKO HINTIKKA

Synthese 87: 3-22, 1991. This translation © 1991 Kluwer Academic Publishers.

4 LUDWIG WITTGENSTEIN

EDITOR'S NOTE

The text of the typescript is rendered here as accurately as possible. All alternatives which have been typed into the typescript, both those indicated by the symbols / / ... / /, as well as those written in over the line, are rendered in the edited text. On the other hand, all handwritten additions by Wittgenstein (alternatives, corrections and marginal notes) are given in footnotes. '

In the margins of the pages of the typescript there are also numerous diagonal lines and crosses entered in handwriting. These notations, whose meaning or weight cannot be determined unambiguously, have not been included in this edition. However, the question marks above the lines as well as the broken underlinings - both indications of discontent or uncertainty - were retained.

I did not want to alter Wittgenstein's orthography or his notation, and without noting it I have corrected only a couple of obviously erronemis parts of the text.

HEIKKI NYMAN

TRANSLATORS NOTE

We wish to thank Professor G. E. M. Anscombe for going over our translation with us, and Mr. D. Hudson Mulder for his helpful comments on a draft of the translation.

C. G. LUCKHARDT

M. A. E. AUE

PHILOSOPHY 5

86

DIFFICULTY OF PHILOSOPHY NOT THE INTELLECTUAL DIFFICULTY OF THE

SCIENCES, BUT THE DIFFICULTY OF A CHANGE OF ATTITUDE. RESISTANCES

OF THE WI L L MUST BE OVERCOME.

As I have often said, philosophy does not lead me to any renunciation, since I do not abstain from saying something, but rather abandon a certain combination of words as senseless. In another sense, however, philosophy requires a resignation, but one of feeling and not of intellect. And maybe that is what makes it so difficult for many. It can be difficult not to use an expression, just as it is difficult to hold back tears, or an outburst of anger I /ragel I.

I(Tolstoy: the meaning (meaningfulness) of a subject lies in its being generally understandable. - That is true and false. What makes a subject difficult to understand - if it is significant, important - is not that some special instruction about abstruse things is necessary to understand it. Rather it is the contrast between the understanding of the subject and what most people wan t to see. Because of this the very things that are most obvious can become the most difficult to understand. What has to be overcome is not a difficulty of the intellect, but of the will.)1

Work on philosophy is - as work in architecture frequently is -actually more of alia kind of! I work on oneself. On one's own conception. On the way one sees things. (And what one demands of them.)

Roughly speaking, in Ilaccording toll the old conception - for instance that of the (great) western philosophers - there have been two kinds of problems in fields of knowledge Iitwofold kinds of problems ... .I I: essential, great, universal, and inessential, quasi-accidental problems. And against this stands our conception, that there is no such thing as a g rea t, essential problem in the sense of "problem" in the field of knowledge.

87

PHILOSOPHY SHOWS THE MISLEADING ANALOGIES IN THE USE OF LANGUAGE.

Is grammar, ~~ ~ ~_~~ ~~_~ ,,:,()_~~, only the description of the actual


handling of language I /languagesl I? So that its propositions could actually be understood as the propositions of a natural science?

That could be called th~ descriptive science of speaking, in contrast to that of thinking.

Indeed, the rules ?f ~h~_~~ could be taken as propositions from the natural history of man. (As the games of animals are described in books on natural history.)

If I correct a philosophical mistake and say that this is the way it has always been conceived, but this is not the way it is, I always point to an analogy I II must always point to ... .I I that was followed, and show that this analogy is !!1:~9.~~~_C:~' I I . ... I must always point to an analogy according to which one had been thinking, but which one did not recognize as an analogy.! I

The effect of a false analogy taken up into language: it ~~~!!~ a constant battle and uneasiness (as it were, a constant stimulus). It is as if a thing seemed to be a human being from a distance, because we don't perceive anything ~~~!!!!~, but from close up we see that it is a tree stump. The moment we move away a little and lose sight of the explanations, 0 n e figure appears to us; if after that we look more closely, we see a different figure; now we move away again, etc., etc.

(The irritating character of grammatical unclarity.)

Philosophizing is: rejecting false arguments.

The philosopher strives to find the liberating word, that is, the word that finally permits us to grasp what up until now l has intangibly weighed down our consciousness.

(It is as if one had a hair on one's tongue; one feels it, but cannot grasp I Iseizel I it, and therefore cannot get rid of it.)

The philosopher delivers the word to us with which one I III I can express the thing and render it harmless.

(The choice of our words is so important, because the point is to hit upon the physiognomy of the thing ~_~~.':~l}, because only the exactly aimed thought can lead to the correct track. The car must be placed on the tracks r~~_~~~~}X ~~, so that it can keep rolling correctly.)

PHILOSOPHY 7

One of the most important tasks is to express all false thought processes so characteristically that the reader says, "Yes, that's exactly the way I meant it". To make a tracing of the physiognomy of every error.

Indeed we can only convict someone else of a mistake if he acknowledges that this really is the expression of his feeling. / /. . .. if he (really) acknowledges this expression as the correct expression of his feeling.! /

For only if he acknowledges it as such, is it the correct expression. (Psychoanalysis. )

What the other person acknowledges is the analogy I am proposing to him as the source of his thought.

88

WHERE DOES THE FEELING THAT OUR GRAMMATICAL INVESTIGATIONS

ARE FUNDAMENTAL COME FROM?

(Questions of different kinds occupy us, for instance "What is the specific weight of this body", "Will the weather stay nice today", "Wh02 will come through the door next", etc. But among our questions there are those of a special kind. Here we have a different experience. The questions seem to be more fundamental than the others. And now I say: if we have this experience, then we have arrived at the limits of language. )3

Where does our investigation get its importance from, since it seems only to destroy everything interesting, that is, all that is great and important? (As it were all the buildings, leaving behind only bits of stone and rubble.)

Whence does this observation derive its importance: 4 the one that points out to us that a table can be used in more than 0 n e way, that one can think up a table that instructs one as to the use of a table? The observation'that one can also conceive of an arrow as pointing from the tip to the tail, that I can use a model as a model in different ways?


What we do is to bring words back from their metaphysical to their correctS (normal) use in language.

(The man who said that one cannot step into the same river twice said something wrong; one can step into the same river twice.)

And this is what the solution of all philosophical difficulties looks like. Their6 answers, if they are correct, must be homemade and ordinary.7 But one must look at them in the proper splik-aocfihen it doesnS- matter. 8 ------ --

Where do / /did/ / the old philosophical problems get their importance from?

The law of identity, for example, seemed to be of fundamental importance. But now the proposition that this "law" is nonsense has taken over this importance.

I could. ask: why do I sense a grammatical joke as being in a certain sense dee'p? (And that of course is what the depth of philosophy is.)

Why do we sense the investigation of grammar as being fundamental?

(When it has a meaning at all, the work "fundamental" can also mean something that is not metalogical, or philosophical.)9

The investigation of grammar is fundamental in the same sense in which we may call language fundamental - say its own foundation.

Our grammatical investigation differs from that of a philologist, etc.: what interests us, for instance, is the translation from one language' into other languages we have invented. In general the rules that the philologist totally ignores are the ones that interest us. Thus we are justified in emphasizing this difference.

On the other hand it would be misleading to say that we deal with the essentials of grammar (he, with the accidentals).

"But that is only an external differentiation / Ian external difference/ /." I believe there is no other.

Rather we could say that we are calling something else grammar than he is. Even as we differentiate kinds of words where for him there is no difference (present).

----------

The importance of grammar is the importance of language.

PHILOSOPHY 9

One could also call a word, for instance 'red', important insofar as it is used frequently and for important things, in contrast, for instance, to the word 'pipe-lid'. And then the grammar of the word 'red' is important because it describes the meaning of the word 'red'.

(All that philosophy can do is to destroy idols. And that means not creating a new one - for instance as in "absence of ar idol".)

89

THE METHOD OF PHILOSOPHY: THE PERSPICUOUS REPRESENTATION

OF GRAMMATICAL / /UNGUISTIci / FACTS.

THE GOAL: THE TRANSPARENCY OF ARGUMENTS. JUSTICE. lO

Someone has heard that the anchor of a ship is hauled up by a steam engine. He only thinks of the one that powers the ship (and because of which it is called a steamship) and cannot explain to himself what he has heard. (Perhaps the difficulty doesn't occur to him until later.) Now we tell him: No, it is not t hat steam engine, but besides it a number of other ones are on board, and one of these hoists the anchor. - Was his problem a philosophical one? Was it a philosophical one if he had already heard of the existence of other steam engines on the ship and only had to be reminded of it? - I believe his confusion has two parts: what, the explainer tells him as fact the questioner could easily have conceived as a possibility by himself, and he could have posed his question in a definite form instead of in the form of a mere admission of confusion. He could have removed this part of his doubt by himself; however, reflection could not have instructed him about the facts. Or: the uneasiness that comes from not having known the truth was not removable by any ordering of his concepts;

The other uneasiness and confusion is characterized by the words "Something's wrong here" and the solution is characterized by (!~~ ,:,:<?_r:~~): "Oh, you don't mean t hat steam engine" or - in another case - " .... By 'steam engine' you don't mean just a piston engine."

The work of the philosopher consists in assembling reminders for a particular purpose.

A philosophical question is similar to one about the constitution of a particular society. - And it would be as if a society came together


without clearly written rules, but with a need for them; indeed also with an instinct following which they observed / /followed/ / certain rules at their meetings; but this is made difficult by the fact that nothing is clearly expressed ~~?_ll~ ~~~~ and no arrangement is made which clarifies / /brings out clearly/ / the rules. Thus they in fact view one of them as president, but he doesn't sit at the head of the table and has no distinguishing marks, and that makes doing busine,ss difficult. Therefore we come along and create a clear order: we seat the president in a clearly identifiable spot, seat his secretary next to him at a little table of his own, and seat the other full members in two rows on both sides of the table, etc., etc.

H one asks philosophy: "W hat is - for instance - substance?" then one is asking for a rule. A general rule, which is val i d for the word "substance", i.e., a rule according to which I have decided to play. -I want to say: the question "What is .... " doesn't refer to a particularpractical - case, but we ask it sitting at our desks. Just remember the case of the law of identity in order to see that taking care of a philosophical problem is not a matter of pronouncing new truths about the subject of the investigation (identity).

The difficulty lies onlyll in understanding how establishing a rule helps us. Why it calms us after we have been so profoundly12 uneasy. Obviously what calms us is that we see a system whlc-h-(s-ystematically)

------------------

excludes those structures that have always made us .~neasy, those we were unable to do anything with, and which we still thought we had to respect. Isn't the establishment of such a grammatical rule similar in this respect to the discovery of an explanation in physics, for instance, of the Copernican system? A similarity exists. - The strange thing about philosophical uneasiness and its resolution ~~g_~~ ~t?.t:~ ~<? ~~ that it is like the ~_ll~~~_~i_I1.g of an ascetic who stood raising a heavy ball, amid groans, and whom someone released by telling him: "Drop it." One wonders: if these sentences make you uneasy and you didn't know what to do with them, why didn't you drop them earlier, what stopped you from doing it? Well, I believe it was the false system that he thought he had to accommodate himself to, etc. 13

(The particular peace of mind that occurs when we can place other similar cases next to a case that we thought was unique, occurs again and again in our investigations when we show that a word doesn't have

PHILOSOPHY 11

just 0 n e meaning (or just two), but is used in five or six different ways (meanings). )

Philosophical problems can be compared to locks on safes, which can be opened by dialing a certain word or number, so that no force can open the door until just this word has been hit upon, and once it is hit upon any child can open it. I I . ... and if it is hit upon, no effort at all is necessary to open the doorl I itl I. I I

The concept of a perspicuous representation is of fundamental significance for us. It earmarks the form of account we give, the way we look at things. (A kind of 'Weltanschauung', as is apparently typical of our time. Spengler.)

This perspicuous representation produces just that comprehension I lunderstandingl I which consists in "seeing connections". Hence the importance of i n t e r m e d i ate cas e sl I of finding i n t e r m e d i -ate cases.11

A sentence is completely logically analyzed when its grammar is laid out completely clearly. It might be written down or spoken in any number of ways.

Above all, our grammar is lacking in per s pic u i t y.

Philosophy may in no way interfere with the real I lactual! I use of lan-guage I I . ... with what is really saidl I; it can in the end only describe it.

For it cannot give it any foundation either.

It leaves everything as it is. It also leaves mathematics as it is (is now), and no mathematical

discovery can advance it. A "leading problem of mathematical logic" (Ramsey) is a problem

of mathematics I ike any 0 the r.

(A simile is part of our ~~_i!!~~; but we cannot draw any conclusions from it either; it doesn't lead us beyond itself, but must remain standing as a simile. We can draw no inferences from it. As when we compare a sentence to a picture (in which case, what we understand by 'picture' must already have been established in us earlier I Ibeforel I) or when I compare the application of language with, for instance, that of the calculus of multiplication.


Philosophy simply puts everything before us, and neither explains nor deduces anything.)

Since everything lies open to view there is nothing to explain either. For what might not lie open to view is of no interest to us. I I . ... , for what is hidden, for example, is ... .I I

The answer to the request for an explanation of negation is really: don't you understand it? WefC ir yo-li--unders'tand it, "Y_~~t ~~ there _~~t~_ ~~ ~~£~~~~, what business is there left for an explanation?

We must know what ex pIa nat ion means. There is a constant danger of wanting to use this word in logic in a sense that is derived from physics.

When14 methodology talks about measurement, it does not say which materia~ would be the most advantageous to make the measuring stick of in order to achieve this or that result: even though this too, after all, is part of the method of measuring. Rather this investigation is only interested in the circumstances under which we say that a length, the strength of a current (etc.) is measured. It wants to tabulate the methods which we already used and are familiar with, in order to determine the meaning of the words "length", "strength of current", etc.)

If one tried to advance the s e s in philosophy, it would never be possible to debate them, because everyone would agree to them.

Learning philosophy is rea 11 y recollecting. We remember that we really used words in this way.15

The aspects of things I lof language II which are philosophically most important are hidden because of their simplicity and familiarity.

(One is unable to notice something because it is always (openly) before one's eyes.) --------

The real foundations of his inquiry do not strike a man at all. Unless t hat fact has at sometime struck him Ilhe has become aware off I. (Fraser, etc., etc.)

And this means he fails to be struck by what is most striking (powerful).

(One of the greatest impediments for philosophy is the expectation of new, deep Ilunheard of! I elucidations.)

PHILOSOPHY 13

One might also give the name philosophy to what is possible Ilpresenti I b e for e all new discoveries and inventions.

This must also relate to the fact that I can't give any explanations of the variable "sentence". It is clear that this logical concept, this variable, must belong to the same order as the concept "reality" or "world".

If someone believes he has found the solution to the. 'problem of life' and tried to tell himself that now everything is simple; then in order to refute himself he would only have to remember that there was a time when this 'solution' had not been found; but at t hat time too one had to be able to live, and in reference to this time the new solution appears like Ilasll a coincidence. And that's what happens to us in logic. If there were a 'solution' of logical (philosophical) problems then we would only have to call to mind that at one time they had not been solved (and then too one had to be able to live and think). ---

All reflections can be carried out in a much more homemade manner than I used to do. And therefore no new words have to be used in philosophy, but rather the old common words of language are sufficient. lithe old ones are sufficientl I

(Our only task is to be just. That is, we must only point out and resolve the injustices of philosophy, and not posit new parties - and creeds.)

(It is difficult not to exaggerate in philosophy.)

(The philosopher exaggerates, shouts, as it were, in his helplessness, so long as he hasn't yet discovered the core of his confusion.)

The philosophical problem is an awareness of disorder in our concepts, and can be solved by ordering them.

A philosophical problem always has the form: "I simply don't know my way about."

As I do philosophy, its entire task consists in expressing myself in such a way that certain troubles I Iprotilemsl I disappear. ((Hertz.»

------------

If I am correct, then philosophical problems must be completely solvable, in contrast to all others.

If I say: here we are at the limits of language, then it always seems


/ /sounds/ / as if resignation were necessary, whereas on the contrary complete satisfaction comes, since no question remains.

The problems are dissolved in the actual sense of the word - like a lump of sugar in water.

/People who have no need for transparency in their argumentation are lost to philosophy./

90

PHILOSOPHY.

THE CLARIFICATION OF THE USE OF LANGUAGE. TRAPS OF LANGUAGE.

How is it that philosophy is such a complicated building / /structure/ /. After all, it should be completely simple if it is that ultimate thing, independent of all experience, that it claims to be. - Philosophy unravels the knots in our thinking; hence its results must be simple, but its activity is as complicated as the knots that it unravels.

Lichtenberg: "Our entire philosophy is correction of the use of language, and therefore the correction of a philosophy, and indeed of the most general philosophy."

(The capacity16 for philosophy consists17 in the ability 18 to receive a strong ~rl~ lasting impression from a grammatical -i~ct-.l9

Why are grammatical problems so tough and seemingly ineradicable? - Because they are ~~~J}?-~~!~_~ with the oldest thought habits, i.e., with the oldest images that are engraved into our language itself. ((Lichtenberg.) )

/Teaching philosophy involves the same immense difficulty as instruction in geography would have if a pupil brought with him a mass of false and far too simple / / and falsely simplified/ / ideas about the course and connections of the rmites of rivers / /rivers/ / and mountain chains

---------------

/ /mountains/ /.I

/People are deeply imbedded in philosophical, i.e., grammatical confusions. And to free them from these presupposes pulling them out of the immensely manifold connections the-Y-are-caught up in. One must

PHILOSOPHY 15

SO to speak regroup their entire language. - But this language came about I I developed I I as it did because people had - and have - the inclination to think i nth i s way. Therefore pulling them out only works with those who live in an instinctive state of rebellion against IIdissatisfaction ~~~~II language. Not with those who following all of their instincts live within the herd that has created this language as its 1?!5?~~! expression.!

Language contains the same traps for everyone; the immense network of well-kept I Ipassablel I false paths. And thus we see one person after another walking the same paths and we know already where he will make a turn, where he will keep on going straight ahead without noticing the turn, etc., etc. Therefore wherever false paths branch off I should put up signs which help one get by the dangerous places.

One keeps hearing the !_~l1)_~~!<. that philosophy really makes no progress, that the same philosophical problems that had occupied the Greeks are still occupying us. But those who ~~X that don't understand the reason it is Ilmust bel I so. The reason is that our language has remained the same and seduces us into asking the same questions over and over. As long as there is a verb 'to be' which seems to function like 'to eat' and 'to drink', as long as there are adjectives like 'identical', 'true', 'false', 'possible', as long as one talks about a flow of time and an expanse of space, etc., etc., humans will continue to bump up against the same mysterious difficulties, and stare at something that no explana-

-------------- -------------tion seems able to remove.

And this by the way satisfies a longing for the supra-natural I !transcendental! I, for in believing that they see the "limits of human understanding" of course they believe that they can see beyond it.

I read" .... philosophers are no nearer the meaning of 'Reality' than Plato got .... ". What a strange state of affairs. How strange in that case that Plato could get that far at all! Or, that we were not able to get farther! Was it because Plato was so smart?

The conflict in which we constantly find ourselves when we undertake logical investigations is like the conflict of two people who have concluded a contract with each other, the last formulations of which are expressed in easily misunderstand able ~<?~~~, whereas the explanations of these formulations explain everything unmistakably. Now one of the


two people has a short memory, constantly forgets the explanations, misinterprets the conditions of the contract, and continually gets Iitherefore continually runsl I into difficulties. The other one constantly has to remind him of the explanations in the contract and remove the difficulty.

Remember what a hard time children have believing (or accepting) that a word really has Ilcan havel I two completely differe-nt me-1in{ngs.

The aim of philosophy is to erect a wall at the point where language stops anyway.

The results of philosophy are the uncovering of one or another piece of plain nonsense, and are the bumps that the understanding has got by running its head up against the limits I !the endl I of language. These bumps let us ':l!!~~~~_t_~!l.~ I Irecognizel I the value of the discovery.

What kind of investigation are we carrying out? Am I investigating the probability of cases that I give as examples, or am I investigating their actuality? No, I'm just citing what is possible and am therefore

----------

giving grammatical examples. Philosophy is not laid down in sentences but in a language.

Just as laws only become interesting when there is an inclination to transgress them Ilwhen they are transgressedl I ~~!..t_~!~ grammatical rules are only interesting when philosophers want to transgress them.

Savages have games (that's what we call them, anyway) for which they have no written rules, no inventory of rules. Let's now imagine the activity of an explorer, who travels through the countries of these peoples and -takes -1in-{nventory of their rules. This is completely analogous to what the philosopher does. «But why don't I say: savages have languages (that's what we .... ) .... without a written grammar?) )20

PHILOSOPHY 17

91

WE DON'T ENCOUNTER PHILOSOPHICAL PROBLEMS AT ALL IN PRACTICAL

LIFE (AS WE DO, FOR EXAMPLE, THOSE OF NATURAL SCIENCE). WE EN

COUNTER THEM ONLY WHEN WE ARE GUIDED NOT BY PRACTICAL PURPOSE

IN FORMING OUR SENTENCES, BUT BY CERTAIN ANALOGIES WITHIN OUR

LANGUAGE.

Language cannot express what belongs to the essence of the world. Therefore it cannot say that everything flows. Language can only say what we could also imagine differently.

That everything flows must lie in how language touches reality. Or better: that everything flows must lie in the nature of language. And, let's remember: in everyday life we don't notice that - as little as we notice the blurred edges of our visual field ("because we are so used to it", some will say). How, on what occasion, do we think we start noticing it? Isn't it when we want to form sentences in opposition to the grammar of time?

When someone says 'everything flows', we feel that we are hindered in pinning down the actual, actual reality. What goes on on the screen escapes us precisely because it is something going on. But we are describing something; and is that something else that is going on? The description is obviously linked to the very picture on the screen. There must be a false picture at the bottom of our feeling of helplessness. For what we want to describe we can describe.

Isn't this false picture that of a strip of film that runs by so quickly that we don't have any time to perceive a picture?

For in this case we would be inclined to chase after the picture. But in the course of something going on there is nothing analogous to that.

It is remarkable that in everyday life we never have the feeling that the phenomenon is getting away from us, that appearances are continually flowing, but only when we philosophize. This points to the fact that we are dealing here with a thought that is suggested to us through a wrong use of our language.

For the feeling is that the present vanishes into the past without our being able to stop it. And here we are obviously using the picture of a strip that constantly moves past us and that we can't stop. But of course


it's just as clear that the picture is being misused. That one cannot say "time flows" if by "time" one means the possibility of change.

That we don't notice anything when we look around, look around in space, feel our own bodies, etc.', etc., shows how natural these very things are to us. We don't perceive that we see space perspectivally or that the visual image is in some sense blurred near its edge. We don't notice this, and can never notice it, because it is the mode of perception. We never think about it, and it is impossible, because the form of our world has no contrary.

I wanted to say that it is odd that those who ascribe reality only to things and not to our mental images move so self-confidently in the world of imagination and never long to escape from it.

I.e., how self-evident is the given. Things would have to have come to a pretty pass for that to be just a tiny photograph taken from an oblique angle.

What is self-evident, Ii f e, is supposed to be something accidental, unimportant; by contrast something that normally I never worry my head about is what is real!

I.e., what one neither can nor wants to go beyond would not be the world.

Again and again there is the attempt to define the world in language and to display it - but that doesn't work. The self-evidence of the world is expressed in the very fact that language means only it, and can only mean it.

As language gets its way of meaning from what it means, from the world, no language is thinkable which doesn't represent this world.

In the theories and battles of philosophy we find words whose meanings are well-known to us from everyday life used in an ultraphysical sense.

When philosophers use a word and search for its meaning, one must always ask: is this word ever really used this way in the language which created it! Ifor which it is createdl/?

Usually one will then find that it is not so, and that the word is used against Ilcontrary tol I its normal grammar. ("Knowing", "Being", "Thing" .)

(Philosophers are often like little C_~!!~_t:~!l' 21 who first scribble

PHILOSOPHY 19

~~~~_<?~22 lines on a piece of paper with their pencils, and now I !thenl I . ask an adult "What is that?" - Here's how this happened: now and then the adult had drawn something for the child and said: "That's a man", "That's a house", etc. And then the child draws lines too, and asks: now what's t hat ?)

92

METHOD OF PHILOSOPHY.

THE POSSIBILITY OF QUIET PROGRESS.

The real discovery is the one that makes me capable of stopping doing philosophy when I want to.

The one that gives philosophy peace, so that it is no longer I Ibeingl I tormented by questions which bring its elf in question.

Instead, we now demonstrate a method by examples; and one can break off the series of examples I land the series of examples can be broken offl I.

But more correctly, one should say: Problems are solved (uneasiness I Idifficultiesl I eliminated), not a sin g I e problem.

Unrest in philosophy comes from philosophers looking at, seeing, philosophy all wrong, i.e., cut up into (infinite) vertical strips, as it were, rather than (finite) horizontal strips. This reordering of understanding creates the g rea t est difficulty. They want to grasp the infinite strip, as it were, and complain that it I Ithisl I is not possible piece by piece. Of course it isn't, if by 'a piece' one understands an endless vertical strip. But it is, if one sees a horizontal strip as a piece Iia whole, definite piecell. - But then we'll never get finished with our work! Of course I Icertainlyl I not, because it doesn't have an end.

----------

(Instead of turbulent conjectures and explanations, we want to give quiet demonstrations23 I Istatementsl I of linguistic facts II[bout linguistic fac't;ii~Yii-;;e-~~nt the q~iet-;;~ting24 of linguistic facts'! I

We must plow though the whole of language.

(When most people ought t025 engage in a philosophical investigation, they act like someone who is looking for an object in a drawer


very nervously. He throws papers out of the drawer - what he's looking for may be among them - leafs through the others hastily and sloppily. Throws some back into the drawer, mixes them up with the others, and so on. Then one can only tell him: Stop, if you look in t hat way, I can't help you look. First you have to start to examine one thing after another methodically, and in peace and quiet; then I am willing to look with you and to direct myself with you as model in the method.

J -- ---- --------

93

THE METHODOLOGY IN THE FORMS OF OUR LANGUAGE. «PAUL ERNST.»

In ancient rites we find the use of an extremely well-developed language of gestures.

And when I read Frazer, I would like to say again and again: All these processes, these changes of meaning, we have right in front of us even in our language of words. If what is hidden in the last sheaf is called the 'Cornwolf', as well as the sheaf itself, and also the man who binds it, then we recognize in this a linguistic process we know well.

The scapegoat, on which one lays one's sins, and who runs away into the desert with them - a false picture, similar to those that cause errors in philosophy.

I would like to say: nothing shows our kinship with those savages better, than that Frazer has at hand a word like "ghost" or "shade", which is so familiar to him and to us, to describe the views of these people.

(This is quite different than if he were to relate, for instance, that the savages imagined / /imagine/ / that their head falls off when they have slain an enemy. Here 0 u r des c rip t ion would contain nothing superstitious or magical.)

Indeed, this oddity refers not only to the expressions "ghost" and "shade", and much too little is made of it that we include the words "soul" and "spirit" in our own educated vocabulary. ~~!1:lE~~~~ ~<? this it is insignificant that we do not believe that our soul eats and drinks.

------.---------

An entire mythology is laid down in our language.

PHILOSOPHY 21

Driving out death or killing death; but on the other hand it is portrayed as a skeleton, and therefore as dead itself, in a certain sense. "As dead as death." 'Nothing is as dead as death; nothing as beautiful as beauty itself!' The picture according to which realitv is thought of here . ilTe t~ pure (concentr,ted) sUbstances IS that beauty, death, etc., IS the pure ~ concentrated) substance,

h . b 'f I b' th~x ate . d d . w ereas m a eaut! u 0 Ject It IS contame as an a mIxture. - And don't I recognize here my own observations about 'object' and 'complex'? (Plato.)

The primitive forms of our language: noun, adjective and verb, show the simple picture ~~_t5? whose form l_~~~~~~~ tries to force everything.

So long as one imagines the soul as a t h i n g , abo d y , which is in our head, this hypothesis is not dangerous. The danger of our models does not lie in their imperfection and roughness, but in their unclarity (fogginess).

The danger sets in when we notice that the old model is not sufficient but then we don't change it, but ony sublimate it, as it were. So long as I say the thought is in my head, everything is all right; things get dangerous when we say that the thought is not in my head, but in my spirit.

NOTES

1 Handwritten alternative: then. 2 In the original typescript: he. The initial letter "w" is a handwritten addendum. 3 Handwritten marginal note: belongs to "must", "can". 4 The typescript has: its importance:, the. 5 Handwritten alternative: normal. There is a handwritten wavy line under "correct":

6 Handwritten alternative: our. 7 Handwritten alternative: ordinary and trivial. 8 At the end of the remark there is the handwriting: < ["plain nonsense"]. 9 The parentheses are a handwritten addition. 10 Under the title, in handwriting: V p. 40/3? This is a reference to page 40 of the typescript. Wittgenstein had apparently wanted to include a remark or a part of one from page 40 in page 414. 11 Handwritten alternative: now. 12 Handwritten alternative: deeply. 13 At the end of the remark there is a handwritten addition: hen and chalk trick. 14 Before the remark, in handwriting in the margin: VII 7. 15 In handwriting, in the margin: VII 164. 16 Handwritten alternative (with an unbroken wavy line under the original word): talent.


17 Handwritten alternative (with an unbroken wavy line under the original word): lies. 18 Handwritten alternative (elevated, with broken underlining): susceptibility. 19 Handwritten marginal remark: for 'humor', 'depth'. 20 In the typescript the parentheses are missing at the end of the remark. 21 Handwritten alternative: (Philosophers} often behave like little children .... 22 Handwritten alternative: some. 23 Handwritten alternative: reflection. 24 Originally in the manuscript: establishment. 25 Unclear textual point in the manuscript. The typewriting gives the impression that the original words "want to" were overstruck to produce "ought to".

Luckhardt: Dept. of Philosophy Georgia State University Atlanta, GA 30303-3083 U.S.A.

Aue: Dept. of German Emory University Atlanta, GA 30322 U.S.A.

BURTON DREBEN AND JULIET FLOYD

TAUTOLOGY: HOW NOT TO USE A WORD

In 1923 C. I. Lewis wrote to F. J. Woodbridge, editor of The Journal of Philosophy:

Have you looked at Wittgenstein's new book yet? I am much discouraged by Russell's foolishness in writing the introduction to such nonsense. I fear it will be looked upon as what symbolic logic leads to. If so, it will be the death of the subject. 1

Nonsense or no, Lewis would, nine years later, pay homage to Wittgenstein's account of logic. In the Introduction to Lewis and Langford's Symbolic Logic, published in 1932, Lewis wrote:

the nature of logical truth itself has become more definitely understood, largely through the discussions of Wittgenstein. It is 'tautological' - such that any law of logic is equivalent to some statement which exhausts the possibilities; whatev~r is affirmed in logic is a truth to which no alternative is conceivable. From the relation of mathematics to logic, it follows that mathematical truth is similarly tautological. 2

No dictionary in 1932 would have glossed "tautological" as "exhausting the possibilities". For example, in the second edition (1934) of the Merriam-Webster New International Unabridged Dictionary (for which Lewis was a consultant) we find the adjective "tautological" under "tautology", derived from the Greek tautologia, "speaking the same":

tautology ..• 1. Rhet. Repetition of the same words or use of synonymous words in close succession; also, an instance of this. 2. Repetition of a statement, of acts, experiences, etc., esp. when superfluous. Syn. and Ant. - See REDUNDANCY.

But Lewis was not alone in misspeaking. Russell, Ramsey and Carnap also took Wittengstein as giving them license to misspeak. This paper will discuss the (linguistic) misdeeds of Russell, then briefly of Ramsey and Lewis. (Carnap is for another time and another place.)

l.

First, a bit of prehistory. In the Jasche Logic, after defining analytic propositions as "those propositions whose certainty rests on identity of

Synthese 87: 23-49, 1991. © 1991 Kluwer Academic Publishers.

24 BURTON DREBEN ANI7JULIET FLOYD

concepts (of the predicate with the notion of the subject),,,3 Kant goes on, in a section entitled "Tautological Propositions," to further divide analytic propositions into two kinds: 'explicit' and 'non-explicit'. He says:

The identity of concepts in analytic judgments can be either explicit (explicita) or non-explicit (implicita). In the former case analytic propositions are tautological.

Note 1. Tautological propositions are virtualiter empty or raid of consequences, for they are of no avail or use. Such is, for example, the tautological proposition, Man is man. For if I know nothing else of man than that he is man, I know nothing else of him at all.

Implicitly identical propositions, on the contrary, are not void of consequences or fruitless, for they clarify the predicate which lay undeveloped (imp/icite) in the concept of the subject through development (explicatio). 4

In the Prolegomena to any Future Metaphysics, Kant emphasizes that

all analytic judgments depend wholly upon the law of contradiction .... For the predicate of an affirmative analytical judgment is already contained in the concept of the subject, of which it cannot be denied without contradiction. Such is the nature of the judgments "All bodies are extended," and "No bodies are unextended (that is, simple,,).5

Kant's insistence that a proposition such as "Man is man" is tautological and "void of consequences" is presumably directed against Leibniz, who, in 'On the General Characteristic' (c. 1679) wrote:

The first of the true propositions are those which are commonly called identical; such as A is A, non-A is non-A, and if the proposition L is true, it follows that the proposition L is true. And however much useless 'coccysm,6 there seems to be in these judgments, they nevertheless give rise to useful axioms by a slight change. Thus from the fact that A is A, or for example, that three-legged is three-legged, it is obvious that anything is as much as it is or is equal to itself. Hence (to show how useful identities are by an example) philosophers have long ago demonstrated that a part is less than the whole by assuming only this definition. 7

For Leibniz, in the sense of being resolvable to identity, all truth is from God's point of view what Kant called 'analytic'; that is:

An affirmative truth is one whose predicate is in the subject; and so in every true affirmative proposition, necessary or contingent, universal or particular, the notion of the predicate is in some way contained in the notion of the subject, in such a way that if anyone were to understand perfectly each of the two notions just as God understands it, he would by that very fact perceive that the predicate is in the subject. 8

Leibniz would never have called instances of the law of identity 'tautologous'. Kant did. But Kant still cites the law of identity in his

TAUTOLOGY: HOW NOT TO USE A WORD 25

Logic9 as one of the fundamental laws, along with the other two traditional "laws of thought", the principle of contradiction and the law of the excluded middle. 10 The point is tha_t he groups it (as does Leibniz) with the law of contradiction, 11 because instances of the law of identity such as "Man is man", although tautologous and therefore "void of consequences", still have a legislative or negative role to play. Though nothing follows from "Man is man", to say that "Man is not man" violates the law of contradiction. Indeed all of formal logic, that is, what Kant calls "general logic", as opposed to "transcendental logic", plays this negative role. In the Critique of Pure Reason Kant writes:

General logic resolves the whole formal procedure of the understanding and reason into its elements, and exhibits them as principles of all logical criticism of our knowledge. This part of logic, which may therefore be entitled analytic, yields what is at least the negative touchstone of truth. Its rules must be applied in the examination and appraising of the form of all knowledge before we proceed to determine whether their content contains positive truth in respect to their object. But since the mere form of knowledge, however completely it may be in agreement with logical laws, is far from being sufficient to determine the material (objective) truth of knowledge, no one can venture with the help of logic alone to judge regarding objects, or to make any assertion. 12

Here Kant is being quite traditional with respect to formal logic. General logic deals with the "form of thinking" as he says in his Logic,!3 and not the matter. Formal deductive inference, which for Kant is essentially syllogistic, makes explicit in the conclusion what is implicit in the premises. It is analytic, but not tautologous. Clearly Kant does not view formal logic as pointless or trifling, as did Locke. 14 Still, he warns us against the tendency to exaggerate the scope of formal logic. He wrote,

There is, however, something so tempting in the possession of an art so specious, through which we give to all our knowledge, however uninstructed we may be in regard to its content, the form of understanding, that general logic, which is merely a canon of judgment, has been employed as if it were an organon for the actual production of at least the semblance of objective assertions, and has thus been misapplied. General logic, when thus treated as an organon, is called dialectic. 15

The Idealists pressed Kant's restriction of the scope of formal logic to the point of denigrating it. For Hegel the fundamental laws of thought are "opposed to each other, they contradict one another". 16

Moreover,

the Law of Identity ... in its positive expression A = A is, in the first instance, nothing

26 BURTON DREBEN AND JULIET FLOYD

more than the expression of an empty tautology. It has therefore been rightly remarked that this law of thought has no content and leads no further. 17

Similarly for the law of contradiction ... "A cannot at the same time be A and not-A"; this is merely "a negative form" of the Law of Identity. 18

Bradley, whose Principles of Logic (1883) is the main source for the Idealist conception of logic which the young Russell embraced in his early book, Foundations of Geometry (1897), says:

The principle of Identity is often stated in the fQrm of a tautology, "A is A." If this really means that no difference exists on the two sides of the judgment, we may dismiss it at once. It is no judgment at all. As Hegel tells us, it sins against the very form of judgment; for, while professing to say something, it really says nothing .... We never at any time wish to use tautologies. No one is so foolish in ordinary life as to try to assert without some difference. We say indeed "I am myself" and "Man is man and master of his fate." But such sayings as these are no tautologies .... Every judgment is essentially synthetic. 19

and also, in a footnote:

Every possible judgment, we shall see hereafter, is both analytic and synthetic. 20

For Bradley, then, "Whatever is, is" must be interpreted, if it is to be a judgment at all. "The real axiom of identity," he says,

is this: What is true in one context is true in another. 21

Bradley also feels compelled to interpret the other two traditional laws of thought - the law of contradiction and the law of the excluded middle - in order to prevent them from collapsing into mere tautologies. 22

Russell, in The Foundations of Geometry (1897), reiterated the Idealist position that "every judgment is both synthetic and analytic. ,,23 And in his transitional Philosophy of Leibniz (1900), Russell argues that all analytic judgments are tautologies, "and so not properly propositions at all. ,,24 This latter position is stated in more detail in Moore's 1900 paper 'Necessity'. Says Moore,

there is much doubt whether any truths are analytic. Any proposition, it would seem, must contain at least two different terms and their relation; and, this being so, the relation may always be denied of the two terms without a contradiction. It takes two propositions to make a contradiction: the law of contradiction itself excludes the possibility of any single proposition being both true and false, or self-contradictory. And hence the definition of an analytic proposition as a proposition, the contradictory of which is selfcontradictory can apply to nothing ....


Moreover, the law of contradiction itself, than which nothing is commonly supposed to be more plainly analytic, is certainly synthetic. For suppose some one to hold that not every proposition is either true or false. You cannot deny that this is a proposition, unless you are also willing to allow that the law which it contradicts is not a proposition; and he may perfectly well maintain that this is one of those propositions which is true, and the contradictory of which, your law, is false, although this is not the case with every proposition. Whereas, if you urge that it is included in the notion of a proposition that it should be either true or false, either your law becomes a pure tautology and not a proposition, or else there is something else in the notion of a proposition beside the property that it is either true or false, and then you are asserting a synthetic connexion between this property and those others. 25

Thus the (newly-minted) anti-Idealists, Moore and Russell, reject Kant's class of non-tautologous analytic judgments by exploiting the Idealist argument against purely analytic judgments. For Moore and Russell, all purported analytic judgments are mere tautologies, and hence not judgments at all.26

Now what of Frege? In the Grundlagen, Frege proposes his celebrated definition of 'analytic':

these distinctions between a priori and a posteriori, synthetic and analytic, concern, as I see it, not the content of the judgement but the justification for making the judgement .... When a proposition is called a posteriori or analytic in my sense, this is not a judgement about the conditions, psychological, physiological and physical, which have made it possible to form the content of the proposition in our consciousness; ... rather, it is a judgement about the ultimate ground upon which rests the justification for holding it to be true.

This means that the question is removed from the sphere of psychology, and assigned. if the truth concerned is a mathematical one, to the sphere of mathematics. The problem becomes, in fact, that of finding the proof of the proposition, and of following it up right back to the primitive truths. If, in carrying out this process, we come only on general logical laws and on definitions, then the truth is an analytic one.27

Hence a proposition is analytic for Frege if and only if it is derivable from purely logical laws. Therefore, presumably, purely logical propositions are analytic also. Having defined the primitive notions of arithmetic in what for him counted as purely logical terms, arithmetic was for Frege, as it had not been for Kant, analytic. Pure logic, given in the Begriffsschrift, constituted for Frege the set of maximally general laws governing any scientific or rational discourse whatsoever. 28 So for Frege, as for Leibniz, logic, although 'analytic', was surely not empty of content. 'Tautologous' was the last adjective Frege would have applied to a logical truth. 29 Thus Frege's notion of 'analytic' is a strengthening and extension of Kant's non-tautological analytic.


2.

In the Tractatus, when at 6.1 and 6.11 Wittgenstein asserts that the propositions of logic are tautologies, say nothing, and are the analytical propositions, he is continuing the Idealist and Moore-Russell traditions of identifying the class of analytic propositions with tautologies30 -

indeed, Wittgenstein is denying that they are genuine propositions3 ! -

and is directly attacking Frege's conception of logic. At the same time, Wittengstein is attacking Russell's longstanding

claim that logic is synthetic. From 1900 through 1913 Russell took his (and Frege's) "reduction" of mathematics to logic to show that logic was synthetic, since mathematics was of course synthetic, as Kant, according to Russell, had demonstrated. In The Principles of Mathematics (1903) Russell writes:

Kant never doubted for a moment that the propositions of logic are analytic, whereas he rightly perceived that those of mathematics are synthetic. It has since appeared that logic is just as synthetic as all other kinds of truth. 32

In his debate with Poincare, whose Science and Hypothesis he reviewed in 1905, Russell summarily dismissed Poincare's characterization of formal logic as tautologous. Chapter I of Science and Hypothesis (1905) opens thus:

The very possibility of mathematical science seems an insoluble contradiction. If this science is only deductive in appearance, from whence is derived that perfect rigour which is challenged by none? If, on the contrary, all the propositions which it enunciates may be derived in order by the rules of formal logic, how is it that mathematics is not reduced to a gigantic tautology?33

Poincare continues:

it must be granted that mathematical reasoning has of itself a kind of creative virtue, and is therefore to be distinguished from the syllogism. The difference must be profound. We shall not, for instance, find the key to the mystery in the frequent use of the rule by which the same uniform operation applied to two equal numbers will give identical results. All these modes of reasoning, whether or not reducible to the syllogism, properly so called, retain the analytical character, and ipso facto, lose their power.34

So for Poincare, formal logic is empty, tautologous, uninformative, but mathematics is not. Hence he searches for a mode of reasoning that explains the creativity of mathematics, that protects mathematics from the sterility of logic. And Poincare finds this mode in mathematical induction, a form of inference which contains within itself, or so he


says, an infinite number of syllogisms, and is therefore synthetic. He thus returns, at least verbally, to Kant's view that mathematical truths are synthetic a priori. (Goldfarb has convincingly shown that Poincare's use of Kantian terminology has little to do with K--ant. 35)

Poincare's argument directly clashes with Russell's own for logicism. Recall that the key to. the Frege-Russell reduction of arithmetic to logic is its treatment of mathematical induction, resting on the notion of the ancestral of a relation. Hence, in his review, Russell writes:

M. Poincare gives uq reasons for the view that deduction can never give new truths. The fact is that the general principles of deduction are analogou~, in this respect, to what he conceives mathematical induction to be; that is to say, they lead to conclusions which are other than themselves, so that in this sense they are synthetic. We shall conclude, therefore, that mathematics does not, as M. Poincare affirms (p. 24), contain an inductive element, and yet is not 'a vast tautology'. 36

Seven years later, in his Problems of Philosophy (1912), Russeil writes:

[Kant 1 perceived that not only the connexion of cause and effect, but all the propositions of arithmetic and geometry, are 'synthetic', i.e., not analytic: in all these propositions, no analysis of the subject will reveal the predicate. His stock instance was the proposition 7 + 5 = 12. He pointed out, quite truly, that 7 and 5 have to be put together to give 12: the idea of 12 is not contained in them, nor even in the idea qf adding them together. 37

Russell also discussed the traditional "laws of thought" iIi Problems of Philosophy. Here we find a defense of the view that logic is obvious, apparently trivial, a priori, yet fruitful and informative. The truth of a principle of logic says Russell, echoing Leibniz,

is impossible to doubt, and its obviousness is so great that at first sight it seems almost trivial. Such principles, however, are not trivial to the philosopher, for they show that we may have indubitable knowledge which is in no way derived from objects. 38

And again:

The name "laws of thought" is also misleading, for what is important is not the fact that we think in accordance with these laws, but the fact that things behave in accordance with them; in other words, the fact that when we think in accordance with them we think truly. 39

In the same year (1912) Coffey published his neo-scholastic work, The Science of Logic.40 This is the one logic textbook we can assume Wittengstein read, since he reviewed it in the Cambridge Review in 1913.41 Coffey's version of the principle of identity is


simply the self-evident truth that Everything is identical with itself; Everything is its own nature. It is in,Volved in every judgment - more directly in every affirmative judgment -and demand~ that throughout every thought-process the objects represented by our concepts and expres~ed by O\lr terms remain identical with themselves. It thus expresses the unambiguity of the judgment a~d the immutable character of truth. It does not give us any positive information about a thing, beyond what we possess by thinking of the thing. But we cannot think definitely about anything without mentally marking it off from all that is not itself. Hence the principle is not a bare tautology, capable of being expressed by the statement that A is A. 42

Like Russell, Coffey stresses that the laws of thought are self-evident truths grounded in the nature of things, not merely of thought.

Nowhere yet, at all events, has any valid reason been advanced why we should doubt the soundness of man's spontaneous convictions that the necessary truth of those selfevident first principles is rooted in the nature of things no less than in the nature of thought. They not merely assure us that we cannot think that a thing can be other than itself, or that we cannot conceive a thing being and not being at the same time and in the same respect, or that we are forced to think that a thing must either possess a certain attribute or not possess it: they assure us that the things themselves are so, as we think them and that it is not merely a matter of how we must think about things, but also a matter of how things really are. 43

Wittgenstein's review of Coffey is scathing:

The author's Logic is that of the scholastic philosophers, and he makes all their mistakes -of course with the usual references to Aristotle. (Aristotle, whose name is so much taken in vain by oUf logiciaps, would turn in his grave if he knew that so many logicians know no more about logic today than he did 2,000 years ago.) The author has not. taken the slightest notice of the great work of the modern mathematical 10gicians - work which has brought about an advance in logic comparable only to that which made Astronomy out of Astrology, and Chemistry out of Alchemy .

. . . The worst of such books as this is that they prejudice sensible people against the study of Logic. 44 [Written ten years before C. 1. Lewis's letter!)

Not a word, either in Russell's twelve years of proclaiming the syntheticity of logic nor in Wittgenstein'spaean to the new logic, gives us the slightest hint that the pejorative term "tautology" could in any way be appropriately applied to "the great work of the modern mathematical logicians". Yet in his eight lectures, The Philosophy of Logical Atomism, given in the early spring of 1918, Russell professes a new faith:

Everything that is a proposition of logic has got to be in some sense or other like a tautology. It has got to be something that has some peculiar quality, which I do not know how to define, that belongs to logical propositions and not to others. 45


This totally unexpected use of "tautology" is given no justification whatsoever in these lectures. Russell's concern is to find an adequate characterization of logic, since total generality will not do, that is, not all "propositions which can be expressed in the language of pure variables ... are ... propositions of logic". 46 A worthy goal, but in no way achieved by a label which is unexplained and indeed which Russell "do[ es] not know how to define".

In his prison document of 1918, Introduction to Mathematical Philosophy (published in 1919), Russell further professes his new-found faith in the tautologousness of logic:

All the propositions of logic have a characteristic which used to be expressed by saying that they were analytic, or that their contradictories were self-contradictory. This mode of statement, however, is not satisfactory. The law of contradiction is merely one among logical propositions; it has no special pre-eminence; and the proof that the contradictory of some proposition is self-contradictory is likely to require other principles of deduction besides the law of contradiction. Nevertheless, the characteristic of logical propositions that we are in search of is the one which was felt, and intended to be defined, by those who said that it consisted in deducibility from the law of contradiction. This characteristic, ... for the moment, we may call tauto[ogy.47

If we have the temerity to ask, Why should we call this characteristic "tautology"?, Russell has only the following to say:

It is clear that the definition of "logic" or "mathematics" must be sought by trying to give a new definition of the old notion of "analytic" propositions. Although we can no longer be satisfied to define logical propositions as those that follow from the law of contradiction, we can and must still admit that they are a wholly different class of propositions from those that we come to know empirically. They all have the characteristic which, a moment ago, we agreed to call "tautology" .... For the moment, I do not know how to define "tautology". [FN: The importance of "tautology" for a definition of mathematics was pointed out to me by my former pupil Ludwig Wittgenstein, who was working on the problem. I do not know whether he has solved it, or even whether he is alive or dead.) It would be easy to offer a definition which might seem satisfactory for a while; but I know of none that I feel to be satisfactory, in spite of feeling thoroughly familiar with the characteristic of which a definition is wanted. 48

So there is no argument in Russell for his use of the word "tautology"; there is just the footnote referring to Wittgenstein.

When and how did Wittgenstein first point out to Russell the "importance of 'tautology'''? Presumably, in a November 1913 letter from Norway. Wittgenstein writes:

Lieber Russell,


... a logical prop [osition] is one the special cases of which are either tautologous - and then the prop [osition] is true - or "self-contradictory" (as I shall call it) and then it is false. 49

Most remarkably, Wittgenstein bases his new characterization of logic on the claim that there is a decision procedure for all of logic. He begins with what is probably the first statement of a decision procedure for truth-functional logic. What he calls his "ab-Notation" is essentially equivalent to the truth-table notation, hence his "ONE symbolic rule" is essentially equivalent to what today would be the standard truthtable method for showing truth-functional validity, contravalidity, or consistency:5o

Now listen: I will first talk about those logical prop[osition]s which are or might be contained in the first 8 Chapters of Princ[ipia] Math[ ematica] .... ONE symbolic rule is sufficient to recognize each of them as true or false. And this is the one symbolic rule: write the prop [osition] down in the ab-Notation, trace all Connections (of Poles) from the outside to the inside Poles: Then if the b-Pole is connected to such groups of inside Poles ONLY as contain opposite poles of ONE prop[osition], then the whole prop [osition] is a true, logical prop[osition]. If on the other hand this is the case with the a-Pole the prop[ osition] is false and logical. If finally neither is the case the prop [ osition] may be true or false but is in no case logical. 51

Wittgenstein then claims that his decision procedure can be extended:52

Of course the rule I have given applies first of all only for what you called elementary prop[ osition ]s. But it is easy to see that it must also apply to all others. For consider your two Pps in the Theory of app[arent] var[iable]s *9.1 and *9.11. Put there instead of ¢>x, (3y). ¢>y.y = x and it becomes obvious that the special cases of these two Pps like those of all the previous ones becomes tautologous if you apply the ab-Notation. The ab-Notation for Identity is not yet clear enough to show this clearly but it is obvious that such a Notation can be made up ... there is one Method of proving or disproving all logical prop[osition]s and this is: writing them down in the ab-Notation and looking at the connections and applying the above rule. 53

The crucial question for us is, Why did Wittgenstein think that a general decision procedure would show that the propositions of logic are generalizations of tautologies? An answer begins to emerge in his very next letter to Russell. This letter (R. 23), of late November or early December 1913, from Norway opens thus:

I want to repeat again, in a different form, what I wrote about logic in my last letter. All the propositions of logic are generalizations of tautologies and all generalizations of tautologies are propositions of logic. There are no other logical propositions. (I regard this as definitive. )54


And it concludes:

The big question now is, how must a system of signs be constituted in order to make every tautology recognizable as such IN ONE AND THE SAME WAY? This is the fundamental problem of logic [Grundproblem der Logik]!55

But in the middle of this letter we not only read his admission that a general decision procedure is not quite at hand,56 but, more importantly, why Wittgenstein's use of the term "tautology'l is not arbitraryas Russell's 1918-19 usage appears to be - given the history of its use we sketched from Kant onward.

As to what tautologies really are, however, I myself am not yet able to say quite clearly but I will try to give a rough explanation. It is the peculiar (and most important [hOchst wichtigeJ) mark of non-logical propositions that one is not able to recognize their truth from the propositional sign alone. If I say, for example, "Meier is stupid", you cannot tell by looking at this proposition whether it is true or false. But the propositions of logic - and only they - have the property that their truth or falsity, as the case may be, finds its expression in the very sign for the proposition. I have not yet succeeded in finding a notation for identity that satisfies this condition; but I have NO doubt that it must be possible to find such a notation. 57 For compound propositions ("elementary propositiorts") the ab-notation is sufficient. 58

It therefore seems that the picture gripping Wittgenstein is this: if truth can be discerned from the propositional sign alone, then no claim is made upon reality, there is nothing corresponding to the proposition that makes it true or false, and hence, intuitively, the proposition is uniformative, superfluous, empty, perhaps not even a genuine proposition: in short, tautologous.59 This suggestion of what moved Wittgenstein - and what led him to think that Russell would accept his characterization of logic - gains some support from various passages in the 'Notes on Logic', especially when we keep in mind that for more than a year the two questions absolutely central to Russell and Wittgenstein were: What makes a proposition true? (i.e., What corresponds to a proposition when it is true?) and, What is it to understand a proposition, whether true or false?60 We must also keep in mind that in the 'Notes' Wittgenstein is building on but drastically restructuring Frege's Sinn/Bedeutung (sense/meaning61) distinction. First:

The meaning of a proposition is the fact which actually corresponds to it.62

Second:


A [molecular] function is like a line dividing points of a plane into right and left ones; then "p or not-p" has no meaning because it does not divide the plane.63

Third:

A proposition is a standard to which facts behave [sich verhalten, are related, edd.], with names it is otherwise; it is thus bi-polarity and sense comes in; just as one arrow behaves [sich verhiilt, is related, edd.] to another arrow by being in the same sense or the opposite, so a fact behaves to a proposition. 64

Fourth:

Every proposition is essentially true-false: to understand it, we must know both what must be the case if it is true, and what must be the case if it is false. Thus a proposition has two poles, corresponding to the case of its truth and the case of its falsehood. We call this the sense of a proposition.65

Finally:

Signs of the form "p v - p" are senseless, but not the proposition "(p).p v - p". If I know that this rose is either red or not red, I know nothing. The same holds of all ab-functions. 66

Further substantiation is gained from the only other source67 of Russell's acquaintance with Wittgenstein's views on logic and tautology before 1919: 'Notes Dictated to G. E. Moore in Norway in April 1914,.68 Indeed, the first two remarks in these 'Moore Notes' exploit what was not explicit in the "Notes on Logic", namely, the show/say distinction, to state that logical propositions say nothing, and hence that they are not genuine propositions:

Logical so-called propositions shew [the ] logical properties of language and therefore of [the] Universe, but say nothing. [Cf. 6.12.]

This means that by merely looking at them [the so-called logical propositions] you can see these properties; whereas, in a proposition proper, you cannot see what is true by looking at it. [Cf. 6.113.]69

But now there is an all-important shift of emphasis; there is no longer tHe insistence on a general decision procedure for seeing (i.e., recognizing) a true logical proposition:

We want to say ... what properties a symbol must have, in order to be a tautology. Many ways of saying this are possible: One way is to give certain symbols; then to give a set of rules for combining them; and

then to say: any symbol formed from those symbols, by combining them according to one of the given rules, is a tautology. This obviously says something about the kind of symbol you can get in this way.


This is the actual procedure of [the] old Logic: 70 it gives so-called primitive propositions; so-called rules of deduction; and then says that what you get by applying the rules to the propositions is a logical proposition that you have proved. The truth is, it tells you something about the kind of proposition you have got, viz. that it can be derived from the first symbols by these rules of combination (= is a tautology).

Therefore, if we say one logical proposition follows logically from another, this means something quite different from saying that a real proposition follows logically from another. For so-called proof of a logical proposition does not prove its truth (logical propositions are neither true nor false) but proves that it is a logicfll proposition = is a tautology. [Cf. 6.1263.fl

The die has been cast: henceforth the tautologousness of logic will be insisted upon come what may;56 it will simultaneously play the role both of informing and following from the basic Tractatus doctrines -almost all of which are at least adumbrated in the 'Moore Notes' -limning the nature of language (thought) and its relation to reality, to the world. "Tautology" is no longer defined or specified in terms of "one Method of proving or disproving all logical prop[osition]s" (R. 22). In the Tractatus, a decision procedure, when applicable, is just an aid to recognizing

a tautology as such ... [For example] in cases in which no sign of generality occurs in the tautology. (Tractatus 6.1203.)

And as we have already seen in the "Moore Notes",

Proof in logic is only a mechanical expedient to facilitate the recognition of tautology, where it is complicated. (Tractatus 6.1262.)

No wonder there is not even an attempt at an argument in Russell's calling logic "tautologous". He did not accept, or perhaps even understand, Wittgenstein's basic doctrines. In a letter received by Russell in January 1915 Wittgenstein writes:

I find it inconceivable that Moore wasn't able to explain my ideas to you. Were you able to get anything at all out of his notes? I'm afraid the answer is, No.72

And in a letter to Russell dated 22 May 1915:

I'm extremely sorry that you weren't able to understand Moore's notes. I feel that they're very hard to understand without further explanation, but I regard them essentially as definitive. 73


3.

Russell, of course, was not alone in adopting Wittgenstein's word. Ramsey, Carnap and Lewis followed suit - though we find virtually no argument in their work for the application of (the term) 'tautology' to logical truth (except to cite Russell and Wittgenstein), and when we do we see none of them agreed with each other about why application of the term to logic is warranted. They did agree" however, in rejecting the Tractatus distinction between logic and mathematics; each accepted the logistic reduction in some form or other and applied 'tautologous' to the propositions of mathematics as well. That is, each ignored Wittgenstein's Tractarian criticisms of the logistic reduction, in particular, his criticism of the Frege-Russell definition of the ancestral as circular. 74 More importantly, each rejected the core of the Tractatus account of logic, namely, the say/show distinction and the Sinnlos/Unsinnig (lacking in sense/nonsensical) distinction. Logical propositions in the Tractatus are Sinnlos, tautologous, having no subject matter. In the Tractatus Wittgenstein is refusing to justify the idea that deduction is informative in the traditional way, that is, by viewing a given deduction as making explicit in the conclusion what is implicit in the premises. He rejects, in other words, the Kantian notion of the non-tautologous, analytic character of formal logic.

Kant and others had seen in the law of identity, "A is A", or, "Whatever is, is", a fundamental law of logic, an underlying boundary point beyond which thought and the world cannot go, which, despite its fundamental character, is expressed in a tautology; an empty proposition, redundant and "void of consequences". Such are all the (pseudo-) propositions of logic in the Tractatus. "We can get on without logical propositions,,,75 as Wittgenstein says, though they show us the "scaffolding of the world".

Ramsey dismissed the say/show distinction with his famous quip, "But what we can't say we can't say, and we can't whistle it either". 76 In his 'Foundations of Mathematics' Ramsey invokes the passage from Russell's Introduction to Mathematical Philosophy (quoted above), where Russell insists that the propositions of logic are to be called 'tautologies,.77 Then, after introducing Wittgenstein's truth-table analysis, Ramsey writes:

We have here, thanks to Mr. Wittgenstein, to whom the whole of this analysis is due, a clearly defined sense of tautology; but is this, it may be asked, the sense in which we


found tautology to be an essential characteristic of the propositions of mathematics and symbolic logic? The question must be decided by comparison. Are the propositions of symbolic logic and mathematics tautologies in Mr. Wittgenstein's sense?78

But the "sense in which we found" logic and mathematics to be tautologous is simply Russell's words in Introduction to Mathematical Philosophy. Russell, however, as we have seen, had offered 'tautology' as a mere label for that characteristic of logic which he confessed he could not define, although he felt "thoroughly familiar" with it. But now Ramsey asks whether the Tractatus captures the characteristic with which Russell was grappling! With the help of Russell, Wittgenstein had created a climate in which it was taken to be already demonstrated that logic is tautologous! The only task remaining, according to Ramsey, is to give a precise definition of it.

'Tautology' and its cognates occur throughout Lewis and Langford's Symbolic Logic (1932). For Lewis, as we saw on page 23 above, "tautologous" means "exhausts all possibilities". 79 Although this use of "tautology" was inspired by Wittgenstein's truth-table analysis, Lewis in no way restricted his use to the applicability of truth-tables. In fact, he labelled all the theorems of his various systems of modal logic 'tautologies'. Lewis's basic explanation of 'tautology' rests on the notion of 'analytic'. He writes:

any logical principle (and, in fact, any other truth which can be certified by logic alone) is tautological in the sense that it is an analytic proposition.80

And 'analytic' for Lewis is akin to 'analytic' for Kant. Lewis writes:

The only truth which logic requires, or can state, is that which is contained in our own conceptual meanings - what our language or our symbolism represents. Or to put it otherwise: there are no laws of logic, in the sense that there are laws of physics or biology; there are only certain analytic propositions, explicative of 'logical' meanings, and these serve as the 'principles' which thought or inference which involves these meanings must, in consistency, adhere to.8!

Lewis is exploiting the traditional account that logic informs by making the implicit explicit. For Lewis, a tautology is true in virtue of meaning. And this directly undercuts the Tractatus notion of tautologies as Sinnlos. In fact, the claim that the propositions of logic are Sinnlos was strongly criticized by Lewis in spite of his insistence that they are tautologous.

There has always been some confusion about the nature of analytic propositions, which


are true by definition or follow from the meanings of terms; and there has been a tendency to say that such propositions 'make no assertion' or 'are not significant,' or even that they 'are not propositions.' They are not of course, 'assertions' or 'significant' in the sense that synthetic propositions are, such as generalizations from experience, like the physical law v = gt. Such natural laws state something which could quite conceivably be false. Whether what could not conceivably be false - such as logical principles and arithmetical sums - is 'significant' or not, or 'makes an assertion' or not, is merely a question of propriety in the use of language, and is not worth arguing. We can only ask that those who deny significance or the quality of assertion to analytic propositions should be a little more explicit as to what they mean by 'significant I or 'an assertion.'82

(In fairness to Lewis, we must point out that he added a footnote to his homage to Wittgenstein with which we began this paper. The footnote reads:

With the further detail of Wittgenstein's conceptions the present authors would not completely agree.83)

4.

In the third edition (1961) of the Merriam-Webster New International Unabridged Dictionary (for which Max Black was a consultant) we find:

tautologous 1: TAUTOLOGICAL 2a: ANALYTIC b: true in terms of the sentential connectives of a truth table c: true purely by virtue of the meanings of component terms.

And:

analytic ... logic: of or relating to a truth, a proposition, or a statement that is true in all possible worlds, that is true independently of any facts by reference to meanings alone, or that is logically true or definitionally reducible to logical truth.

Finally, in the second edition of the Oxford English Dictionary (1989):

tautological l.a. Pertaining to, characterized by, involving, or using tautology; repeating the same word, or the same notion in different words ... b. Mod. Logic. Characterized by or involving tautology (in sense f.) 1922 tr Wittgenstein's Tractatus 97 In the one case the proposition is true for all the truth-possibilities of the elementary propositions. We say that the truth-conditions are tautological 1926. F. P. RAMSEY in Proc. London Math. Soc. XXV 341. The idea to be defined is one of the essential sides of mathematical propositions, their content, and their form. Their content must be completely generalized, and their form tautological ... 1950 R. CARNAP Logical Found. Probability iv 289 With respect to the tautological evidence 't'.

tautologous ... repeating what has been said ... 1940 W. V. QUINE Mathematical Logic i 50 Statements which are true by virtue solely of the truth-functional modes of composition will be called tautologous. 84


tautology ... a. A repetition of the same statement. b. The repetition (esp. in the immediate context) of the same word or phrase, or of the same idea or statement in other words: usually as a fault of style ... f. Mod. Logic. A compound proposition which is unconditionally true for all the truth-possibilities of its elementary propositions and by virtue of its logical form. 1919 B. RUSSELL, Introd. Math. Philos. xviii 203 The characteristic of logical propositions that we are in search of is the one which was felt ... by those who said that it consisted in deducibility from the law of contradiction. This characteristic we may call tautology. Ibid. 205 The importance of 'tautology' for a definition of mathematics was pointed out to me by ... Ludwig Wittgenstein, who was working on the problem. 1922: tr. Wittgenstein's Tractatus 97 The tautology ... is unconditionally true ... 1964 M. BLACK Compan. Wittgenstein's Tractatus xliii 231 Johnson's ... 'formal truth' and 'formal falsity' ... seem to correspond exactly to W.'s 'tautology' and 'contradiction'.

And (for fun):

analyticity ... Philos. The property, in propOSItIons or statements, of being analytic ... 1953 W. V. O. QUINE From a Logical Point of View ii. 21 Kant's intent, evident more from the use he makes of the notion of analyticity than from his definition of it, can be restated.

One way to avoid the charge of misspeaking is to change the language. 85

NOTES

I From Lewis's cover letter for his 'A Pragmatic Conception of the A Priori', in The Journal of Philosophy 20 (1923): 169-77. 2 C. I. Lewis and C. H. Langford, Symbolic Logic (New York: Century Company, 1932), p.24. 3 Immanuel Kant, Logic eds. and trans. Robert S. Hartman and Wolfgang Schwarz (New York: Dover Publications, 1988), I Section 36 (p. 117). (Page references, in parentheses, are to this translation.) 4 Ibid., I Section 37 (p. 118). 5 Immanuel Kant, Prolegomena to Any Future Metaphysics (1783), ed. and trans. Lewis White Beck, (Indianapolis: Bobbs-Merrill Company), Preamble, Section 2 (p. 14). 6 In Leibniz's Philosophical Papers and Letters, ed. Leroy E. Loemker. The editor notes (p. 227) that

"coccysm" was proverbial for wordiness or redundancy, from the reputation of John Cocceius, Professor of Theology at Leyden, and his followers.

7 Leibniz, 'On the General Characteristic' (c. 1679) (in Philosophical Papers and Letters, (hereafter L) ed. Leroy E. Loemker (second edition, Chicago: University of Chicago Press, 1976): pp. 221-8) pp. 225-6. 8 'Necessary and Contingent Truths' (c. 1686) (in Leibniz, Philosophical Writings (hereafter LPW) ed. G. H. R. Parkinson (London: J. M. Dent & Sons, 1973): pp. 96-105),


p. 96. In 'First Truths' (c. 1680-84) Leibniz calls the principle of identity a "First Truth" (L, p. 267). In the second letter to Samuel Clarke (1715-16) (L, p. 677) he claims it underlies all of mathematics. In the Monadology (1714) Sections 31-2 (L, p. 646) Leibniz says:

31. Our reasonings are based on two great principles: the principle of contradiction, by virtue of which we judge to be false that which involves a contradiction, and to be true that which is opposed or contradictory to the false; 32. and the principle of sufficient reason, by virtue of which we consider that no fact can be real or existing and no proposition can be true unless there is a sufficient reason, why it should be thus and not otherwise, even though in most cases these reasons cannot be known to us.

See also 'On the General Characteristic' (1679) (L, p. 226). 9 Kant, Logic, Introduction VIIB (p. 58). 10 Ibid. Kant, following Leibniz, also cites the principle of sufficient reason as a fundamental law. In the quotation from Leibniz's Monadology in footnote 8 above, note his claim that the principle of contradiction and the principle of sufficient reason underlie all our reasoning. Kant echoes this idea in Logic, Introduction VIIB (p. 57).

11 See Leibniz's remarks at L, p. 385, 633, and Benson Mates, The Philosophy of Leibniz (Oxford University Press, 1986) p. 153. 12 Kant, Critique of Pure Reason, trans. Norman Kemp Smith (New York: St. Martin's Press, 1967) (hereafter KRV) A60/B85. 13 Kant, Logic, p. 15. 14 See Locke, An Essay Concerning Human Understanding (ed. Peter H. Nidditch (Oxford University Press, 1975) Book IV, Ch. xvii, s. 4.) Locke says (p. 493ff) of the abuse of language, which he calls "affected obscurity", that

To this abuse, and the mischiefs of confounding the signification of Words, Logick, and the liberal Sciences, as they have been handled in the Schools, have given Reputation; and the admired Art of Disputing, hath added much to the natural imperfection of Languages, whilst it has been made use of, and fitted, to perplex the signification of Words, more than to discover the knowledge and Truth of Things: And he that will look into that sort of learned Writings, will find the Words there much more obscure, uncertain, and undetermined in their Meaning, than they are in ordinary Conversation.

15 KRV A60-61/B85-86. 16 Hegel, The Science of Logic (ed. H. D. Lewis, trans. A. V. Miller (Atlantic Highlands: Humanities Press International, 1989», p. 411 (Vol 1, Bk 2, Ch 2, A). 17 Ibid., p. 413 (Vol. 1, Bk. 2, Ch 2, Remark 2). 18 Ibid., p. 416 (Vol. 1, Bk. 2, Ch 2 A, Remark 2). 19 F. H. Bradley, The Principles of Logic (London: Kegan Paul, Trench & Co., 1883), pp. 131-2. 20 Ibid., p. 48, fn. 21 Ibid., p. 133. 22 Ibid., Book I, Ch V, Sections 11, 12, 18,24.


23 Russell, An Essay on the Foundations of Geometry (Cambridge University Press, 1897), p. 58. 24 Russell, A Critical Exposition of the Philosophy of Leibniz: With an Appendix of Leading Passages (Cambridge University Press, 1900), pp. 16--17. 25 G. E. Moore, 'Necessity', Mind (1900), 289-304. Quotation is from p. 295. 26 For Moore's and Russell's reactions to Idealism, see Peter Hylton, Russell, Idealism, and the Emergence of Analytic Philosophy (Oxford University Press, 1990). 27 Gottlob Frege, The Foundations of Arithmetic (trans. J. L. Austin, second edition, Evanston: Northwestern University Press, 1980), pp. 3-4. , 28 For an account of Frege's conception of logic as maximally general laws see Thomas G. Ricketts.' triad of papers 'Objectivity and Objecthood: Frege's Metaphysics of Judgment', (L. Haaparanta and J. Hintikka, eds., Frege Synthesized (D. Reidel, 1986», 'Generality, Meaning and Sense in Frege', (Pacific Philosophical Quarterly 67 (1986): 172-95) and 'Frege, the Tractatus, and the Logocentric Predicament' (Nous, XIX, No.1 March 1985: 3-15). For Frege's 'logistic reduction' see George Boolos, 'Reading the Begriffsschrift' (Mind 94 (July 1985): 331-4) and Charles Parsons's 'Frege's Theory of Number' (in Parsons's Mathematics in Philosophy, Selected Essays (Ithaca: Cornell University Press, 1983): pp. 150-75). For Frege's relation to Kant (and as a precursor of Wittgenstein) see Joan Weiner, Frege in Perspective (Cornell University Press, 1990). 29 In Section 73 of The Foundations of Arithmetic (p. 85) Frege writes:

Our next aim must be to show that the Number which belongs to the concept F is identical with the Number which belongs to the concept G if the concept F is equal [gleichzahlig] to the concept G. This sounds, of course, like a tautology. But it is not; the meaning of the word "equal" ["g/eichzahlig"] is not to be inferred from its etymology, but taken to be as I defined it above.

30 Fritz Mauthner, named in the Tractatus at 4.0031 - where Wittgenstein distinguishes his "Sprachkritik" from Mauthner's - pursued the rare, if not unique, philosophical program of combining Locke with Schopenhauer. As a result, he held not only that the Laws of Thought and all analytic propositions are tautologies, but even that all truths, once known, become tautologies. See Mauthner, Beitriige zu einer Kritik der Sprache (first edition, Stuttgart: J. G. Cotta'sche, 1902), Vol. 3, pp. 326--7 and p. 364ff, especially p. 378. We thank Professor Ignacio A. Angelelli for calling our attention to the discussion of tautology in Mauthner. 31 In Wittgenstein's Notebooks 1914-1916 (eds. G. H. von Wright and G. E. M. Anscombe, trans. G. E. M. Anscombe (Second edition, Oxford: Basil Blackwell, 1979); hereafter NB), in the entry for 29 October, 1914 (NB, p. 21) we read:

There are no such things as analytic propositions.

32 Bertrand Russell, The Principles of Mathematics (Cambridge University Press, 1903; second edition with a new introduction (pp. v-xiv) 1938), p. 457. Where Russell differs from Kant and agrees with Frege is in denying that (Kantian) intuition is needed for mathematics; hence for both Frege and Russell mathematics is of the same character as logic. Still, it would be an overstatement to equate Russell's use of "synthetic" with Frege's "analytic", since Frege would hardly say "logic is just as analytic as all the other kinds of truth". !lor a discussion of Kantian intuition see Jaakko Hintikka's 'Kantian


Intuitions' (Inquiry 15 (1972): 341-5); his 'On Kant's Notion of Intuition (Anschauung), (in Terence Penelhum and J. J. MacIntosh, eds., Kant's First Critique (Belmont: Wadsworth, 1969): 38-53); as well as Parsons's 'Kant's Philosophy of Arithmetic' (Mathematics and Philosophy, Selected Essays: pp. 110-49). 33 Henri Poincare, Science and Hypothesis (Walter Scott Publishing Company, 1904; republished by Dover Publications, 1952), pp. 1-2, Dover reprint. Russell's references to this work refer to the original edition. 34 Ibid., p. 3. 35 Warren Goldfarb, 'Poincare against the Logicists' (Minn~sota Studies in the Philosophy of Science, Vol. XI, History and Philosophy of Modern Mathematics, William Aspray and Philip Kitcher, eds., (University of Minnesota Press, 1988), pp. 61-81). 36 Russell's review appeared in Mind, 1905 and is reprinted in his Philosophical Essays (London: George Allen & Unwin, 1966). The quotation is from p. 73 of Philosophical Essays. 37 Russell, Problems of Philosophy (London: William & Norgate, 1912), Chapter 8, Paragraph 3. 38 Ibid., Chapter 7, Paragraph 5. 39 Ibid., Chapter 7, Paragraph 8. 40 P. Coffey, The Science of Logic (London: William and Norgate, 1912). 41 Wittgenstein's Review, 'On Logic and How Not to Do It' was printed in The Cambridge Review 34 (1912-13), p. 351. It is reprinted in Brian McGuinness's Wittgenstein, A Life (Berkeley: University of Calfornia Press, 1988), pp. 169-70. 42 Coffey, The Science of Logic, Vol. I, p. 23. 43 Ibid., Vol. I, p. 26. 44 McGuinness, Wittgenstein, A Life, p. 170. 45 Russell, Philosophy of Logical Atomism (first published in the Monist 28, October 1918, pp. 495-527; then again at La Salle, IL: Open Court Publishing Company, 1985). References are to the Open Court edition. The quotation is from pp. 107-8. 46 Ibid., p. 107:

There are ... two propositions that one is used to in mathematical logic, namely, the multiplicative axiom and the axiom of infinity. These can be expressed in logical terms but cannot be proved or disproved by logic.

47 Russell, Introduction to Mathematical Philosophy (New York, The Macmillan Co., 1919), Chapter XVIII, Paragraph 19. As is often the case, remnants of the old faith persist in the new. In Chapter XVI, Paragraph 7 we find

Logic, I should maintain, must no more admit a unicorn than zoology can; for logic is concerned with the real world just as truly as zoology though with its more abstract and general features.

48 Ibid., Chapter XVIII, Paragraph 21. 49 Ludwig Wittgenstein: Letters to Russell, Keynes and Moore, ed. G. H. von Wright, English trans. by Brian McGuinness (Ithaca: Cornell University Press, 1974), hereafter LRKM, p. 37 (letter R.22 according to von Wright's numbering scheme). 50 Wittgenstein sketched his ab-Notation in a short document, now called 'Notes on Logic', whose mostly German Ur-text(s), unfortunately lost, were obtained by Russell


from Wittgenstein in early October 1913. (Wittgenstein did not see or speak to Russell from mid-October 1913 until December 1919.) For the provenance of these 'Notes' see Brian McGuinness's 'Bertrand Russell and Ludwig Wittgenstein's "Notes on Logic'" (Revue Internationale de Philosophie (1972): 444--60). ('Notes on Logic' (hereafter NL) is printed as Appendix I in the second edition of Wittgenstein's Notebooks 1914-1916.) In two letters (R.20, R.21) of November 1913 that immediately precede the present letter (R.22), Wittgenstein peremptorily answered some questions of Russell about the Notation. Wittgenstein chided Russell in letter R.20:

If you had only remembered the WF scheme of -p you would never have asked this question (I think). In fact all rules of the ab symbolism follow directly from the essence of the WF scheme. (LRKM, p. 33).

The phrases "WF scheme" and "TF scheme", accompanied with very brief discussion, appear in 'Notes on Logic' (pp. 94-9); according to McGuinness (Wittgenstein: A Life, p. 160), Wittgenstein showed Russell the truth-table notation (i.e., "the WF scheme") in the winter of 1912. 51 LRKM, p. 36 (letter R.22). 52 Post also tried to extend his truth-table decision procedure to all of logic. But by the end of 1921 he (correctly) conjectured that there was no such method, and that "a complete symbolic logic is impossible". (See E. L. Post, 'Absolutely Unsolvable Problems and Relatively Undecidable Propositions: Account of an Anticipation', unpublished paper printed in Martin Davis, ed., The Undecidable (Raven Press Books, 1965), pp. 348, 397, and 416. The phrase quoted is from page 416.) Unlike the young Wittgenstein, however, the failure to extend his method leads the young Post to view logic (and mathematics) as essentially creative, not empty (tautologous). 53 LRKM, p. 37 (R.22). 54 LRKM p. 41 (English translation of letter R.23; German original, p. 39). 55 LRKM, p. 43 (English translation of letter R.23; German original, p. 41). 56 One cannot help but be struck by an enormous historic irony: Turing and Wittgenstein discussed in the late 1930s the nature of logical and mathematical rules, indeed of algorithms. And even more remarkably, they each continued to call the formulae of Principia Mathematica (at least, those in Volume I) "tautologies". See Wittgenstein's 1939 Lectures on the Foundations of Mathematics, ed. Cora Diamond (Chicago: University of Chicago Press, 1975). 57 Wittgenstein had previously written to Russell (29 October 1913):

Identity is the very Devil and immensely important; very much more so than I thought. It hangs - like everything else - directly together with the most fundamental questions, especially with the questions concerning the occurrence of the SAME argument in different places of a function (LRKM, p. 31 (R.19)).

To understand why Wittgenstein never would find his "notation for identity" see the discussions of "occurrence of the same argument in different places of a function [quantificational formula)" in Burton Dreben and Warren Goldfarb, The Decision Problem: Solvable Classes of Quantificational Formulas (Addison-Wesley, 1979) and Harry R. Lewis, Unsolvable Classes of Quantificational Formulas (Addison-Wesley, 1979). To appreciate the full magnitude of the question see Hao Wang, 'Dominoes and The AEA


case of the Decision Problem,' Proc. Symposium on the Mathematical Theory of Automata (New York: Polytechnic Press, 1963) and Stal O. Aanderaa and Harry R. Lewis, 'Linear Sampling and the V3V-case of the Decision Problem', Journal of Symbolic Logic 39: 519-47. Finally, to see how truly difficult is the problem of identity see Warren Goldfarb, 'The Unsolvability of the Godel Class with Identity', The Journal of Symbolic Logic 49: 1237-52. 58 LRKM, p. 42 (English translation of letter R.23; German original, pp. 39-40). 59 Even Quine says:

Ontology is internally indifferent also, I think, to any;theory that is complete and decidable. Where we can always settle truth values mechanically, there is no evident internal reason for interest in the theory of quantifiers nor, therefore, in values of variables. (Ontological Relativity and Other Essays (New York: Columbia University Press, 1969), p. 63).

60 See McGuinness, Wittgenstein, A Life, pp. 89-91, 162ff; and David Pears's two papers 'The Relation between Wittgenstein's Picture Theory of Propositions and Russell's Theories of Judgment', (Philosophical Review (April 1977): 177-96) and 'Russell's 1913 Theory of Knowledge Manuscript' (in E. Wade Savage and C. Anthony Anderson (eds.), Rereading Russell: Essays on Bertrand Russell's Metaphysics and Epistemology (Minnesota Studies in the Philosophy of Science, XII; Minneapolis: University of Minnesota Press, 1989: pp. 169-82)). 61 The justification for reading "meaning" as "Bedeutung" and "sense" as "Sinn" in the 'Notes on Logic' rests on the fact that the original source of the 'Notes' was mostly in German (see footnote 50 above) and on Wittgenstein's letter to Russell of November 1913 (R.21), LRKM, p. 35. 62 NL, p. 94. 63 NL, p. 94. 64 NL, p. 95. 65 NL, p. 98-99. 66 NL, p. 104. 67 Pedantry - or scholarly integrity - demands that we note letters R.24, M.3 and MA where "tautology" occurs: 15 December 1913 (to Russell):

The question as to the nature of identity cannot be answered until the nature of tautology has been explained. But that question is fundamental to the whole of logic list die Grundfrage aller Logik]. (R.24, LRKM p. 45.)

30 January 1914 (to Moore): Have you ever thought about the nature of a tautology? That's what I am now bothered with. (M.3, LRKM p. 146.)

18 February 1914 (to Moore):

It ... all turns on the question as to the nature of deduction. And - I think - the clue to it all lies in the fact that cPx :Jx IjJX only then expresses the deductive relation when this prop[osition] is the generalization of a tautology. (MA, LRKM p. 147.)

68 These 'Moore Notes' are printed as Appendix II to Wittgenstein's Notebooks


1914-1916: pp. 108-19. Hereafter we will refer to them (by page .number in the Notebooks) as MN. Unlike the 'Notes on Logic', where the word "tautology" never appears, and only one occurrence of a cognate (i.e., "tautologous") in a context offering little support for Wittgenstein's characterization of logic, here "tautology" and its cognates frequent Wittgenstein's discussion. Also, unlike the letters to Russell of November and December 1913, the so-called propositions of logic are no longer generalizations of tautologies, but are tautologies themselves. 69 MN, p. 108. The bracketed references are to the Tractatus. 70 The logic of Frege and Russell. 71 MN, p. 109. The citation in brackets is to the Tractatus. 72 LRKM, p. 59 (R.30). 73 LRKM, p. 62 (R.31). [February 1991. Two letters from Russell to Wittgenstein, which were recently found in Vienna, are most instructive. In the first, dated 10 May 1915, Russell writes, "I have got from Moore everything he had to report about tautologies etc., but it was intelligible to me only in very small measure". In the second, dated 13 August 1919, Russell writes:

I have now read your book [manuscript of the Tractatus] twice carefully. - There are still points I don't understand - some of them important ones - I send you some queries on separate sheets. I am convinced you are right in your main contention, that logical props are tautologies, which are not true in the sense that substantial props are true. (Russell: The Journal of the Bertrand Russell Archives, New Series 10,2, Winter 1990-91, pp. 103 and 107.)]

74 Tractatus 4.1273. 75 Ibid., 6.122:

Whence it follows that we can get on without logical propOSItions, for we can recognize in an adequate notation the formal properties of the propositions by mere inspection.

76 Ramsey, The Foundations of Mathematics and Other Logical Essays, ed. R. B. Braithwaite (Paterson: Littlefield, Adams & Co., 1960), 'General Propositions and Causality·. p. 238.

Professor Nickolas Pappas has pointed out to us the following passage from Act II of Shaw's Man and Superman:

TANNER: ... Let me remind you that Voltaire said that what was too silly to be said could be sung. STRAKER: It wasn't Voltaire: it was Bo Mar Shay. TANNER: I stand corrected: Beaumarchais of course. Now you seem to think that what is too delicate to be said can be whistled. Unfortunately your whistling, though melodious, is unintelligible. (Man and Superman, Penguin Books, New York, 1946, p. 106.)

77 Ramsey, The Foundations of Mathematics, p. 4. 78 Ibid., p. 11. 79 G. H. von Wright and particularly Jaakko Hintikka have explored and interestingly developed this new sense of "tautologous". See von Wright, 'Form and Content in Logic' and 'On the Idea of Logical Truth (I)', both reprinted in his Logical Studies (London:


Routledge & Kegan Paul, 1949) and his "On the Idea of Logical Truth (II)" (Societas Scientiarum Fennica. Commentationes Physico-Mathematicae XV No. 10 (1950): 1-45). See also Jaakko Hintikka, Distributive Normal Forms in the Calculus of Predicates (Acta Philosophica Fennica, 6, Helsinki: 1953); Logic, Language-Games and Information (Oxford: Clarendon Press, 1973), especially chapter VII; '0. H. von Wright on Logical Truth and Distributive Nonnal Fonns' (in The Philosophy ofG. H. von Wright (La Salle: Open Court). 80 Lewis and Langford, Symbolic Logic, p. 211. 81 Ibid., p. 211. 82 Ibid., p. 212. 83 Ibid., p. 24. 84 Lest any reader be misled:

The term "tautology" is taken from Wittgenstein. The present notion of tautologous statements, as those true by virtue solely of truth-functional composition, seems to agree with his usage; he contrives to make the term cover truths which involve also quantification, but this is consequent only upon an effort to explain quantification as a sort of infinite mode of truth-functional composition. A broader use of the term "tautologous" has arisen in subsequent literature, because of Wittgenstein's doctrine that all mathematics and logic is tautologous. This doctrine was intended by Wittgenstein as a thesis, not as a definition of tautology; and indeed it is a difficult thesis to defend. But some who do not maintain the thesis in any such form, and who regard the inferences of logic and mathematics as "merely verbal transformations" or "disguised repetitions" only in some much broader sense, have been led thus to transfer the term "tautologous" to this broader sense. It is not clear just what this broader sense is (cf. my 'Truth by Convention'); but, whatever it is, there is already a term of long standing ready at hand for it - Kant's term "analytic". Hence, following a suggestion of Carnap's, I am confining the term "tautologous" to the narrower sense - though in abstraction from Wittgenstein's theories. (W. V. Quine, Mathematical Logic (Norton, 1940) Section 10, p. 55)

85 We are indebted to John Rawls for helpful comments on an earlier version of this paper. We are also indebted to the members of the Centennial Wittgenstein Conference held in April 1989 at the Florida State University, Tallahassee - especially to Jaakko Hintikka, David Pears and David Stern.

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Dreben: Dept. of Philosophy Harvard University Cambridge, MA 02138

Floyd:

Dept. of Philosophy Boston University 745 Commonwealth Ave. Boston, MA 02215 U.S.A.

Dept. of Philosophy The City College of New York New York, NY 10031 U.S.A.

DAVID CHARLES MCCARTY

THE PHILOSOPHY OF LOGICAL WHOLISM*

Words are like a filin on deep water

LUDWIG WITTGENSTEIN

Notebooks 1914-1916

ABSTRACT. The present paper is one installment in a lengthy task, the replacement of atomistic interpretations of Wittgenstein's Tractatus by a wholistic interpretation on which the world-in-logical-space is not constructed out of objects but objects are abstracted from out of that space. Here, general arguments against atomism are directed toward a specific target, the four aspects of the atomistic reading of Tractatus given in the Hintikkas' Investigating Wittgenstein (Hintikka & Hintikka 1986). The aspects in question are called the semantical, metaphysical, epistemological and formal.

What follows a precis of the Hintikkas' rendering of Wittgenstein's perspective is a characterization of the wholistic interpretation, comparing Wittgenstein's world and the transcendental conditions it sets upon possible notation to a blank page and the conditions it sets upon what is about to be written there. There will not be occasion to bring arguments against each plank in the atomist's platform or in support of each facet of wholism. But there is an extended treatment of the first two aspects - the seman tical and metaphysical - which takes off from Wittgenstein's determination that, in his hands, "logic must take care of itself".

The second half of the paper contains a negative assessment of the support the atomistic reading can glean from the texts of Tractatus and Notebooks. From a detailed look into a range of relevant textual and translational issues, we find little there to encourage that interpretation and much to discourage it.

The paper closes on a preliminary consideration of one segment of the formal aspect of the Hintikkas' atomism, the idea that the analysis of Tractatus is the analysis of Russell or is, at worst, a near relative. Examination shows that Wittgenstein would have little reason to model his analysis on that of Russell. The fundamentally wholistic vision expressed in Tractatus requires a distinctively non-Russellian, decompositional version of analysis.

1. INTRODUCTION

If there was a specifically "early" Wittgenstein, he was not a logical atomist but a logical wholist. By this, I mean to break with a long interpretative tradition and to turn a standard view of Wittgenstein's Tractatus and contemporaneous writings on its very head. By my lights,


52 DAVID CHARLES MCCARTY

Wittgenstein's Welt, the world-in-Iogical-space, was not the great logical fabrication, built up by iterable semantic constructions out of independent units of meaning, the logical atoms. To read Wittgenstein's treatise is not to read a mild revision of Russell's semantics, or of any semantics, provided that a semantics is codified as a set of principles of meaning, a knowledge of which would constitute an understanding of language. Wittgenstein's logic, his perspective on the logical, was not an extension of a line first drawn by Frege and extended into our century by Russell, but a determined attempt to rub that line out.

The tradition of logical atomism and of atomistic interpretations of Wittgenstein was established in Russell's troubled Introduction to Tractatus, where he wrote "the naming of simples is shown to be what is logically first in logic" (Russell 1981, p. xiii). It was extended through The Philosophy of Logical Atomism (Russell 1985), and commentaries such as Black's A Companion to Wittgenstein's Tractatus (Black 1964). More recently, it is upheld in Merrill and laakko Hintikkas' Investigating Wittgenstein (Hintikka & Hintikka 1986). Toward this book are my remarks principally directed. However, it is clear that many apply far more widely.

Banishing logical atomism and welcoming logical wholism is setting up an opposition between two ways of reading Tractatus or, better, of picturing to ourselves Wittgenstein's world. For the atomists - those who favor the attribution to Wittgenstein of logical atomism - the world of Tractatus is semantically structured. Its image is absolutely clear, preternaturally sharp: a logical mosaic tiled with purely referential units, each lying at the lower limit of conceptual and perceptual resolution. For the wholists, Wittgenstein's world has no philosophical image at all, no picture of a logically primeval landscape which later gets reported in the grammar of our language. The world there is not one which is represented to us. It is not there to be an object of our intelligence but emerges to make intellection possible. Certainly, it is not a world constructed from seman tical ephemera.

I caution the reader that this opposition is not one between philosophical views comparable with the outposts of warring tribes which overlook a neutral terrain. We ought to refuse the temptation to borrow a metaphor from the information-processing trade and call atomism a "bottom up" version of Wittgenstein while wholism is "top down". There is danger in this metaphor's false suggestion: that the two readings might go variously up and down the same ladder and then meet

THE PHILOSOPHY OF LOGICAL WHOLISM 53

in the middle. There is no ladder. Hermeneutic evil awaits us should we think that there is, in Tractatus, a single idea or set of ideas, some fixed content on which, if it were only formulable in a fair fashion, atomist and wholism might both agree. It is not as if Tractatus bears a message which is interpretation ally untainted, as if Wittgenstein's words formed a plain brown wrapper which, once removed, reveals a Tractarian world - either simple or conglomerate - within a single logical space, a world which one party - of which the Hintikkas are subscribers - prefers to survey from the soil up while the other, somewhat perversely, wishes to take in from the stratosphere and on down. Atomists and who lists do not have a world in common.

The distance between the two readings, wholism and atomism, is not like that between two painted dots on a single canvas; it is much more like the distance between two so-called styles of painting. Indeed, it bears marked similarity to the distance between impressionism and expressionism. The extent of the distance is measurable from the extent that we disagree over seemingly simple terms, words such as 'philosopher' or 'logician.' When the Hintikkas wrote that Wittgenstein was a "philosopher", they meant that he was a twentieth century analytic philosopher. As such, he would have shared some intellectual concerns, a standard of discourse and a certain method with philosophers of the Hintikkas' milieu. As it happens, these sentiments of solidarity would be much more appropriate to the eighteenth century philosopher Hume than to the twentieth century Wittgenstein. Hume shares with his latter day sympathizers a commitment to semantical atomism, a philosophical aesthetic according to which the world comes readymade to be talked about by us. It is constructed or built up - in just the way our language is supposed to be - out of discrete units of ideation, each containing a precise measure of thought. Hume is also, and self-consciously so, a scientist-philosopher. He declared himself a full partner in the great firm of empirical science. He saw philosophical inquiry as apiece with the scientific (or what he took to be the scientific) redescription of everyday life, a redescription ratified by a hidden reality, an intelligible structure behind our words, structure invisible to ordinary mortals but open to philosopher-scientists.

Wittgenstein was never a philosopher of this Humean, or analytical, persuasion. He shunned the comforts both of semantical atomism and of the scientifically-based worldview. In both the early Notebooks and Tractatus, Wittgenstein wrote:


At bottom the whole Weltanschauung of the moderns involves the illusion that the socalled laws of nature are explanations of natural phenomena. In this way, they stop short at the laws of nature as at something impregnable as men of former times did at God and fate. And both are right and wrong. The older ones are indeed clearer in the sense that they acknowledge a clear terminus, while with the new system it is supposed to look as if everything had a foundation. (N, 72)1

Wittgenstein is also called "logician". This is accurate insofar as, throughout his life, he experimented in anti-canbnical notations, redesigning forms of concept writing so that crooked lines of thought come out straight. He did not hanker, as do contemporary logicians, after a complete theoretical redescription of the abstract form of correct inference; he thought such description unattainable. Wittgenstein's logic was far more praxis than theoria; like medieval logic, it was a science of personal mental hygiene or, better, a talisman against pernicious and subtle fallacies. Today's logic is in its middle-age; in certain neighborhoods, its business seems firmly established. It is as if our logic had clearcut a vast region of linguistic jungle, exposing a granite landscape of Boolean connectives, quantifiers, incompleteness phenomena and model theory over which it exerts eternal claim. By contrast, Wittgenstein's logic could be a young Turk - an anarchist, in fact - never seeking the establishment of a particular notation but always a disestablishment, a permanent logical revolution. As Wittgenstein wrote of language games in paragraphs 130 and 131 of Philosophical Investigations, his logical way with notations was one of Ahnlichkeiten und Uniihnlichkeiten, similarities and dissimilarities: notations "are much more set up as comparative objects which, through similarities and dissimilarities, are meant to throw light upon the status of our language" (Wittgenstein 1953).

Nor is there in Tractatus the familiar vision of language as mathematical object. In contemporary logic, language is a free semigroup of simple forms, generated in a rule-governed way from a tiny base of linguistic surds. The direction of generative construction is a reconstruction of understanding: we are thought to grasp sentences by cognitive building, first putting semiotic hands on the members of the base and building up, from them, a whole algebra of knowledge by iteration of operations. However, the mathematical language is conceived as, in itself, mute or uninterpreted; its elements cannot speak of their own accord. Only in another language, a semantic language, does the algebra of signs get a voice. This is the distance between syntax and


semantics and there is no greater distance in mathematical logic than that. The gap is so wide it calls for the seeming strangeness of intentionality to bridge it across. For Wittgenstein, all this is changed. If we have a knowledge of meaning, then the logician cannot reconstruct it. The elements of language, the simple forms - Wittgensteinian objects -are not cognitive starting-points but, rather, endings. There is no gap between syntax and semantics; there is no Wittgensteinian syntax without reading and no reading without a world of interpret'ation. Wittgenstein's world is just the perspective on signs we naturally take when we see them as signs. There is no gap to bridge between name and Bedeutung; use a sign as a name, its Bedeutung forms automatically - not as a matter for thought but as a condition of it.

In the sequel, we look to see what kind of philosopher and what kind of logician Wittgenstein was. We look over and, then, overlook the kind of philosopher and logician he was not, an atomistic one.

2. THE PARTS OF ATOMIS~

For many, Tractatus and Notebooks are the twentieth century Urquellen for the semantico-metaphysical doctrine of logical atomism. In place of the emptiness of Wittgenstein's Welt, they put a colored picture-book world, an epistemically crafted and intelligible whole afloat in a limpid logical space. At its base lie logical atoms; riding so low on the logical hierarchy that we might say they are mind-bogglingly simple. The atoms are monadic - themselves miniature worlds. They are classically substantial, existing independently of their fellows, conceivable and -above all - nameable without concern for any other. Atoms are made to combine and, when they do, they give rise to logical molecules, Sachverhalte, atoms fit together by propositional modes of construction. Sachverhalte then bond into even larger units, Tatsachen and these, in their turn, into yet more comprehensive Tatsachen. In this way is the world of atomism built up.

In this world, grammatology recapitulates ontology; the world's structure tells us how to speak. The order of exposition is the order of cognition. The constructional history of the world is semantical, an ontological chronicle of our personal histories in understanding sentences. The world tells us how sentences have to be grasped: first, we come upon atoms as elements in perception and, repeating Adam's work with the animals, assign them names. In the field of our semantic


cognition, they are then joined into sentences by description operators, truth functions, quantifiers and the glue that sticks subjects onto predicates. These are the syntactic shadows of the bonds that create Tatsachen. The latter are, in turn, joined truth-functionally into yet more complex sentences, ones with further Tatsachen as their referents. Parallelism is complete: sentences - properly understood - are constructed out of simple names just as their propositional contents, Wittgenstein's Tatsachen, are constructed out of sensory primitives, their referents. 3

Atomism is resolvable into a constellation of four attributions. In college catalogue style, I call them the semantical, ontological, epistemological and formal. The semantical is the focal point for atomism's vision: as just described, that world is in itself grammatically structured and the grammar is Russell's logical grammar. As Russell explained, it is "the view that you can get down in theory, if not in practice, to ultimate simples, out of which the world is built, and that those simples have a kind of reality not belonging to anything else" (Russell 1956, p. 58). In Tractatus, the simples are Tractarian objects. Available modes of construction - of propositions and complexes from objects - makes for an object its logical form, the weight of its logical contribution. For the atomist, the bulk of logic is the sum of these individual weights. So, the Hintikkas towed the same line as Russell when they wrote "the logic of Tractatus is a logic of simple objects" (Hintikka & Hintikka 1986, p. 100).

In the atomist's semantical household, objects "wear the pants"; there, "the crucial subject matter in trying to understand the Tractatus is obviously Wittgenstein's conception of object" (Hintikka & Hintikka 1986, p. 30). The objects take pride of place because the project of atomism is a project of denotational justification, without which the image of constructed world is empty slogan. The project idea is this: language, in its true character, is fully rational. Although it is possible to mistake that character, logic can discover it. Once that is done, the rationality of language will be visible in the presumptive parallelism between speech and ontology: one can then explain and justify the inner character of language by pointing to the way the world is. What makes Tractarian objects a fit subject for analytical philosophy rather than for science fiction is their putative role in this justificatory project, in a science of atomistic semantics. Objects are semantical quarks, ultimate theoretical entities in the story of meaning, one that begins when names get attached directly to objects. Because the homomor-


phism of syntax to semantics is defined "up from the bottom", the account of sentential combination, Satzge!ilge, is reduced to a theory of objects and their bonds. Ultimately, therefore, logical licenses are granted and grammatical prohibitions issued by the natures of the objects. For instance, if 'a' denotes Terry and 'P~' denotes the function "~is a pirate", and this is known, then we are justified in asserting that 'Pa' is meaningful while 'aP' and 'PP' are not. A justification for this claim is meant to flow from knowing the natures of the ;denotata of 'a' and of 'P' - in Fregean terms, from knowing that Terry is saturated while "~is a pirate" is not. Atomism gives us facts of meaning which facts of metaphysics explain.

At the ground floor of atomism's explanatory structure lie theoretical relations among objects. They establish the second or ontological aspect of atomism in Tractatus. It is divided into three subaspects. First, Tractarian objects are said to fall into diverse metaphysical categories, some of which are distinguished, using Frege's terminology, by saturatedness or by its opposite. Second, as the Hintikkas would have it, the metaphysical categories are split off from one another along traditional lines, those drawn by the ancient semanticists who distinguished particular from universal. Talk of names in Tractatus is interpreted so that they denote both individuals such as Terry and properties such as "being a pirate". (I am not proposing that humans like Terry and properties like "being a pirate" are actual samples of the sorts of things which atomists have in mind when they speak of objects. They are intended as expository models for the kinds of differences thought to obtain.) Finally, objects manage the division into metaphysical types on their own. As a child might say, "they just come like that". Without interference from language or mind, objects sort themselves into the medieval categories just as protons and electrons are sorted by their relative mass.

For epistemological reasons, Terry and "being a pirate" are unlikely to satisfy the atomist as echt Tractarian objects. They are not epistemic primitives, but are instead - or so we are told - composites of primitives. Even though objects in Tractatus fall into a range of metaphysical categories, epistemologically they come as one. They are all Russellian objects of acquaintance. Objects which are particulars are sensory particulars; their esse is really percipi. Objects which are universals include directly intuited predicables - perhaps not blueness or triangularity, but something along those lines. Russell was willing to count logical con-


stants among the objects and to allow us an. acquaintance with such things as truth-functional negation. Via the avenue of acquaintance, the atomist can arrive at a story about how we first come to a knowledge of the basic semantic items, a knowledge from which all other semantic knowledge is constructed.

Finally, there is the formal, the parasitism between logical atomism and symbolic logic. Logic puts down the theoretical routes along which atomistic explanations flow from ontological explanans to linguistic explananda. Also, logic is an instrument of discovery, the eye in which the inner shape of language is reflected. The attribution to Wittgenstein of logical atomism is ringed with formal techniques and logical theories. Most prominent in the Hintikkas' exposition is Tarski's theory of truth, formal semantics for a language with regimented syntax, one specified by rules linking denotation to truth such as

(cpAI/!) is true if and only if both cp and I/! are true.

The Hintikkas asserted not only that Wittgenstein would have approved the details of denotational semantics but also that the picture "theory" of Tractatus was nothing less than a lyrical rendering of what would come out more prosaically from Tarski's pen. 4 Prevalent also is the notion that Wittgenstein took over Russell's analysis of belief contexts as sketched in The Problems of Philosophy. Analysis is viewed as primary means to logical discovery, playing for semantics the role the telescope plays for astronomy. Through it, we see a need for objects, or so it is said. Lastly, Wittgenstein is portrayed not as in revolt against the logical precedents set by Bolzano, Frege and Russell, not as rejecting the unholy union of logic, metaphysics and a foundational mathematics represented by Russell's theory of propositional functions and Frege's hierarchy of concepts, but as the good steward in Frege's vineyard. The Hintikkas wrote:

Wittgenstein is in many respects an integral part of th[e] Fregean tradition, to the extent that his overall philosophy in the Tractatus could almost be described as the metaphysics that naturally accompanies the Fregean conception of logical language. (Hintikka & Hintikka 1986, p. 88)

The section to follow marks the beginning of a critique of the four aspects of atomism and the start of a lengthy demonstration that Wittgenstein held none of the views ascribed to him there. When that is said, there will be occasion to review some few of the remarks of Tractatus


which seem to offer solace to atomism and to confront the semantical aspect of atomism with Wittgenstein's Tractarian anti-semantics. Complete investigation of Wittgenstein's ideas on the internal relations between language and its readings and his logical insights, ones which surround his concept of das eigentliche Zeichen, the real sign, will have to wait for another time. The next section contains a summary statement of the view on language actually contained in Wittgenstein's first writings; I labor under no illusion that it is adequately documented here. I do not doubt, however, that this can be done.

3. THE WHOLE OF LOGICAL WHOLISM

3.1. Four Broken Parts

In Tractatus, there is no semantics of the form which Frege and Russell envisioned; the sense of a sentence is not something thought out by us from principles of sense which a philosopher can discover. Meaning has no philosophical doctrine for a logician to codify. Propositions, although vehicles of knowledge, are not, semantically, objects of it. As Wittgenstein would have it, we "understand the proposition without having its sense explained to us" (T 4.021). The wellsprings of language, the empirical details of its workings, the "deep water" of Wittgenstein's Notebooks, are concealed from our explanatory abilities. What philosophers mistakenly erect as a metaphysical theory which explains our grasp of language is merely a projection of conventional aspects of grammar.

In consequence, it is unimportant that language reflect a world structure rationalizing our knowledge of meaning; even less is it important that this nonexistent knowledge be built up from primitives. In Tractatus, the proprietary relation between Tatsache and Gegenstand is not one of construction but, rather, of abstraction. What makes objects, die Gegenstiinde, stand gegen is an irreversibly destructive process, one bearing a similarity to destructive analysis in Frege (cf. Dummett 1981). Hence, Tractarian objects are not starting points, but endpoints in a process of analysis and (as we shall see) of a transcendental deduction, by Wittgenstein, from the possibility of sense to a need for objects. The precise nature of the objects becomes, not merely a question of no particular import, given that objects no longer afford the ultimate explanans, but, in truth, a foolish question. Their "natures" (were this


term still apposite) are exhausted in their logical locations as analytic termini, which are positions in an essentially symbolic arrangement. Tractarian objects are neither substantial nor monadic in a classical way; they are not metaphysical characters proper to objects in themselves. Nor are there categories into which objects come already sorted. The primitivity of objects is written into the character of their symbols and is revealed in what Wittgenstein called their 'real signs'. The questions of logical atomism, of the justificatory project, need no answers. Questions remaining for logical wholism do not concern the natures of objects but the irreducible structure of the whole.

As for epistemology in Tractatus, something is indeed hidden. It is the direction, path and target of the referential arrow. As Wittgenstein lectured Russell in his letter of August 1919,

the kind of relation of the constituents of the thought and of the pictured fact is irrelevant. It would be a matter of psychology to find out. (N, p. 129)

Hence, if the referential arrow lands on sensory primitives, it is of no concern to Wittgenstein the logician. There is no pressure from the reductive force of atomism to explain our ken of atoms in terms of acquaintance or description, since there is, in Tractatus, no need to explain understanding cognitively at all. In the sequel, we find evidence that Wittgenstein rejected the epistemic plank of atomism outright.

The place of logic in Tractatus is some way off from that marked on the Hintikkas' map. For example, contemporary logicians enforce and exploit the gap between syntax and semantics; it is the joint which bends to allow interpretational variation. And variation is nowadays the principal moving part in accounts of validity: a logical scheme is said to be valid when it is true under every interpretational variation. Wittgenstein's logic would admit no such gap - not even a gap with a bridge - between syntax and semantics or, more appropriately, between real sign and Bedeutung. The first completely determines the second. Examine the following passage from Notebooks:

If a name signifies an object, then it stands thereby in a relation with it, which is wholly determined by the logical kind of the object and which signalizes that logical kind. (N, p. 70)

Recall that the logical kind of an object is fully incorporated in the character of its real sign. Meanings are not the products of casual or incidental ways of addressing language or of standing in attendance to


it. Logical validity is not the fact remaining constant across all variation in possible fact; Wittgenstein's validity is an expression of a possible view, of the prospect that language be viewed as transcendental.

To put it another way, the relevant relation between language and the world is internal (cf. T 4.014). It is contained in the symbol which is created with the sign and is revealed by what is essential to the symbol. That essentiality is, in turn, laid bare by logical investigation, the method of search for the Wittgensteinian real sign.. Passage 3.3411 is a short tutorial on this method:

One could, therefore, say: the real name is that which all symbols, which signify the object, have in common. Thus, successively, it could be shown that all kinds of composition are inessential for the name.

Like the faces in our dreams, our signs would rather hide their true significance. The logician is not, however, utterly powerless; we are able to elaborate the character of the symbols which our signs create. A Tractarian symbol is not an object and, especially, not an abstract object. It is a distillation of use, the essential core of the use of the sign or the sign taken together with its logical role. Here is what Wittgenstein said of it at 3.326: "In order to recognize a symbol by its sign we must pay attention to its meaningful use".

What counts for logic in the sign, what succeeds in signifying, is the essential in the symbol. This is available to the logician as a notational "least common denominator". It is the commonality of all symbols which serve the same purpose that encapsulates the precise logical role of the sign. "What signifies in a symbol is what is common to all the symbols that, according to the rules of logical syntax, may be substituted for it" (T 3.344). What is inessential, what is not part of the real sign, appears as that which can vary under notational change. The hunt for the real sign, then, is just a method of variation. Wittgenstein, therefore, conducted a series of syntactic experiments. Each move from notation to notation put into relief features of the signs which vary from one to the other and, hence, could be ignored. In the words of the schoolboys, notation is changed "just to see what we can get away with". The real sign is that which remains, what we cannot get away without.

If there is alternative notation which succeeds in expressing a particular notion but which does not contain notational feature X, then the adequacy of the alternative shows X to reflect no part of the real sign


for that notion. To take a trivial example, it is no fixed feature of logical notation for formal derivations that it be linear - that it be run out along the horizontal. Both Gentzen and Frege gave us two dimensional signs for derivations. Less trivially, that logical notation be separable into parts which can be repeated is essential to it; no successful notation will be constructed from a single undifferentiated black inkblot. Hence, what Wittgenstein called "articulation" is essential to sentential notation and was part of the real sign for Tatsachen.

Wittgenstein's logic was anything but acquiescence in what had gone on in logic before, what he stigmatized as "the old notation". The method of variation relies entirely upon putting old notation into question and finding alternatives for it. This points up but one inaccuracy in the Hintikkas' picture of the formal side of Tractatus. Wittgenstein rejected the proposed identification between what is today called "Tarskian semantics" and the metaphor of propositions as pictures. In Wittgenstein's works, semantical pronouncements such as "'cats' denotes cats" fail to make connections between word and world. Nothing can point from language to something outside of it; there is nothing in Tractatus which is outside language. Hence, such pronouncements can succeed only in reinforcing connections within the system of signs.5

Moreover, there is evidence that the analysis of which Wittgenstein wrote could not have been Russellian. The material cited in our final section will present some of this evidence.

3.2. The World in Tractatus

From the very first, Tractatus is a rejection of the traditional in philosophy. Since Parmenides, the study of ontology has been a study in world lists or world inventories. The world was something we comprehended by building up to it, following from below an order which we took to lie entirely in it. The first step is to run through all the sorts of things in the world. The world becomes a stockroom whose contents we debate. You say, "Perhaps there are only elementary particles" and I might reply "No, everything is pure spirit or neutral monad". This is the comfortingly familiar approach to philosophy.

In ontology, it would be wholly alien to start the other way altogether - from the world as undifferentiated whole. This would defeat our ontological expectation for world overview by world list. This is why Wittgenstein's first sentence


Die Welt ist alles was der Fall ist.

ought to shock. Neither Russell nor Frege would have taken the whole world as philosophical starting point. Frege dreamt a world intelligible through its regions. As in Caesar's Gaul, there were in Frege drei Reiche: the realm of reference, the realm of ideas and the realm of sense. As in Der Gedanke, nothing remains for a unitary world; it is no more than the sovereign union of the Reiche. Unlike Wittgenstein, there is no seman tical juristic necessary to forge the Reiche into a single domain; structure in Frege is not first in language, but first in the Reiche. Language then waits on that structure.

Kraus wrote "Der Kunstler ist ein Diener am Wort" (Kraus 1987, p. 14): the artist waits on the word. In Tractatus, the world waits upon language. World comes not by assembly or abstraction from an inventory but by taking a stance relative to (all of) language. 6 Language in Wittgenstein is the vehicle of the world. Conceived as divorced from language, Wittgenstein's world is, in itself, empty, as is a blank page waiting for someone to write. What structure it has - either transcendental or empirical - it gets in language. The structure is emergent, springing into existence as we live with new signs. The structure to which logic pertains is transcendental. It is this structure that prohibits the possibility that objects might be, as the atomists aver, of fundamental importance. This world is not come at from below via its individual things because, first, even things (here, objects) are only come at from above; they are only conceivable, even specifiable, from the wholistic perspective. Second, logic is not a matter of things at all. Particular things, even classes of them, are no concern to the logician. In Wittgenstein, logic is first philosophy and "not only from a concern with specific things must logic prescind; but it is as little permitted to occupy itself with predicates and relations" (Wittgenstein 1984, p. 195). On the same page appears: "logic cannot deal in any special groups of things".

How does the world's transcendental structure manifest itself? Wittgenstein did not write 'Die Welt ist alles' so that we could continue to think of it as a collection of all things. He wrote that the world is "alles was der Fall ist". Even a casual acquaintance with 'Fall' (translated 'case' in English, although not everywhere substitutable for it) reveals its link to certain sorts of sentential complements. Germans say "Es kann der Fall sein, dass ... " wherein 'der Fall' refers us to the intrinsic-


ally sentential content of the words to follow 'dass'. Wittgenstein is giving notice: structure comes on dressed in the form of a sentence. Second - and importantly - what is called 'der Fall' is not just any old thing that can go into a sentence. Isolated events or even the events one undergoes during the course of a day will not do as an answer to the question 'Was war der Fall?' They are related as answers to a question such as 'Was ist passiert?' - "What happened?" Appropriate answers to the former are not, then, mere co'llections of reports -one hour's output from a news agency teletype. Nor are they usually narratives, forms of rendition like the plots of suspense novels, extending in time in the same way as the matters they convey.

"Was ist der Fall?" is, rather, a confluence of influences, a pattern of considerations which the speaker assembles in order to explain or to make sense of a complex issue, say, the course of a treaty negotiation or the passage of legislation. The difference marked by 'der Fall' is one of exposition; it lies not in the sort of event told but in the style of the telling. It is an organization we set. Sometimes, we set it by convention; more often, it comes by what we naturally find intelligible. World as alles was der Fall ist is, then, world as structured not in itself but in the arrangement of the story. In this case, it is the whole story. It is, therefore, our contention that one can see the error in atomism from the very first sentence of Tractatus.

Logical investigation reveals the transcendental features of the whole story. Here, that investigation is not one of surveying individual verdicts conveyed in or by formulae of particular logical systems. It is not one of specific formal rules. It is a gauging of the potential in all signs and their symbols, the potential for the battery of signs to become a logical medium of thought. It is a search after the origin of life, of what gives life to the sign. (In a moment, we shall pursue the search, at least metaphorically. The idea of the blank page suggests a kind of creation myth for the transcendental in language.) Before the origin of life, nothing is living. The potential for language sets down absolutely no requirements on the world. There is nothing statable to which we are responsible and to which the content of our sentences must conform. There is nothing which we consciously need to do in order to fulfill such responsibility, since the abstract structure of the world is formed within language and not the other way round. Wittgenstein wrote that "[t]here is no a priori order of things" (T 5.634).

The contrast with Frege is marked. The Fregean logician must obey


the dictates of the laws of thought, records of what exists objectively and for all time in the behavior of special functions, truth functions, and in special objects, the truth values. Frege sought to explain and justify the pretensions of systems of logic by checking that they fulfill requirements for our script set down in the form of a metaphysics. In Tractatus, there is no checking of signs against the features of a semantically structured world. Wittgenstein, like Lewis Carroll, recognized the circularity inherent in any attempt at such checking;. The "metaphysics check" is itself an instance of thought and, as such, calls for logic. In the course of the check, one is supposed to deduce consequences from rules of formation or from semantical principles such as compositionality. One needs to read these rules and principles and, so, must parse them. In the semantics of Frege and Russell, I must think my way from a parsing to a comprehension of them and thinking must be done in accord with "laws of thought" .

Wittgenstein shunned rules and principles as aids to shoring up logic as he did the entire justificatory project which gives to "shoring up" a sense. Also, the world is my perspective on signs; as alles was der Fall ist, it is the whole structure of explanatory narrative. Just as I cannot escape my perspective, I cannot, in trying to explain language, escape the whole structure of explanatory narrative. We cannot, by Wittgenstein's lights, get outside of language by this route. Next, as Wittgenstein wrote, every word is a new symbol. In part, this delphic utterance means that the content of a sign is never fixed exclusively by what the Hintikkas call "a vertical linkage", that is, by the bare fact of its standing in a denotational relation to some bit of the world. The only "fixing" here runs in the opposite direction; the reader will recall that it is the logical role of the sign which fixes the tenor of any relation which strikes us as word-to-world. Every use of a sign is, thus, new because the determining factor, the logical role, consists in the play of the sign against the background afforded by the system of all signs. This is a background in flux; there is "nothing fixed there" by a denotational relation which coerces the logical role. Meaning, then, is a product of the system of signs and there can be no meaning outside that system. No claims stand apart from the system and get their meanings, once and for all, by passing judgments on it from without.

The world without language is a philosophically featureless background against which sense will be made. But, as Wittgenstein would write later (in Wittgenstein 1953, remark 304), there is "not nothing


there"; there is just nothing there for philosophers to read, nothing for them to study with an eye to the rationalization of language. In this regard, it is helpful to compare the world without language to a blank page. It is certainly not the case that the paper has no properties. I could list some which allow me to write words on it, that make it a fit foundation for content. It is semipermanent - it will not evaporate at the touch - and somewhat but not completely porous - so that the letters do not run together. The ink soaks in but not through. My letters, when I make them, must be separate on the page; the paper will not allow me to stack them, one atop another. All these are foundational for writing, but they are not part of a cognized foundation for what gets written. First, the learning of writing is not the learning of these properties of paper. Nor do I check the properties before I set out to write. Next, reference to them is requisite neither for the justification of word formation, grammar and usage nor for the justification of what is written. I cannot write the properties of paper down on the page and then deduce the technology of writing from them. Third, these are not properties I take on mentally when I write; nothing in the morphology of a word or the syntax of a sentence must be settled in my mind to correspond with features of the empty page. All this is to repeat, over and over, that paper is just the start or field of potential for writing; it is not writing itself. And, as the reader will recall from grammar school, the only standard against which to check one's penmanship is writing itself. Staring at the paper will not help.

In ordinary light, the world, as the paper, seems bright, but, before the philosophial ultraviolet of justification, it is the dark water beneath the film of words. The nature of world, as with paper, is not that of a metaphysical medium clear to the philosopher's eye. The writing paper is not something which I read. Rather, I rely silently upon its properties in all that I write. Paper's properties will only shore up my writing in the physical sense, not in the semantical. Also, the subsistence of those properties is revealed in the success of the writing. As with Wittgenstein, signs are themselves silent on the subject of the transcendental features of the world. The latter makes thought possible and is revealed in the most economical means for expression.

As it happens, this address to paper as a logical medium is just the sort of address to which Wittgenstein returned in his Last Writings (Wittgenstein 1982) and in Philosophical Investigations, Part II (Wittgenstein 1953). On page 120 of the former appears the following:


Do I want to say something like 'the certainty of mathematics rests upon the reliability of ink and paper?' No. (That would be a vicious circle.) ... It is completely clear that one could not calculate with certain sorts of ink and paper, if they were, for instance, under the sway of certain queer changes, however, that they do alter themselves can only be determined through memory and the comparison with other means of calculation. And these cannot, indeed, be tested by comparison against something else.

The world is a logical medium as paper is a medium for writing. As such, media set limits. They are not limits which might, in the course of the medium mediating, actually be broken, however. We need no guarantee that what we put on the page with a pen will not abuse the paper itself, perhaps cause it to vanish or turn into a pool of water. The paper is a frame around my written message but I do not shatter the status of the frame by writing clear off the paper and onto the tabletop. Should I do so, paper plus tabletop provide the frame; we might say that, like time, the notional page expands to fill the needs of the project. Should I choose to "write vertically" and, instead of spacing my letters across the sheet, try to trace one letter's outline right atop another, I shall not have violated the limits so much as ceased to write at all.

In several respects, paper resembles other media, the physical space exploited by the sculptor, for instance. The sculptor need not check that the laws of geometry are still valid before taking a first swing at the chisel. Nor need the sculptor be concerned that the final product will violate those laws. Speculations of string theorists aside, a sculpture cannot require nineteen independent dimensions for its execution. The logical world of Wittgenstein is also a medium and, as such, its being in place (and our being placed relative to it) are all that is important. It does not call for questioning. It sets inviolable limits, even though they go without saying. However, they do not, as Wittgenstein would have it, go without showing.

These analogies also have limits, ones that do call for questioning. The world features Wittgenstein called 'transcendental' are, unlike the permeability of paper, not material properties or any sort of Fregean concepts. Nor are they to be housed within a special realm of being, a Fregean Reich, a nebulous land of items waiting for us to speak and to write them. Also, we do not conceive the permeability of paper as inherent in writing or in the prospect of it but as existing in the paper. By contrast, it is only their standing relative to the prospect of thought that makes the world's features transcendent; they do not exist apart


from their manifestations in signs. In the latter respect are Wittgenstein's transcendental features immanent; they must appear in the concrete lives of signs just as committees inhere in their members, symphonies in their scores and sizes in shoes. Wittgenstein would, in general, allow no abstracta which are not immanent. Even the Wittgensteinian numbers (and by that we mean numbers and not numerals) are indices of linguistic operations and those, in turn, are inherent in the concrete prospect that signs be repeated. Numbers - and all that is transcendental - exist only in the prospects of the system of signs.

Systematicity is itself transcendental. There is no writing which is nothing but a single sign; to extend the metaphor, a single dot on a single page made by one person on a single occasion is not writing. We make do with nothing less than a realm of signs, the geography of which is not exhausted in any list of individual signs. It is only exhausted by drawing a map of the signs which displays their relative logical locations. In general relativity, matter becomes a modulation in spacetime. In the hands of Wittgenstein, signs are vortices or modulations in logical space, inseparable from their relations with one another. Logical space, the background of the map on which those relations are displayed, is a field of comparison. As will be detailed anon, the determinacy of these relations require that signs create symbols of quite determinate articulation. These articulations resolve themselves into a need for objects. This chapter in the creation myth, "How there came to be objects", waits on my later explanation of how logic can "take care of itself". There I tell how the features of world without language become a world whose only features are language. The storyline now bends to follow the fault lines dividing atomism from wholism.

Need I now say that the wholist sees Wittgenstein as a linguistic idealist, as someone wanting what we call the world to be in language? Wittgenstein's logical world is neither the empirical world, nor the metaphysical world, nor the everyday world. In abstraction from everything linguistic, it is without form and void. As signs are formed, as the hand begins to write, the structure it gains is written as an epiphenomenon of signs. This structure Wittgenstein also calls Gerust, scaffolding. Everything that comprises physical world and everyday world must fit within it. (In the case of paper, one might consider the spaces between words and that around the perimeter of the message as essential scaffolding or support for the writing.) It only emerges as a feature of the signs; scaffolding only arises together with the building


and in the process of its creation. It is something we construct. Wittgenstein wrote at passage T 4.023 that a

proposition constructs a world with the help of a logical scaffolding and this is why one can see, on the proposition, how everything logical stands, if the proposition is true.

(For future reference, note that, although Wittgenstein speaks here of a kind of construction, it is not construction out of given materials. Konstruieren, the word used for "construction:', applies, in everyday German, to abstract geometrical construction and not to physical construction or literal "building up". Words for that would be 'bauen' or 'aufbauen'.) To steal a metaphor from Dummett (1976), the world's structure comes into existence as we begin to probe linguistically. Structure only becomes visible by reflection, as it were, against the symbolic aspect of the world. This is part of what Wittgenstein sought to convey by describing objects, facts and propositions as formal concepts at and following T 4.126.

Be warned, though. To imbibe this sort of tipple is not to drink the cup of idealism to the dregs. Wittgenstein is not committed to maintaining that, since Geriist is coeval with language, there were, for instance, no real dinosaurs before there were humans to speak. This confused commitment results from collapsing two distinct attitudes or ways of addressing language, the empirical and the transcendental. As empirical objects, objects of the languages of science and the languages of sensation, there were real dinosaurs and there are actual languages. The latter are attenuated entities, but no more so than Roman law or Greek democracy; scholars trace their roots and chart their spread. Dinosaurs and languages can be dated and traced. They are located upon a temporal continuum; time is, in Wittgenstein, a feature of the real signs of empirical language. Qua empirical, dinosaurs certainly antedate language. Qua transcendental, as objects (or complexes) in the Tractarian sense, dinosaurs and languages are not so much timeless as untimed. It is only relative to language as the medium of thought that we make sense of dinosaurs or of languages such as Urdu as objects at all, as subjects of predication, as substantial and not hallucinatory, as timed or timeless, as admitting of identity or difference. It is only with an eye to logical relations between dinosaurs and the system of signs, an eye to the transcendental peephole, that we conceive a dinosaur in this way. In this sense - that dinosaur as object is not conceivable apart from the medium - are they all coeval: individual languages,


dinosaurs and the medium of language. As Tractarian objects, languages and dinosaurs share a birthday.7

This is the principal error of atomism: that the world is ordered in itself and the sign must obey its order; this is its diagnosis: that the atomists ignore the transcendental, the respect in which there is a world of logic, a world which is servant of the sign. There are three more errors and three diagnoses in the short Sections 3.3, 3.4 and 3.5 to follow. The first is the error of asking after the metaphysical natures of objects, the second of adopting for Wittgenstein the goal of analytical philosophy - of retelling the genesis of comprehension - and the third of seeing a retelling in a theory of truth or in a logical grammar.

3.3. The Nature of Objects: Working Within the System

In language, as in the world, we start from the whole. What impresses immediately about a calculus such as Frege's is its interconnectedness; it is only by working within the whole system that we express content and trace inferential paths. Signs do not come singly but arrive tightly interlocked; without the connections, they lose their powers. There is a thicket of signs but one can still pick out from it logical traces. There is repetition in the system and, according to Wittgenstein, we select out logical relations by focusing on constancies and variations in those repetitions. Two sorts of constancies are Tatsachen and Gegenstande; they stand out as lulls among changes. For instance, the object we think of as a is better symbolized as

~la~2'

a pattern we can discern around a and repeated in Fa and in Rab. An object is the condensation of this kind of pattern. One might say that, from propositions, we abstract their simpler elements. This is hardly a process of building up. After all, we started from the very top level, that of the system. It is better described as a process of breaking down. Confirmation for this suggestion is at T 1.2: "The world decomposes into facts". (Later on, this passage becomes a matter of great concern.)

The idea of destructive analysis in Wittgenstein had its precursor in the purely decompositional analysis Frege created for Begriffsschrift. The parts, pieces or patterns which come to light by this analysis Frege thought to carry no claim to independent existence; they cannot be prized away from the decomposition process. In other words, the parts


into which a proposition decomposes are functional parts; they derive their modus vivendi from service to the analytical whole. By means of decompositional analysis, Frege separated function and argument out from what he then called 'judgment'. This was his preferred route to a correct assessment of a judgment's contribution to the validity (or invalidity) of an argument. When measured in terms of progress in linguistic knowledge, the analysis was unidirectional: it is always "top down". In the unpublished Boole's Logical Calculus, Ftege wrote apropos destructive analysis:

As opposed to this, I start out from judgements and their contents, and not from concepts. I only allow the formation of concepts to proceed from judgements .... The content of possible judgement is thus split into a constant and a variable part .... And so instead of putting a judgement together out of an individual as subject and an already previously formed concept as predicate, we do the opposite and arrive at a concept splitting up the content of possible judgement. (Frege 1979, pp. 16-17).

The products are wholly dependent upon entire judgments for their existence and intelligibility. In Begriffsschift, Frege viewed functions and arguments as artifacts of logical analysis, as generalized parts of linguistic expressions which correspond to no extralinguistic reality and which exist solely to serve analytical purposes. On this subject, Frege wrote:

This distinction (between function and argument) has nothing to do with conceptual content; it concerns only our way of looking at it. (Frege 1977, p. 12).

In Tractatus, Bedeutungen of signs - facts and objects - are individuated functionally. To a certain extent, it is not wrong to think of Wittgenstein's logical world on the model of the social studies' description of a corporation. The corporation is first introduced as an indissoluble whole, the functional means for the creation of wealth and the provision of goods and services. No understanding of the corporation comes via a separate grasp of each of its parts, as if the parts were to be assembled like a jigsaw puzzle. As with Wittgenstein's world, the corporation is "articulated" - it is naturally organized into parts but it is not constructed out of its elements. Presidents, vice-presidents, board chairmen and marketing managers are distinguished, but not by their heights or races. They are presented in term of their respective offices. To describe the "typical corporation president" is just to describe that office. The offices are distinguished by reference to their varied services to the corporation. In the same way, facts are logical offices and are


distinguished from each other and from objects or complexes by their logical services and not via their constituents. A Tractarian object is a Tractarian object in virtue of its functional role as the Bedeutung of a name. One could say that an object is nothing more than a role.

The metaphor of corporation bears certain dialectical benefits. To the extent that the realm of facts and objects really is like a corporation, I am absolved of facing metaphysical questions about the true nature of objects, questions that bear down so hard onlthe atomist. Corporate executives do not comprise a natural kind nor do they constitute a separate blood group. We do not ask after their intrinsic natures or their individual subatomic makeups. We do not ask "What colors are they?" or "How do they interact with the other political parties, namely, Republicans and Democrats?" To ask such questions about corporate executives is to confound functional with natural or other nonfunctional comparisons. In the same way, to ask certain metaphysical questions about objects is to confound transcendental features of language with material or medieval comparisons. Objects do not comprise a natural or perceptual kind nor do they constitute a traditional metaphysical group. This is because objects too are functional, more like doorstops and executives than tigers. There is no more call to answer the questions "What colors are Tractarian objects?" or "Are they particulars like Terry or universals like 'being a pirate'?" or "What are they in themselves?" than one has to answer the same questions about executives. The only sure reply to the question "What is an executive really?" is in terms of the corporate organization. In this way is "executive" a "formal concept" in the world of economics, just as "o'clock" is a "formal concept" in the world of telling time. The only guaranteed reply to the question "What is a Tractarian object really?" is in terms of transcendental organization. In this way is "object" a formal concept in the world of Tractatus.

3.4. Understanding as Standing

In Frege and Russell, understanding is epistemic contact and cognitive control, just the talents and materials required to build up an accurate representation in mind: one must grab hold of basic semantic materials and marshal them. Wittgenstein will have none of this. In his sight, understanding is much more like standing. In standing, one takes a


position or adopts a perspective within an objective setting. The operative setting is what I choose to call "the mechanism of language". It is a mechanism over which we exert little control, especially of an intellectual sort. As mechanism, language is an automaton; like the vast subterranean machines of Lang's Metropolis, a major part of its working is in operating us. The language mechanism is infinite - boundless and all-embracing. It is complic~ted beyond intelligibility. We are linked to it and in it but we have no real notion of the details 'of its workings. Certainly, we do not work it by grasping it or by lodging its governing principles in our minds.

Mankind possesses the ability to build languages with which to give expression to any sense, without having any notion how and what each word signifies. - Just as one also speaks, without knowing how individual sounds are brought about. Colloquial language is a part of the human organism and is no less complicated. (T 4.002)

The notion that language works with us, rather than the other way around, appears at 6.124:

in logic it is not that we express, by means of signs, what we wish, but rather in logic it is the nature of the naturally necessary signs which itself speaks out.

Wittgenstein's language is truly a mirror; it reflects but is not transparent.

To grasp Wittgenstein's approach to understanding, it helps to set understanding language off sharply from understanding a code, a language-surrogate whose mere existence is parasitic upon that of language. A code is certainly a system of representation which we construct and over which we hold complete cognitive sway. Codes we master by internalizing the rules and principles of their representation. Code is transparent because, by thinking, we determine everything that is relevant to the job of a code. But language in Tractatus is unlike code: it waits on nothing for its meaning, we hold no cognitive sway over it and its working is largely opaque to us.

If analogy is required, language is, in this respect, more like music or like a monetary system. We create music by setting down notes; this is one way in which we respond to the influence music has over us. As parents of teenagers know, there is little chance of establishing control over that power. Humans make music( al notes); they do not make music's power. Nor have they any real understanding of the means by which music takes effect. Language is also akin to a monetary system. Monetary units are not codes or replacements for goods. 'One dollar'


is not, for instance, a code word for "two loaves of bread". The workings of the monetary system are little understood (at least by the vast majority of us). What understanding we have is not from studying its inner arrangements or underlying principles. As with language, we learn to live within it. We merely grow accustomed to doing our business with slips of colored paper; we do not have to fit an entire system, somehow, into our heads. The system itself is transformed and renewed every day through monetary transactions but few individuals exercise any measure of control over it. To a frightening degree, it controls us. To that degree is it similar to language.

3.5. Through the Great Looking Glass

It was for Wittgenstein crucial that we stand in no need of a mastery of language that comes from semantic knowledge; we do not need to pick up what "comes naturally". As he was to ask in Last Writings, "What do you need to know to find a smell repulsive?" (Wittgenstein 1982). We should not, as Frege did, conceive of Sinne as objects of knowledge rather than, merely, as vehicles of it. There is, therefore, no knowledge of meaning or of language which is a subject of a philosophical inquiry that ends in principles we know in virtue of a mastery of language. How, then, are we to treat the sayings which semanticists present as expressive of such mastery, putative rules of denotation such as

"'cats' denotes cats"?

What would be a suitably Wittgensteinian reaction to a pretended semantic pronouncement? Consider the claim to have discovered that

Names denote both particulars and univerals.

No longer is it to be counted as a candidate for universal truth about language. Nor is it to be construed as commentary on the real semantic structure of an elementary proposition. These have no significant logical syntax but are mere combinations of names. As a specifically philosophical pronouncement, Wittgenstein would have thought it an expression


of a linguistic fantasy which is parochial - which is only at home among incidental features of language. It is viewed as a failed attempt to see an inessential feature of English, that its sentences divide into subject and predicate, as an essential aspect of the world. Wittgenstein tells us that language is a mirror, a looking glass; when we look into it, what we see in it can be nothing more than our own faces in reverse. The distinction between particulars and universals is made with respect to the idiosyncracies of the locatives and temporal particles of English, parts of the inessential and not, according to Wittgenstein, of the real sign. (Or, if they turn out to be parts of a real sign, this is not now known to be so, and, hence, is not now within the province of logic. I do not believe that Wittgenstein ever shared with Frege the presumption that the real sign might be presented once and for all time to come. Logic, in Wittgenstein, is a course in perennial linguistic investigation.) It would seem that a knowledge of the features that make for the division into particulars and universals is no more tightly bound to a knowledge of meaning than is knowing American paper money is green central to knowing the bases of monetary exchange. To put it another way, the arrow of denotation in Wittgenstein always points back at us and at our language.

What of the other trappings of denotational semantics and conventional philosophical logic: unsaturatedness, arity or logical typing? As they are usually addressed - as elements in the conditions which the world sets down for meaningfulness - they fail. At best, they are reflections on the character of the signs, either essential or incidental. There is also no place in the world for indeterminacy, vagueness and generality. At T 5.1311, you see

That one can conclude from (x).fx to fa shows that generality is present in the symbol (x).fx.

There is nothing in the world of Gegenstande and Tatsachen that corresponds to these. As we shall see, that world has, as its raison d'€tre, complete determinacy and complete specificity; in fact, it is merely the objective guarantee of the determinacy of sense. It is correct to hold that Wittgenstein's world resolves itself into a juxtaposition of objects and, as such, the need for vagueness, generality, propositional functions and classes must be referred back to ourselves and to our signs.


4. WHY THERE IS NO TRACTARIAN SEMANTICS OR WHY LOGIC

MUST TAKE CARE OF ITSELF

There is no Tractarian semantics. There is no doctrine in Tractatus of the actual mechanisms by which our signs are interconnected. Wittgenstein thought the mechanisms to be hidden from us. In our dream life we shall not find a scientific account of the true relations between dream images and the neuronal firings which, I presumably, give rise to those images. So Wittgenstein took the incidental details of the Umgangssprache, like dream images, to offer no sure guide to the workings of language. Philosophers' efforts to come at those workings through the dream images of metaphysics was counted by him a failure. To carry the analogy with the dream further, Wittgenstein's efforts in logic are not directed toward those inner workings; his writings are not prolegomena to a science of language or a science of dreams. They take their start from expressions such as 'dream world', the very prospect that there might be such a thing as a world of dreams, as there is a world of logic. And also from the fact that, in logic as in dreaming, certain types of errors do not arise. We do not make mistakes in reporting our dreams. One might say that "dreams take care of themselves" .

Therefore, the semantical aspect of logical atomism, the nub of the attribution of atomism to Wittgenstein, is false and the whole of atomism, as an interpretation, is falsified with it. Still, matters of delicacy remain; there are things to be explained and to be debated. For example, the epistemological part of the Hintikkas' description of Tractatus is plainly and simply false; it stands in direct contradiction to the text. It is just false to say that Wittgenstein's Tractarian names were intended to denote Russellian objects of acquaintance. By contrast, it is not just false to say that, in Wittgenstein's "fully analyzed propositions", names will denote items of different logical types, among them properties and relations. Wittgenstein allowed that there were readings of 'names denote properties and relations, too' under which it makes a sensible claim. One of these will be as a none-too-useful grammatical commentary, something of the same order as "nouns and verbs are different parts of speech". However, these are not readings pleasing to the semanticist or ontologist. With 'names denote properties and relations', the ontologist wants (Wittgenstein) to say: "despite what you may have heard from formalistic and nominalistic philosophers, Plato was right in thinking that there are special classes of semantical entities such as properties and that the expressions of our language denote them and


that is how the relevant parts of the language function". Those who see Wittgenstein as an atomist want Tractatus to include this ontological proposal.

When the ontologist speaks of properties and their roles, he is drawing a caption on a picture, the icon of the grammatical world. In the picture is a pre structured world, standing ready across the intentional gap from language. It is made up of a realm of items with which words can collaborate and, so, get their semantic powers. Through collaborations here and there, individual words or names get their meanings and, thereby, semantic licenses are issued. Some strings of words receive legitimacy while the world forces us to treat others as illegitimate. In the grammatical picture, all this collaborating and licensing must go on before logic, since logic presupposes that our names name and our sentences have meanings. Metaphysics (such as Russell's doctrine of types) is prologue to logic.

Accordingly, the logician is thought to wait on the grammatical world to serve up judgment on language. First, there must be an ontology check. We can, in fact, see Frege carrying out such a check for the logic of his Grundgesetze. The three sections 29, 30 and 31 together comprise what we might call the "proof of a metatheorem", in this case, that announced in the title of Section 32: every proposition of Begriffsschrift expresses a thought. Proof is by structural induction. Since Sinn is the mode of presentation of a denotation, Frege starts with a proof that every name in his concept writing has a unique denotation. Frege has already divided the class of names up into simple and complex names, the latter formed by applying various means of combination on the former. He checks for unique denotation in the case of each of the simple names. Then, in Section 31, he demonstrates that the property of bearing unique denotation is preserved through legitimate combination. It follows from this that every name has a unique denotation and, given Frege's understanding of Sinn, that an unambiguous sense has been assigned to each properly formed expression of the system. Clearly, Frege thought these considerations to constitute a quasi-mathematical foundation to the later creation of the logical edifice. He conceived this as a necessary metaphysical check and only begins to derive logical laws in earnest after the material on definitions (of which Sections 29 through 32 form a crucial part) is complete. Frege's definitions and the metalogical strictures on them are conceived so as to forge the connections between word and structured world. From these, thought Frege, his logic derived its legitimation.


In Tractatus, logic is not metaphysically legitimated; the play of logic needs no prologue. As Wittgenstein wrote in the first entry of Notebooks and, in very much the same context, at T 5.473,

Logic must take care of itself. (N, p. 2)

Just as Notebooks begins from this point, one can start here and follow Wittgenstein's course to the anti-semantical conclusion that there are no seman tical principles which shore up laws of logic. If we care to speak of 'legitimation', this is completely reverse. At the bottom, the world is a semiotic realm and gets its legitimation from the sign. The world of Tractatus is just a perspective on the sign, a particular way of seeing otherwise mute items, alphabet letters, footprints or musical notations as signs. In this case, the perspective is not merely an inner or mental orientation. The word 'perspective', like its cousins 'point of view' and 'position' (in German, 'Einstellung') embraces in its sense a fruitful duality. A perspective involves both conditions we contribute of our own individual accord and enabling conditions which are there regardless of what we do. For example, my perspective on a scene may be that of a view from a high hill. I have that perspective because I walked up there. I also have it because the hill is itself high. Or a local official could take the perspective of the village mayor. He can adopt this outlook because he ran for office and won and, also, because the village is governed so that there is such an office as mayor. This is a prefiguring of the duality which Wittgenstein clearly exploits, that between transcendental and empirical attitudes toward language. It is the unpacking of this duality of perspective that results in the words of Tractatus. What follows here is a truncated wholistic rereading of the first six sections of the book, presenting its main conclusions as those of a transcendental deduction.

Transcendental conditions in Tractatus are those which need be in place if a mark is to be a sign in any language whatsoever. Those other conditions which actually obtain when the mark is a sign of some particular language(s) comprise the empirical. For instance, for a mark to be a sign in any language whatsoever, it must be comparable differentially with other signs; we must be able to trace lines of similarity between it and the others of the system. Signs cannot be lonely but must form a determinate system. As with Saussure, so with Wittgenstein: the individual item is sign insofar as it is one cog in a formal or differential mechanism, a working together of signs.


For the sake of comparison, each sign need be composite (in a quite specific fashion) or, as Wittgenstein wrote, it must be "articuliert". At T 5.5261, we are told that comparison is the real sign for articulation.

Characteristic sign of composite symbols: it has something in common with other symbols.

Such articulation, a prospect for comparison, yields immediately division into function and argument. Because, if I compare two signs, I select points of similarity around which there can be planes of variation. Or, to use a metaphor appropriate to Wittgenstein (who took details of the vector calculus to be especially revelatory of transcendental signific conditions), if I compare signs, I must select axes of similarity, dimensions along which features of the signs can vary in an assessible fashion. To do so is to separate the sign up into function and argument; each of which is a field of variation around a point of constancy; they are both Form and Inhalt or content. Recall that the expression glag2 may be more real as a sign for an object than a; in the former, decomposition into form and content is plain. There are many different ways in which the sign can decompose into function and argument; none is prima inter pares. There is no more preeminent division than there is, to extend the vectorial metaphor, a special scale on the x axis which is demanded by the structure of space itself.

The ultimate role of Hauptsatz 6 in Tractatus, the claim that

The general form of truth function is [p, g, N(t)]. This is the general form of a proposition.

is to yield, in concise form, the delicate balance between precision and generality required for the prospect of logic, in other words, the signific conditions which comparison among signs will - of their own accord -satisfy. When Wittgenstein wrote of naturnotwendige Zeichen, the naturally necessary sign, the "nature" at issue is in full display in the Wittgensteinian variable-expression,

[p,t,N(O]·

The fields of the expression indicate, by exemplification, the sorts of articulation required for the transcendental aspect of the signific perspective. First, starting at the right, there is logical articulation; that is the particular office of the Sheffer-like logical sign N. As Wittgenstein explained, the N acts, in the real sign for a proposition, as punctuation mark. Here, it reminds us that signs are punctuated so as to admit


arbitrary truth-functional comparisons with the other signs of the system. Second, t is a propositional variable and, hence, a sign of generality. In Tractatus, a sign of generality is a specification of a range of propositions by means of the similarity conveyed by the form of the variable itself.

As Wittgenstein liked to remind us, sense must be determinate. This will assure, first, that the comparisons by similarity and difference which make for the form of a proposition must be wholly unambiguous. One way to guarantee this is that each proposition admit of unique readability; it must be uniquely parsable in terms of a single recursive mode of combination. As far as truth-functional logic is concerned, each proposition must come uniquely punctuated in terms of N. But, this is insufficient guarantee of the determinacy of sense; famously, two distinct propositions may have identical truth-functional forms. Truthfunctional punctuation cannot, then, exhaust the sense of a proposition. What remains of its sense is the contribution of Elementarsiitze, propositions which admit only of a trivial or normalized parsing in terms of N. Sense is determinate provided that, further, each proposition be resolved into a unique selection among elementary propositions. To say that these comparisons are required for the determinacy of propositional sense is to say that there must be Tatsachen, facts. 8

Of course, the determinacy of sense or of reading, the unambiguousness of the comparison, must extend to elementary propositions as well. Such determinacy would be insured if elementary propositions were, in a sense, digitally rather than analogically individuated. This will be the case if, first, there is a specific, delimited array of axes or avenues of comparison among them. Further, each elementary proposition has a unique resolution in terms of a specific number of such axes and a single point or vector determined by units measured along the axes. So, I am thinking of the comparisons between elementary propositions accomplished by viewing each as a vector in a vector space over a field which is not continuous (such as the real numbers) but discrete, such as the naturals. Then, a pair of elementary propositions can be compared by lining them up along the relevant axes and juxtaposing vectorial magnitudes, their modes of combination, if you will.

The suggestion implicit in the terminology of 'resolution', 'axes' and 'combination' is not accidental; Wittgenstein took quite seriously the proposal that the real sign of an elementary proposition is a vector, an element of a vector space. The image of the real sign as a vector


pervades his early writings. The following quotation from Notebooks (pp. 20-21), shows that the vector idea was not mere metaphor for Wittgenstein.

The internal relation between the proposition and its Bedeutung, the way of signifyingis the system of coordinates that pictures the state-of-things in the proposition. The proposition corresponds to the basis coordinates. One could consider two coordinates ab

and bp as a proposition which asserts that the material point P fipds itself at the place (ab).

When, in solving a physical problem, I apply the vector calculus, I "coordinatize" the given space, the space of the problem, by comparing it, as a sign, with an abstract vector space (usually R3 ) and with the latter's coordinate axes. This form of comparison takes place by selecting, in the space of the problem, what might be called "instantiations" of the abstract coordinate axes of the vector space. I "locate" coordinate axes in the space of the problem. Now, I am ready to apply features or results of the abstract space and the calculus inherent in it to the presented problem space. The instantiations or locations of axes are Wittgenstein's Bedeutungen, the objects of Tractatus. The digitalized axes along which elementary situations are compared are Tractarian objects. The ambient space coordinatized by the array of objects is logical space. The magnitude of a vector within that space reflects the precise way in which a proposition or situation, a vector, is to be resolved into its objects; this is its pictorial form.

There are at least two things to note about this retelling of the genesis of objects. First, the object is not some new kind of thing, something for which we were not prepared by the name in its logical setting. After all, the application of the vector calculus, the fact that we might apply it, was not a happy discovery of Descartes or of Newton; application and calculus evolved as one. The coordinatization of the problem space does not occur when I draw some malleable or incidental connection between a name and a particular thing, recognized independently of the name. I am, instead, confirming what Wittgenstein would call an "internal" relation between two signs or, equivalently, I am reading the space of the problem as an instantiation of a vector space. In other words, I am turning it into a vector sign (or space of such signs) itself.

Second, the comparison between coordinate axes and names casts light, from a new direction, on the metaphysical aspect of atomism. It would be indicative of a failure of comprehension on the part of the


student of vector geometry to ask, after the first lesson, "Well, what is an axis really? Could our rockets run aground on them as they travel through outer space?" or "Do axes have colors?" Perhaps all the instructor could do in reply is to repeat her presentation of the vector space concept; a coordinate axis has no more to its nature than its place as a gear in the mathematical mechanism of vector calculus. To ask after the true nature of Tractarian objects or to ask whether they are particulars or universals is to ask questions of a 'similar kind. Objects are exhausted by their logical roles.

Transcendental conditions establish the possibility of comparisons. Empirically, in the case of any particular human language, actual comparisons will be in force. These will determine the particular class of objects of that language by setting the referential relations in which names stand to them. But that there be objects - the condition that there must be some objects or other - is transcendental. It is the demand that there be simple names such that, in virtue of their functioning as simple names, we say that Bedeutungen are associated with them. By Wittgenstein's lights, this is implicit in the very nature (again, 'naturnotwendige Zeichen') of signing. All of this comes from a reflection upon the differential comparisons that confirm the mark as the sign; the comparisons are not wholly arbitrary but give the mark a definite position within the system of signs. The sense of a proposition is determined by its position in the system, in the space of signs. The Bedeutung of a name is wholly determined by its position. Facts and objects - or sentences and names - are ways of addressing the definiteness of those positions.

There is yet more to analysis; there is the dissolution of complexes. To see the need for it, one returns to the general form of a proposition and to Hauptsatz 6. The need derives not from the appearance of Sheffer's N but from the presence of a notation for generality, t. To carry on a decomposition analysis of a complex is to expose the precise ways in which lines of similarity are drawn between the elements of propositions. As the generality notation indicates, suitable propositional signs will include variables, indices of generality. These are specifications of ranges of propositions, ways of collapsing, in a single sign such as ~, a whole panoply of signs. The general signal supplies notational economy at the price of some notational indefiniteness. Wittgenstein wrote, at 3.24,


[t]hat a propositional element indicates a complex one can see from an indeterminacy in the propositions in which enters. We know that everything is not yet determined through this proposition. (The generality sign contains a prototype.)

A sign containing generality index g, say Fg, does manifest indefiniteness. If F~ is the collapse or synopsis of this range of propositional signs:

Fa, Fb, Fe,

then, with respect to negation, Fg admits an ambiguity of scope. It is exposed by asking what the denial of Fg could involve. One can deny Fg - or put forward its negation - by denying Fa or by denying Fb or by denying Fe or by denying any positive combination of these. Hence, is the sense of the negation of F~ indefinite and indefiniteness is something Wittgenstein's world will not allow.

By having a determinate sense, each proposition fixes the world on either 'yes' or 'no' in an unambiguous fashion: determinacy of sense applies to proposition and negation equally. Wittgenstein's world is simply the transcendental rationale for the determinacy of sense. Therefore, such indeterminacy we find in F~ must be a phantasm of the sign, a shadow in the thicket and not what the thicket hides. By analysis is it shown to be mere appearance. By analysis, all indefiniteness, all generality in the sign, must be expanded out; each variable must ultimately vanish and be replaced by the range of propositions for which it is a collapse. As we shall see, this makes a marked contrast between Wittgenstein's and Russell's concepts of analysis. Russell's analysis via definite and indefinite descriptions is the logical tyranny of generality: naming is traded away for quantifiers. In Wittgenstein, things are just the opposite: analysis is the elimination of all generality. (Cf. the final section of the present paper.)

In sum, Wittgenstein's world is a perspective on the system of signs. The exegetical world of the present writing is a perspective on the signs of Tractatus. From this perspective, the first part of Tractatus reappears as a transcendental deduction. It takes its start from the observation that we calculate successfully with signs - and with signs alone - using the techniques of propositional logic. It has as its goal a satisfying answer to the question "What makes pure logic and mathematics possible?" That which is deduced is Wittgenstein's Hauptsatz 6 and what comes from its unpacking: the system of signs falling apart into truth


functions, elementary propositions, functions, arguments and names. Objects and facts are, then, fields of logical similarity between propositions and between names, respectively.

To say that the world falls apart into facts and facts into objects is not, belatedly and reluctantly, to give credence to the Hintikkas' logical atomism. To emphasize Zerfall, either in the form of the logical fallingapart of sign into function and argument or in the form of decompositional analysis, is not to embrace the bottom-up cognitive process of semantic composition. The sense of a proposition is not a cognitive value which I win in a game of semantic calculation. That game has no rules here; there are no principles of semantic composition which legitimize the sign and guarantee for it a sense. I do not build Wittgenstein's world of meaning out of a mindedness of atoms. Just as the role of the executive in the corporation is not a mere composite of individual tasks but a systematic array of them, so also the role of the propositional sign in a system of signs is not a mere composite of individual, atomic roles, each of which independent of the others.

I freely admit that there are simple objects or Tractarian atoms. But I insist that there is no more to them than their functional role, a role which we abbreviate by speaking of them as the Bedeutungen of simple names. Atoms are functional units, such as the electromotive force and the resistance in an electric circuit. Analysis of circuity is conducted by a division - into force and resistance; the points of division are determined only by the limits set by laws such as Ohm's. Atoms are not independent substances. They serve the purposes of the means by which they are seen, the need for precision in the logical comparisons of signs. For these reasons, Wittgenstein's logic must be "top down" and not "bottom up". Logic cannot begin, as in the icon of atomism, by the examination of the logical atoms. Put another way, speaking or reading cannot begin with naming. In this regard, one should compare T 5.526: "One can describe the world completely through entirely generalized propositions, that means, therefore, without correlating, from the beginning, any name with a definite object".

Logical properties do not "flow upward" through language from the properties of the elements of the putative foundation. Language and its logic do not stand against the world, mirroring it by copying its grammatical structure atom by atom. This is just another way of painting the picture of the certification of language by ontology, a picture which must be rejected if we are to start reading Tractatus properly.


As Wittgenstein wrote at 5.634, "there is no a priori order of things" and the intended order of atoms is an a priori order if anything is.

But what has all this to do with logic as a process of calculation and assessment? How do comparison, articulation and Zerfall prepare for its success, for the fact that we can succeed? First, there must be articulation in logic; it is essential to representing the validity of modus ponens (and invalidity of asserting the consequent) that signs are repeated and their locations compared. We look to displays such as

P~Q

P Therefore, Q.

Second, logic goes on without further ado. We do not check the logic as Frege did; we do not try to stare outside the penumbra of light cast by the signs to see that, once we have set down the symbols of the calculus and their relations to each other, once we have indicated how the logical tool is to be put to work, we can apply it. We can then judge, with perfect accuracy, of the validity of contentual inferences in everyday discourse. We use the signs just as they are to give logical "proofs". Of this feature of the logical tool, Wittgenstein said:

And we do this when we "prove" a logical proposition. For, without bothering ourselves a whit over sense or Bedeutung, we form abstractly rbi/den] the logical proposition from others according to mere rules for signs. (T, 6.126)

This is a kind of aprioricity for logic. The question remains "What makes this property of logic possible?" A Wittgensteinian answer is that the signs of logic need no special license, once they are constituted as signs. That means: once they are incorporated into the perspective on which they are viewed as signs. By the attainment of such perspective (with its dual aspect), certain conditions are au\omatically imposed -without further ado. For logic, these are the transcendental conditions for what I called "the mechanism of language", not a pseudolanguage or scheme of representation living in our minds but a language setting in which we live. From the aprioricity of logic (and the transcendental deduction), we appreciate that the conditions are in place. Matters such as unique parsing are not conditions which the logician qua ontologist has to check before he can proceed; there is no call for him to look over his shoulder. Transcendental conditions are emergent characteristics of the signific medium; they evolve automatically as the mark becomes


sign. Here is a fragment of the Notebooks entry from 15 December 1914.

It is obvious, we can introduce whatever we want as the written sign of the ab-functions [truth functions) the real sign will form itself abstractly [bilden sieh) and automatically. And which properties will form themselves thereby?

Again, the logician need no more look over his shoulder than the sculptor has to check that the laws of spacetimy are still operative in his studio or than the mathematician needs to check that pencil and paper are still suitable media for the conveyance of mathematics.

The philosopher's icon of naming - an inexplicable triple liaison between the epistemic subject, a mute, structureless tag and some isolated item - has no role to play here. Naming is no prerequisite for concept writing. Nor is there a place for the philosopher's icon of meaning: special act of thinking or intending. Again, the page is blank; there can be no writing while the page is still empty. There can be no thought before thought can begin. The beginning of thought is coeval (v.s.) with logic. Any slack left by the banishment of philosophers' meaning and naming is fully taken up by comparative similarity. Allow me to repeat sections from T 5.526 and 5.5261.

One can describe the world completely through entirely generalized propositions, that means, therefore, without correlating, from the beginning, any name with a definite object. (5.526)

An entirely generalized proposition is, as with other propositions, composite. (This is revealed in the fact that we, in '(3x, q,). q,x', mention 'q,' and 'x' separately. Both stand independently in signifying relations to the world, as in an ungeneralized proposition.) The characteristic mark of a composite symbol: it has something in common with other symbols. (5.5261)

If there is a legitimate need for a "connection between word and world", comparative similarity is all that is required, as the possibility for fully generalized description shows.

4.1. The Ineffability of (what remains to) Semantics

Wittgenstein wrote that reality is itself determined as 'yes' or 'no' through the proposition. The ultimate locus of this determination and of the space of propositions is language transcendental, "the" language, where "the" language is neither one or another particular language nor some conjectured ideal language. It is semiotic language, language


as all-embracing scheme of presentation. As is clear from the early Notebooks, what we consider experience - Erfahrung - is already included within language. Experiential episodes are themselves read. Experience is itself a panoply of signs and, as such, becomes a facet of the language. Experience does not stand outside of language and opposed to it. A fortiori, it is not a field to which I can refer for advice on the construction of an appropriate language, as the atomists would like.'

What, in the first place, the proposition determines in reality is a truth-conditional arrangement of such 'yes's' and 'no's'. One might think of this as a tagging of states-of-things. (Or, though there is some danger of confusion, one could conceive of the arrangement as the graph of the (possibly infinitary) Boolean function defined by the logical form of the proposition.) This arrangement in logical space serves as the content of a thought in Tractatus. Wittgenstein held that the conditions under which a sign is well-formed, under which it is capable of expressing a sense, do not themselves constitute the content of a thought. They do not themselves admit of formulation which in turn admits of truth or falsehood; these are things which go unsaid. Indeed, this unsayability or ineffability (to use the Hintikkas' expression) must apply to at least some propositions if certain assumptions are imposed. First, assume that every statable condition requires there to be some proposition which determines it. Second, assume that no proposition contributes to the determination of its own well-formedness. And, lastly, assume that a determination of well-formedness is always wellfounded: there is no infinite w-chain of propositions each of which serves, if only in part, to determine the well-formedness of the preceding proposition in the chain.9 The latter two conditions will follow from the assumptions that everything going into the determination of the meaningfulness of a sign is, when properly understood, part of the symbol attached to that sign and that the process of analysis, the subdivision of the symbol which occurs naturally in the creation of sense, is well-founded. As Wittgenstein wrote at T 3.332, no propositional sign can be contained in itself and, if the process of analysis were not well-founded, the prospect of self-containment would open up. It is clear that the well-foundedness of analysis is required for the determinacy of sense.

Ineffability, the fact that those conditions which go into making a sign fit to express a sense are themselves not statable, was for Wittgenstein


characteristic of language transcendental. Everything statable is spoken within and in accord with the transcendental conditions of language, conditions which are themselves unconditioned. The transcendental perspective is a tectonic plate on which Wittgenstein's exposition is founded and which breaks through and surfaces at crucial junctures. One of these is T 2.0211. Wittgenstein here insisted that the very possibility of sense depends upon a radical independence of conditions on meaningfulness from conditions on truth. Whether one proposition has meaning cannot, he said, depend upon whether another is true. This draws a firm line across philosophical logic; Wittgenstein's investi~ gations of the sign lie on one side and semantics - both Russell's theory of types and Frege's theory of function and object - on the other. On the far side of the line, with Russell and Frege, lies the notion that meaninglessness is simply a species of falsehood, a kind of "superfalsehood" if you will. Here, it is assumed that, as the truth of a proposition certifies it as a faithful report on the factual dispositions of objects, so also the meaningfulness of a proposition certifies it as a faithful report upon their metaphysical dispositions.

To see a doctrine of meaninglessness as falsehood at work, consider a Frege-style explanation of the fact that 'Bill is tall', as ordinarily understood, expresses a sense while 'is tall Bill' does not. (I ignore, for the moment, Frege's reaction to the vagueness of predicates such as ' ... is tall'.) Of the many possible destructive analyses or "dissolutions" of 'Bill is tall' into arrays of logically significant fragments, one was of crucial import for Frege. It is the one that presents the true semantical Bausteine or building blocks of the sentence. Unquestionably, it would be the dissolution into a saturated term 'Bill' and an unsaturated expression (written in a highly un-Fregean style) ' ... is tall'. No account of our semantical ken of 'Bill is tall' could be adequate (for Frege) and exclude a description of this division and its denotational congruence to two "items", one an individual named by 'Bill' and the other an unsaturated nonindividual, a function or concept, the Bedeutung of ' ... is tall'. To expose the sense of 'Bill' is to expose the cognitive means by which it attaches to the individual Bill and, mutatis mutandis, the same applies to ' ... is tall'.

It is in terms of these extralinguistic attachments and, in particular, of the metaphysical properties of and relations among items of these sorts - whether they be saturated or unsaturated, of which level they


belong and of what number of arguments they can take - that Frege would care to offer an explanation of the capacities of signs to make sense. For instance, it is the unsaturatedness of the function signified by ' ... is tall' which will, supposedly, account for the facts that atomic sentences exhibit a logical grammar. 'Bill is tall' can express a sense while 'Bill Bill', 'is tall is tall' and 'tall is Bill' do not. 'Is tall is tall' is senseless since the unsaturatedness in ' ... is tall' is not properly completed by an unsaturated nonobject such as ' ... is taU' itself. Notice, however, that, strange as it may seem, the ability ascribed to us by this explanation requires that we be able to do something akin to reading the supposedly senseless inscription 'is tall is tall'. We must, in con-fronting 'is tall is tall', discern two occurrences of the' ... is tall' radical, associate with each the Bedeutung which is the " ... is tall" function and, then, note that the attempted congruence or fit fails, due to the logical dispositions, the unsaturatedness, of the "is tall" function. We thereby record, in a statable condition, the situation which corresponds to a particular failure of a sign. In Russell, flaunting of a typing rule will generate a precisely analogous explanation of and report upon the failure of a sign. It will also require that, per impossible, we read a sign which the theory says cannot be read. In this way do Frege and Russell treat the blank page as if it were a highly subtle form of writing, rather than a voiceless medium. This is a reason for Wittgenstein's rejection of semantics.

This is not merely a long-winded way of saying that Wittgenstein refused the Fregean metaphysics of sense. Wittgenstein certainly refused to take Sinne as real but nonactual objects, strange citizens of das dritte Reich. He did not do so after the fashion of some contemporary philosophers who reject the "ontological commitment" but continue to do homage to the cognitive role of senses in some other, "less committed" fashion. A certain sort of knowledge does flow through Tractatus from a grasp of sense (as we see in 4.024), but, if there is something called 'knowledge' which is prerequisite to it, it is not knowledge of a liaison among objects. Nor is it a knowledge of a set of constructions by which we might build a seman tical whole out of epistemic parts. Wittgenstein did not refrain from all talk of Sinn. He clearly recognized the need for a (a kind of) sense-reference distinction. Complete propositions, however, were the only sorts of linguistic expressions to have both. He also worked the notion of sense in a crucial way to explicate


what he intended by 'an expression', ein Ausdruck. However, it is important to note that, unlike Frege, Wittgenstein holds that interpreted propositions do not contain their sense (cf. 3.13).

4.2. Plato's Problem and Other Matters Metaphysical

To preserve the radical independence of sense from truth, to keep language transcendental from slipping into language empirical, requires philosophical effort. Wittgenstein had to push hard against various supposed truisms. As a result, he maintained the following four points:

(1) there is no distinction in fact between a sentence and a mere list of words;

(2) the familiar Fregean explanation for the "creativity of language" is unacceptable;

(3) there is no unsaturatedness, no arity, no generality in the extralinguistic world; and that

(4) de notational semantics, as an attempt to explicate the logical fit between word and world, is a failure.

Point (1): In Sophist, Plato asked after the distinction in fact between a sentence and a mere list of words. In Notebooks, the answer to Socrates's question is plain. On 28 May 1915, Wittgenstein wrote that "'composite sign' and 'proposition' are coextensive". We find, in the entry two days later and following after the words cited at the very start of this article, "It is clear that it comes to the same thing to ask what a sentence is as it does to ask what a complex is".

Wittgenstein is here adverting to the commonplace that, in explaining what a list of words is, we point to an articulate sign. In explaining what a sentence is, we point to an articulate sign as well - perhaps even to the very same sign. What Wittgenstein took to be the telling difference between the explanatory episodes, as subsequent considerations in Notebooks indicate, lies not in the arrangement of the signs on the page or in the air. Nor does it lie "below them", in any special semantic arrangement among the denotations of the portions of the signs. Rather, the differences, if any, lie in the analyses of the signs - in the ways in which comparisons are drawn and in which the signs are marshalled together with others. Differences lie in the ways we draw the lines of similarity and that is a matter of our history rather than of our metaphysics. And to say that it is a 'matter of history' is not to


propose a reduction of semantics to history or a replacement of semantics by history. The facts of history cannot stand in a justificatory relation to our play with signs.

The distance here between atomism and wholism can be measured using the question

What distinguishes a(n idle) mark from a (meaningful) sign?

The atomists have a ready answer. When answered in the style of Russell, it is:

A mark is a sign either when it is a logically proper name, so that its meaning is just its referent, or when it admits, in context, of a uniform analysis so that any significance it has reduces ultimately to that of naming.

To answer in a Fregean voice, we would say:

A mark is a sign when it has been assigned a reference; in the process of assignment, it comes to express a sense and, so, to contribute in a regular fashion to the expression of judgable content, namely, thought.

As we have seen, Wittgenstein's commitment to the absolute independence, the absolute priority, of a (thoughtless, mechanical) logic has him refuse such answers. On either of these alternatives, the meaningfulness of a sign becomes a sort of fact in which the sign can participate or, equivalently, the meaningfulness of a sign is a kind of property of it, one which is itself an object of thought. It is a feature of such accounts to presume that what we call language and what we call grammar are written already into the world itself - that it is a plain fact that 'cat is the mat on the' is not meaningful and that this fact is of much the same sort as the fact that London is on the Thames.

On the views of Russell and Frege, there is a very good sense on which a logical knowledge is posterior to an ability to read these sorts of facts off the world. First, there is given to us a collection of items or quasi-items (objects, functions or objects of acquaintance) which are, in the philosophically explanatory order, prior to language. Then, the mark becomes sign through its attachment by thought to these objects. Once attached, the sort of object it is determines the sorts of linguistic relations in which the mark can sensibly stand. In this way, there come to be various "principles of proper attachment" such as 'a first level concept cannot be predicated of another first level concept' or 'two individuals alone cannot constitute a content of judgment'. These are conditions which the mark is intended to satisfy in order that


it could be a sign. It is by a process of thought that I supposedly determine the mark's qualifications for such a lofty task. Here, both extralinguistic world and thought are suitably prior to language.

To the question "What distinguishes a(n idle) mark from a (meaningful) sign?", one of the answers Wittgenstein might have preferred to give was "Nothing in the world: there is no real difference in fact between a Shakespearean sonnet and any other kind of mark, say, a muddy footprint". There is nothing metaphysical in the world or in the mark per se that qualifies it to be a bearer of meaning. The only difference is a contingent one, an historical difference: that the muddy footprint is yet to be included into the whole structure of signs. Or, simply, that I have yet to read it. And that inclusion is, in turn, nothing philosophically special; we might say that it is nothing more than this: we do not see it as language. It is yet to be linked with the mechanism.

Point (2): The metaphysics of function and object plays a starring role in the Fregean story about what Chomsky has popularized under the title 'the creativity of language'. In that story, we can be creative with language as long as we do not exceed semantic limits. The story starts with the putative datum that we understand sentences which are, to some extent, novel in that we have never encountered this particular sentence before. I suppose one of these might be "My llama has never encountered a lama". The delimited extent to which it is novel is a depiction of the limits of our creativity. It is novel in that it is a new instantiation of an old, recognizable form. It is a combination of known words, such as 'lama', into a form whose principle I have already recognized, at least implicitly.

It is a new linguistic house in a recognized style. We can cope with it because we can build it up semantically, from materials which are familiar and on a familiar plan or so the story goes. We can arrange the old materials - the ones given as basic function and argument - in new and surprising but recognizable ways. For example, even if no one had ever seen the sentence (form) 'Bill is tall and so is Fred' before, anyone who grasped 'Bill', 'Fred', ' ... is tall' and 'and so' should be able to grasp its significance. The occurrence of 'Bill' there continues to stand to its object - Bill - in the same relation as before. As does the expression ' ... is tall'; it refers to the same function as before and one can realize as much. Also, one can attribute a real content to 'and so' along parallel lines: it too denotes a function, but of an attenuated


kind. Our knowledge of these relations and interrelations conspire together to produce a knowledge of the meaning of 'Bill is tall and so is Fred'. In summary, we defer to the objective relations between words and items and to the permanency of our ken of these relations when in comes to the governance of our "creativity" in moving from simple sentences to complex ones. In other words, we can be creative with language as long as we still know what we are doing.

Wittgenstein is refusing to items in the world the s~mantical powers which the story of linguistic creativity attributes to them. They now exert no control over expressive capabilities of signs. Insofar as the purported explanation of that creativity depends upon our remaining within the bounds set by those powers, that explanation must be rejected by him as well. In Wittgenstein's writings, he wipes the explanatory slate clean and declares the creativity of language to be absolute. We are not limited by any "knowing what we're doing" of a semantical kind.

Absolute creativity is a recurrent theme, set as early as the second sentence of the Zweites Manuskript of Aufzeichnungen uber Logik: "Every sentence is a new symbol indeed". The freedom we exercise under the guise of "creativity of language" is - as far as principles of meaning are concerned - absolute. It is literally but trivially true that when we write down a wholly new sentence such as "My pet ferret loves Brahms", we are creating a wholly new sign - what Wittgenstein would have called the 'perceptual part of a symbol'. New relations of similarity are marked out. Simultaneous with this creation of the physical sign is the coming-in to-existence of an immanent nonphysical "object", a symbol, which we can conceive as a convenient condensation of the logical properties of the sign as determineti by the way in which the sign features in logical manipulations. In creating the symbol, our sign is fit into the pictorial mechanism of Tractatus and, thereby, it comes to express sense; it is thereby subject to logical treatment.

The creativity of language, like the creativity of the plastic artist, is absolute. There need be no "world checks" before we begin to speak as there need be no "space checks" before we begin to sculpt. The sculptor's ability to refrain from constructing pieces which violate the laws of three-dimensional geometry is not a function of the sculptor's knowledge but of the sculptor's medium. In the same way, our ability to work logically with the new sign is not a function of semantic knowledge. It is a feature of our standing within the logical medium. There


is no worry; we need no guardian angel to enforce the "law" that our signs continue to carry meaning; the mechanism of language, of symbol, does that for us. Since there are really no laws, there is nothing for us to violate, no prohibitions - of a logical sort - to break. We cannot break out of the logical medium in working with signs. All of the logically (and, hence, philosophically) relevant properties of the interpreted sign, the Ausdruck, must be aspects of the logical medium of the sign, of the objective setting. Hence, the onJy requirement on the fitness of sign to give rise to a symbol, to start to cover a region in the medium, is that it be capable of appearing on the map at all, that it be, in Wittgenstein's terms, articulate. Hence, as far as properties of the sign subject to a logician's enquiry matter, there can be no difference between 'Bill is tall' and 'tall is Bill'. Both of these cover an area in logical space, both can function as maps. In the case of the latter, we just do not know what the scale of the map is yet. And that, according to Wittgenstein, is a relative triviality.

This very point - this very reaction to the creativity of language -surfaces on a number of occasions, each time under the banner headline "Logic must care for itself". The first is at the start of Notebooks 1914-1916; the other is at Tractatus 5.473ff. The idea expressed in both is that, in relation to the rest of philosophy, including semantics, epistemology and metaphysics, logic is foundational. The only conditions set on my creativity are ones I cannot check, the transcendental conditions which make for the prospect of logic. Hence, Wittgenstein is rejecting the Fregean story of the sensibility of signs told in terms of the metaphysical properties of the things which signs name. In each of its appearances, the headline is followed by a reassertion of the absolute creativity of language in the form of the claim that, in contemporary terms, there is no such thing as a logical syntax of atomic sentences. Wittgenstein wrote in Notebooks, "and I say: every possible sentence is well-formed".

Of course, Wittgenstein has to make room somewhere for our strong feelings for grammar and ungrammaticality. After all, there just is something wrong with 'is tall is tall' which is not wrong with 'Bill is tall'. Plato was right, at least, to worry about the problem. Wittgenstein seems to credit our feelings by recognizing a subject of (nonlogical) grammar. He wrote (in the second paragraph of Notebooks):

Let us remind ourselves of the explanation why 'Socrates is Plato' is meaningless. Namely,


because we have not yet come to an arbitrary determination, and NOT because the sign might be, in and of itself, illegitimate.

This sentiment is repeated - and as emphatically - at 5.473ff in Tractatus. The presence of the italics is indicative of Wittgenstein's attitude. The purported grammatic explanation is simply the citation of a fact -and a contingent one - about us: that we, at present, find certain combinations agreeable, others disagreeable but that, in future, we might make determinations so as to change that situation. For Wittgenstein, the study of grammar - logical or otherwise - is an investigative path that always leads us back' to parts of ourselves. Sometimes, as in the case of a study of those particular objects to which we refer in language, our study leads us to essential features of ourselves. In the case of a study of ordinary grammar, it leads - Wittgenstein thought - to certain accidental features of our nomenclature. This is merely the grammatical partner to Wittgenstein's response to denotational semantics: ordinary grammar, like the arrow of denotation, always points back to ourselves.

Point (3): In Tractatus, there are no necessities except the logical, those which are generated by the very prospect of signing, those which limit us as does the blankness of the page. As we have seen, there can be nothing in the nature of a denotation which sets a limit upon the admissible grammar of a sign, or else our creativity would be limited. Also, at T 5.453, we see

All numbers in logic must justify themselves. Or, more to the point, it must be apparent that there are no numbers in logic. There are no privileged numbers.

Start with any of these lines of thought and you arrive at the same place: if there are properties and relations, it is mistaken to think that, in and of themselves, they have arities. Were there to be in the world "out there" a property named by 'left of' and if it, as a binary relation, had the number two as its arity, then it would be a nonlogical necessary truth that the property of "leftness" has arity two. In the same way, arities would set objective, extralinguistic limits to the completions which the fragment 'Charlie is to the left of ... ' can meaningfully take. These would limit the absolute creativity of language. And, if there were arities, then there would certainly be privileged numbers; we might say, as do many logicians, that the possession of an arity of 0 (zero) is the trademark of a logical individual. Passage T 5.553 makes


explicit the connection - in Wittgenstein's thought - between "privileged numbers" and arities:

Russell said there are simple relations among various numbers of things (individuals). But between what numbers? And how is that supposed to be decided? - Through experience? (There is no privileged number.)

Arities are privileged numbers and must fall by the wayside. Unsaturatedness, universality and generality must do so FlS well, at least where these are meant to be semantically explanatory features of a realm of reference. If functions are, as Frege held, in themselves unsaturated, then they will each possess some index of unsaturatedness, an arity, a number which will tell us how many names can be used to fill up the distinguishable failures in saturation. If we feel constrained to mix the metaphors of Tractatus with those of traditional philosophy (a constraint which, I suggest, ought to be avoidable), we might say that everything in the Tractarian world is particular and universality or generality can only be lodged in the character of the sign. But, in truth, it would be better to say that the distinction particular-universal does not apply at all.

Point (4): If denotational semantics is a discipline which purports to expose philosophically important structural connections between sign and signified, then, in Tractatus, there is no denotational semantics. Such a semantics presupposes that there is a semantically explanatory structure in the world itself. According to Wittgenstein, there is no such structure; anything which we, as logicians and philosophers, think to see in the signified has been misplaced from the signifier - or so goes Tractatus. In consequence, the exposition of Tractatus is hardly to find much solace in, say, a model-theoretic rendering of Tarski's "theory of truth" .

Admittedly, there are the occasional passages where Wittgenstein might be read as subscribing to a "theory of truth". Here is one from the early Notes on Logic in which Wittgenstein seems to be identifying the process of setting out the (pictorial) form of an atomic proposition xRy with the process of specifying (what we would call) the satisfaction conditions of the atomic relational predicate uRr. The latter conditions are determined by describing (what we might call) a suitable set of ordered pairs to serve as the extension of R.

The form of a proposition may be symbolized in the following way: Let us consider


symbols of the form "xRy", to which correspond primarily pairs of objects of which one has the name "x", the other the name "y". The x's and y's stand in various relations to each other, and among other relations the relation R holds between some and not between others. I now determine the sense of "xRy" by laying down the rule: when the facts behave in regard to "xRy" so that the meaning (or reference) of "x" stands in the relation R to the meaning (or reference) of "y", then I say that these facts are "of like sense" with the proposition "xRy"; otherwise, "of the opposite sense" .... Thus I understand the form "xRy" when I know that it discriminates the behaviour of x and y according as these stand in the relation R or not. (pp. 98-99)

The Hintikkas seem to have fixed upon passages like these as providing proof positive of the logical aspect of their atomistic interpretation. They seemed particularly enamored of the idea that there is at most a rhetorical distinction between the so called "picture theory" of Tractatus and Tarskian truth theory for languages in standard formalization.

In fact, Wittgenstein came to make a sharp separation between the specification of the form of a proposition and a specification of its conditions of truth. In other words, he seems to have abandoned, in the general case, the sort of identification which is perhaps suggested by the preceding citation. (I happen to think that Wittgenstein never meant to endorse, and did mean to repudiate, an equation between his picture theory and our denotational semantics.) By the time he wrote in his notebooks on 1 November 1914, he was distinguishing between the pictorial relation and the relation of truth in no uncertain terms:

Very close lies the mix-up between the representing relation of a proposition to its Bedeutung and the truth relation. The former is different for different propositions, the latter is one and for all propositions the same. (p. 22)

Further on in Notebooks, we find equally definitive repudiations of the denotational view - at least as applied to what we would take to be paradigmatic examples of unary and relational predications. Wittgenstein is refusing outright to allow that my knowledge of the meaning of sentences such as 'Socrates is mortal' and 'The watch is lying on the table' is to be accounted for on the basis of a knowledge of the denotations of expressions such as the particularizer 'Socrates' and the general expression 'is lying'. In the midst of the longest concerted discussion in Notebooks - the examination of the claim "objects are simple" -Wittgenstein wrote:

However the logic, roughly as it stands in Principia Mathematica, allows itself to be applied perfectly well to our ordinary propositions. For example, from "All men are mortal" and "Socrates is a man" it follows, according to this logic, that "Socrates is


mortal", which is obviously correct, even though I, just as obviously, do not know what structure the thing Socrates or the property of mortality'has. These function, even here, as simple objects. (p. 69)

Further remarks, recorded on the succeeding day, reinforce the point in other terms.

I say to someone "the watch is lying on the table", and now he says "yes, but if the watch were to lie in such-and-such a way, would you still definitely say 'it is lying on the table"'? And I would become uncertain. That shows that I'do not know what I meant by 'lying' in general. (p. 70)

Surely, if I thought my knowledge of the meanings of 'Socrates', 'is mortal' and 'lying' to be encapsulated in a knowledge of standard definitions of the forms, for all x and y,

x is the denotation of 'Socrates' iff <I>(x) x satisfies 'is mortal' iff'l'(x) and x and y satisfy 'is lying on' iff 8(x, y),

for suitable <1>, 'I' and 8, then it would be strange to claim that I obviously do not know the semantically relevant structure of either Socrates or mortality. It would be equally unusual to claim that I do not know the meaning of 'is lying on' in general, since, ex hypothesi, to know the meaning in general is just to be apprised of a suitable statement of satisfaction conditions.

As should be clear from the text which surrounds the passages just cited, Wittgenstein has come to think that there is a good deal more to the "semantic structure" of statements such as 'the watch is lying on the table' and 'Socrates is mortal' than meets the eye of ordinary logical grammar. It is also clear that this is unavailable to the logician and to the denotational semanticist. It is a contingent part of our organism and no less complicated than it. Wittgenstein believed that there may be a further investigation of the relations of reference - an investigation of the actual means by which terms of ordinary English are to be analyzed. But this investigation is the province of the psychologist and not of the logician.

5. TEXT AND TRANSLATION

For the logical atomist, some form of reasonably conventional grammar is of paramount importance. The atomist believes that grammar must


be certified by something outside it, that the world will vouch for what Wittgenstein called the spezielle Haken of grammar. Grammar is elevated to the level of a special description of the true structure of the world. Of course, individual words are not grammatically structured. And, as the stock of grammar goes up, that of individual words must fall in relation to it. Word meaning becomes a subject beneath mention or, if there is a question of the meaning of a word, it is supposed to be settled by gesturing toward an item. There comes to be little in the world for words.

In the face of the text, it is as if those who favor an atomistic reading of Wittgenstein practice what they would have Wittgenstein preach. At their pens, the budget of Wittgenstein's philosophical power has been drained from the flow of words and channeled into motionless backwaters of semantic principles and doctrines. But, in truth, the details of his expression, the particular words chosen by Wittgenstein, come neither before nor behind, but are wholly inseparable from the "content" or message of Wittgenstein's words. This is an ideal to be served in reading Wittgenstein and, once served, an ideal which directs us away from atomism.

5.1. Numbering Tractatus

Objects are of first importance; this is the semantical plank of logical atomism. In Investigating Wittgenstein, the Hintikkas wrote the "crucial subject matter in trying to understand the Tractatus is obviously Wittgenstein's conception of object". By contrast, those concepts which the who list would take to stand equally among the real working parts of the machinery: logischer Raum, Tatsache and Sinn are virtually shunned. I believe that there is at most one mention (and that in a quotation from Wittgenstein) of the concept of logical space in Investigating Wittgenstein. The consecration of objects (and relative denigration of other concepts) stands at odds with the very structure of the text.

In the footnote to page Tl, Wittgenstein troubled to tell us that the numbers on his remarks accord with their relative import. If so, then the Hauptsiitze, whole-numbered propositions 1 through 7, have first claim to attention. After that in importance come remarks whose numbers are single decimals, remarks such as 3.1. Next are the double decimal digit claims, and so on. The notion of object - for which


Wittgenstein often used the logical term 'Gegenstand' - features neither in the Hauptsiitze nor in any proposition with single decimal digit number. In fact, Gegenstiinde receive only one concerted treatment -and that in a relatively brief series of remarks following items 2.01 and 2.02. Rated on the same score card - in terms of numbered appearance, logical space rates much higher than object. Reference to 'logischer Raum' appears, and not for the first time, in the single-digit proposition 3.4,

A proposition determines a place in logical space.

On this scale, the term which is accorded greatest import is 'the world', 'die Welt'. 10 Here, all the points go to the wholist.

The atomist cannot reply that the levels of importance reflected in Wittgenstein's numbering are not semantic or metaphysical but merely thematic. To offer such a reply is already to have swallowed a good dose of atomistic interpretation. On a wholistic view, Wittgenstein does not believe in (the usual sort of) explanatory semantics. Nor does he believe in a metaphysics - or at least a metaphysics which extends beyond the thematic. For the wholistic reader, there is nothing to being a Tractarian object beyond being a theme, an object of conversation. There is no latching on to a difference between order of explanation and order of exposition, since Tractatus, on the preferred reading, does not purport to explain anything.

5.2. Gegenstand, (Ding, Sache)

The very casualness of Wittgenstein's usage discourages the atomist foundational pretensions of objects in Tractatus. Consider 2.01:

A circumstance is a linkage of objects (items, things).l1

The parenthesis (and a similar one at 4.1272) foster the idea that the author meant to make no substantial distinction among the terms translated as 'object' (Gegenstand), 'items' (Sachen) and 'things' (Dingen). One impression is that he wished to use them interchangeably. This is the impression the Hintikkas endorsed when they wrote:

Instead of 'objects' (Gegenstlinde), Wittgenstein sometimes says 'things' (Dinge), cf., e.g., 1.01. Nothing seems to hang on this terminological variation, however. (Hintikka & Hintikka 1986, p. 30)


By my lights, this is not mere "terminological variation" and something does indeed hang on this fact. Wittgenstein was a philosopher of extraordinary care in published writing. He chose terminology scrupulously; he reworked it endlessly. It would be natural to think that Wittgenstein handled fundamental terminology with extreme care. In this regard, there is great difference between the supposed "terminological variation" with respect to 'Gegenstand' and Wittgenstein's treatment of terms for situations and their cognates. He established and respected the distinctions among Sachverhalte (states-of-things), Tatsachen (facts) and Sachlagen (situations) (which, incidentally, play no crucial role for the Hintikkas). Each term has its special position in Tractatus, one it retains throughout. There is no impression that these terms are everywhere interchangeable.

If we look to the German language, we fail to see 'Gegenstand', 'Ding' and 'Sache' comprising a range of terminological variation. Wittgenstein's supposed nonchalance over their uses looks all the more extraordinary, since they are, in no sense, simple "variants" of each other. First, surrounding 'Gegenstand' there is an air of educated refinement, an air lacking in the matter of a (mere) "Sache". As in English, philosophers are said to seek an inventory for the category of physikalische Gegenstande - "physical objects" but worry much less about Sachen - things or, better, "its". Second, 'Gegenstand', even at its most colloquial, as in the question 'Siehst du den Gegenstand auf dem Tisch?' - "Do you see the object on the table?" - carries a certain specificity which 'Sache' and 'Ding' do not. It makes sense to ask "Welche Sachen hast du heute erledigt?" ("What things have you accomplished today?"). You may hear in reply "Zwei Sachen. Ich habe meinen Vortrag gescrieben und dann ging ich zur Post" ("Two things. I wrote my lecture and then I went to the post office"). Therefore, 'Sache' is not ordinarily replaceable by 'Gegenstand'; no circumstances would license the reply 'Zwei Gegenstande' to the previous question. 'Sache' - as with 'Ding' in some of its uses - is wondrously unspecific. Its scope is tremendous, covering not merely particulars but also activities and events. The atomist ought to treat objects as comprising a category distinguished by the intrinsic properties of its members. However, if one treats 'Gegenstande', 'Sachen' and 'Dinge' as marking such categories, then the three categories so marked would be wholly distinct.

Moreover, Wittgenstein's supposed nonchalance is tough to square


with the specificity of the epistemological tenet of atomism, that Tractarian objects are the bearers of Russellian proper names. Wittgenstein would be guilty of criminal nonchalance were he to have encouraged -not just once, but on two occasions - the glossing of the supposedly crucial (and quite refined) notion of 'object of acquaintance' as a mere (and quite unrefined) Sache. The occasions in question are truly and equally important; the first is the initial introduction of Gegenstiinde, the second is part of the page-long explanation 'of the important idea of formal concept.

What seem to be the intrinsic differences between Gegenstand and Sache offer no difficulty to the wholist. For the wholist, nothing is intrinsically an object; to treat something as an object is to adopt a certain logical perspective toward it, a perspective that includes representation as a certain sort of sign, a name. To put it crudely, to be a Tractarian object is to be a topic, a topic of conversation. In itself, nothing is a conversational topic per se. Anything becomes so describable, as topic or as instance, when it plays a functional role with respect to talk. So, there is nothing on earth - short of language itself - which "picks something out" as a topic of conversation. This is very much a suggestion of Wittgenstein's terminology. In German, one can describe a topic as an object, as in den Gegenstand des Gespriichs. This is not the "object" or point of the conversation, but instead, its topic, what one is conversing about. In much the same vein, one can speak of den Gegenstand des Satzes, of the (grammatical) object of a sentence. This is a use which would come naturally to the logician Wittgenstein just as it did to Frege in his" Begriff und Gegenstand".

Either of these uses has better chance of a match with the words 'Ding' and 'Sache'. Although 'Gegenstand', as topic of conversation, is not interchangeable with 'Sache' and 'Ding', it shares with them a vast. generality of application. Anything which one can denote with a noun phrase, anything that one can talk about is a Sache. But it is also ein Gegenstand des Gespriichs, a topic; this holds true even be it an event, an activity, a nation-state or a planetary system. Now, on this treatment of 'Gegenstand', what is it to say that "the world is constructed entirely out of objects?" Read it one way and it comes out a banality: there isn't anything we cannot talk about. But it can be read more deeply; it may say that world is only a construction from out of c{j)nversation and that the conversation is ultimate: it is only within the form of speech that we can conceive of reality as having "units".


5.3. Atomism in Tractatus

Those passages which do seem to lend credence to the atomistic reading need to be reconstrued. Once that is done, those same passages serve not as support for atomism but as arguments against it. One might go so far as to deny that atomism remains as a reasonable alternative reading of Tractatus.

Consider Tractatus 1.2. In the Pears and McGuinness translation, we find what strikes one as a clear statement of logical atomism - at least as regards facts. It is:

The world divides into facts.

Max Black reads in this an emphatic expression of atomism. For this passage, he writes that, in Wittgenstein, "[t]he world is a mosaic of facts" (Black 1964, p. 37). Mosaics, like the atomists' world, are constructed out of their parts. They can and do fall apart into their constituent tiles and they can, in principle, be rebuilt out of them. To an extent, this is because tesserae are real separable parts of mosaics. They can exist independently, outside the mosaic. To reassemble the mosaic from its parts is a task for our intelligence; we must use our wits. So, the mosaic image is one the who list must refuse. Wittgenstein's world does not come apart into independent items out of which it can be reassembled. Nor can thought be the means to reassembly. Thought is just one linguistic aspect of the whole world. And nothing less.

In the German version of the same passage, the mosaic disappears. The verb translated by Pears and McGuinness as 'divides' is 'zerfallen', a word whose logic is inseparable from wholism. In everyday use, 'zerfallen' means decomposition and normally denotes a falling apart with destructive finality. And, short of godly or Frankensteinian intervention, that which decomposes is not reassembled out of its parts. When 'zerfallen' appears in Part II, Section ii, of Philosophical Investigations (Wittgenstein 1953, p. 175), Elizabeth Anscombe translates it as 'disintegration'. Colloquially, 'zerfallen' applies to the process which bodies undergo in the grave; we find "Der Mensch zerfiillt in Staub und Asche" or "humans fall apart into dust and ashes". The elements into which something zerfiillt are not, in general, those out of which it can be reassembled, even in thought. They need not be what we would call 'ordinary parts' of the thing. Nor need they be units which we would choose in explaining the natural behavior of the original thing; we


would not come to an understanding of the nature and function of human bodies by understanding, first, ashes and dust and, then, principles by which these might be combined to form bodies. There is no solace for the atomist's "construction" in the idea of disintegration. (,ZerJallen' is also an echo in Wittgenstein of analysis in Frege, an analysis which is, as we shall see, disintegrative.)

Passages which look to give wholism trouble include T 2.021. In Pears and McGuinness, it is:

Objects make up the substance of the world.

What clearer expression of atomism could be desired? It seems to say that, in its heart, the world is made up of or built out of objects. Black's commentary echoes the natural atomistic reading; he wrote as gloss on 2.021 that objects "are the materials of which atomic facts are constructed, the substance of the world" (Black 1964, p. 57).

Again, the German original dispels atomistic impressions. There we find:

Die GegensHinde bilden die Substanz der Welt.

First, the statement neither says nor implies that objects are substances or that the objects are the substances. In the German, the word 'Substanz' is not in the plural. Hence, the passage does not concern substances. Rather, it appears to concern a Spinozistic sort of "Substance" - an abstract and unitary feature of the world, if anything. And here first appearances are not deceiving: use of the singular and the association between Substanz and an irreducibly abstract feature of the world carries through all of Wittgenstein's remarks on the topic. For instance, Wittgenstein tells us outright, at 2.0231, that the world's Substanz establishes only a form and not any material properties.

Now for the verb of the statement, 'bilden'. The tie with abstraction which the noun introduces is carried further by the verb. Die Gegenstiinde bilden die Substanz der Welt: 'bilden' is an echo of the Spinozistic associations of "Substance". Given the English rendering and the constructional harmonics of words such as 'make up' and 'construct', 'bilden' is not the verb you should expect. One should expect verbs such as 'bauen' or 'konstruieren', verbs reproducing constructional overtones in the German. 'Bilden', unlike 'bauen', does not stand for a concrete sort of agglomerative activity, the kind of "putting together" which the words "make up" suggest. Instead, 'bilden' connotes a thor-


oughly abstract operation for which the English verb 'form' is a fair rendering. 'Bilden' can, for example, refer to the establishment of a company or to the passage from an active sentence to its passive equivalent.

The point here is level of abstractness - 'bilden' is neither for house building nor for applying cosmetics. Wittgenstein's use of 'bilden' throughout Tractatus bears this out. Most often it refers to the formation of propositional signs generally or the formation of a particular sign. For instance, it is applied to the formation of the sign of a negated proposition out of that for the unnegated proposition. And it appears crucially at 5.5151, where one sees:

Muss das Zeichen des negativen Satzes mit dem Zeichen des positiven gebildet werden?

"Need the sign of a negative proposition be formed (gebildet) with that of the positive?" In short, 'bilden' and its cognates replay the main theme, which is the thoroughly abstract - and that means linguistic -nature of what is mistakenly called "Tractarian ontology". To put it another way, the world disintegrates into particulars, voiceless logical surds; any abstraction, any generality, any indefiniteness, Wittgenstein thinks to lie in language. Indeed, insofar as a world requires abstraction, there is no world without language.

Verbs such as 'bauen' and (perhaps) 'konstruieren' naturally carry with them the idea of simple and rather concrete construction out of proper parts. Were the foundational idea of atomism truly at work in the early sections of Tractatus, we might look to find these verbs there. Interestingly, they make their first appearances only on the far side of Hauptsatz 4. With one exception, they appear when we are described as engaging in some relatively ordinary sort of construction, usually of or via signs. Wittgenstein speaks of us as constructing languages and also constructing gramophone records and musical scores. Only once does he speak of the world as possessed of ein Bau, a manner of construction or an architecture (5.5262). But this Bau seems well removed from the concept of Gegenstand. In fact, 'baue~' never seems to stand in close proximity with that word for object. In summary, if we ask what kind of expression of atomism is T 2.01, "Objects make up the substance of the world", then we must reply that it is no expression at all.


5.4. The Force of'Durchgreifen'

There is one more passage I would like to consider in the Pears and McGuinness translation. Even though it does not seem to lend positive support to atomism, it is at least comfortable with it. But this too is appearance; upon inspection, it takes on the aspect of an argument against atomism. The proposition in question is 3.42. In part, their translation reads:

The force of a proposition reaches through the whole of logical space.

In the German, we see

Der Satz durchgreift den ganzen logischen Raum.

One notes immediately that the words 'the force' are wholly absent from the German. It is the proposition itself, if anything, that durchgreift the whole of logical space - and not its "force".

And what is this durchgreifen? First, it is not the separable form 'greifen . .. durch'. This latter denotes reaching through and grasping hold of a relatively concrete sort. For instance,

Der Lehrer greift in der Klasse durch.

means that the teacher reaches through and exerts control over the class. The connection here between what reaches through and what is reached through is a contingent one; as we know, there is at mQst a whimsical and sometime relation between the classes and the control of their teachers. This form, the separable, is indeed the more common.

But what of the other, less common, inseparable forms, 'durchgreifen' and 'durchziehen?' Here, proximity in word is suggestive of a stronger conditioning among ideas. When X durchgreift Y, X surely reaches through Y but, this time, not as a sometime interloper but as a unifying principle. The relation is clearer with durchziehen. When I write

Profitdenken durchzieht die gesamte amerikanische Wirtschaft.

I mean not only that thought of profit runs through the American economy as water through a pipe but also that it unites and brings the economy a systemic unity. It is much the same with 'durchgreifen'. The proposition which runs through the whole of logical space does so in a unifying and systemic way.

The logical cosmology of atomism, wherein lies a logical space which is a semantic patchwork, made up of elementary propositions which


are, in turn, built up from simple objects, is at ease with the suggestion that it is the force of each proposition which reaches through logical space. After all, we might be told, the atoms, the names, out of which one Elementarsatz is produced appear simultaneously in an unlimited number of others. In its atoms, the force of a single proposition might be said to percolate through all the others. On the other hand, there is "inferential force"; like the magnetic force of a single molecule, it is a force that extends without a priori limits throughout physical space. We might say that the inferential force of a single proposition runs through the whole of logical space. After all, infinitely many distinct propositions will follow from it.

These suggestions are readily dispatched. First, Wittgenstein thought that our ordinary concepts of inferential force (and also mathematical proof) are philosophically defective. In fact, he believed that a true view of symbology would result in our giving up altogether on the notion that logical inference is a tracing-out of relations between propositional contents. Second, if force is inferential, then the force of a single elementary proposition cannot reach through the whole of logical space, since any two distinct elementary propositions are logically independent.

In truth, 3.42 strains the mosaic picture of atomism beyond the breaking point. In that picture, Tractarian objects are tesserae and elementary propositions are simple arrangements of a number of such tesserae. But if the tesserae and their arrangements are independently intelligible substantial units, it cannot come about that trivial composites of them "run through" the matrix of all the others. On the one hand, the atomist insists that logical space, and the world in it, are built up out of independently intelligible parts. On the other hand, 3.42 constrains him to admit that the "independently intelligible parts" cannot be prized apart logically, seeing that each one runs through the matrix composed of all the others. Atomism, as a doctrine of understanding, as a purported explanation of the way we come to appreciate senses of individual propositions, requires that I can grasp propositions one-at-a-time or, at most, several-at-a-time - just as independent tiles in the mosaic ought to be assembled into independent groups, each containing a reasonable number of tiles. But the idea that I might bootstrap my way up semantically, launching semantic cognition from atomic propositions and springing up through the truth functions, comes to naught if propositions such as 'my dog has fleas' truly run through


all of logical space and hence are semantically attached to propositions as seemingly divorced as 'butter can undergo Cambridge changes'.

I admit, the force of this word 'durchgreifen' is, at first, difficult to swallow. One wonders how any single propositions can run through and unite the whole logical world. I would like to think that this difficulty comes because Wittgenstein's picture of the proposition, once quite vivid, has been darkened by interpretative overlay. I think it is common to conceive of Wittgenstein's propositions as logical shadow puppets, that words of the sign act like cardboard cutouts and the process of interpretation, the grasping of sense, is thought of as the casting of a shadow from the cutouts onto the world. The "facts" which the sign then reports are just the shadows that get drawn. Perhaps remarks such as 3.12, "a proposition is a propositional sign in its projective relationship to the world" , have encouraged the conventional idea. A reappraisal of the concept of "projective relation" does a good deal to dissolve the overlay of conventionality. Unlike the relation of the cutout with its shadow, the projective relation in which the propositional sign stands is an internal or structural one. First, that means that it is a necessary or essential relation; it could not be the same proposition and yet bear a different projectum. Second, an internal relation is only apparent from the structure of the relevant language and, in the case of projective relations, the structure is entirely intralinguistic. Wittgenstein's comments on the projective relations which obtain between musical scores, their renditions and their recordings (at 4.0141) remind us of this.

As Wittgenstein tells us, we think of the proposition as bipartite; it is perceptible sign and projective relation. And, since the sign is hardly a candidate for durchgreifen, it is the projective relation which runs through and serves as a unitary principle in logical space. Again, propositional signs are not isolated objects of acts of interpretation. Rather, they seem to have much the same ontological status in Tractatus as complex predicates did in the destructive analysis of Frege. They are not real parts of anything but rather Muster, patterns which we can discern running through the whole of the system. The individual proposition which is p is factored out of an infinite range of propositions which include ,p, p~q, pl(qlr), that is, all the propositions which we would normally consider its logical composites. In the appropriate conceptual notation, the patterns which are propositions become apparent in the fact that the sign for any individual proposition will itself be


a propositional variable. This, in turn, is nothing more than a stipulation, a pointing-out, of the course of the pattern as it runs through and unites p with its negations, double negations, implications, and conjunctions and, ultimately, with every other proposition.

Context confirms this construal of the durchgreifende Siitze; in fact, it does this twice. I quote the remainder of 3.42; it precedes the line already quoted in the text.

As much as the proposition permits the determination of only one'spot in logical space, so must the whole logical space be already given through it. (Otherwise, would, through negation, logical sum, logical product, etc., new elements -in coordination - always be brought into play.) (The logical scaffolding surrounding the picture determines logical space.)

It is in its "logical scaffolding" that the proposition reaches through and grasps all of logical space and, as the passage indicates, the welds in this scaffolding are joins made by the logical operations. Once again, the Siitz is a slot within a system, a sequence of coordinates which manages to pick out a place only in relation to all the other possible sequences, only in relation to a grasp of the system of coordinates as a whole.

Brilliant and beautiful reconfirmation of this reading comes in an entry from Wittgenstein's early Notebooks, dated 15 December 1914. Wittgenstein refers to the durchgreifender Siitz in even more emphatic terms after a brief consideration of the role of the sentence within a system of logic. It is worth citing at length, since it also affords a plain statement of what we might call Wittgenstein's logical transcendental idealism: that, "before language", the world is unstructured and that, "with language" a logical structure emerges. Moreover, the logical structure is revealed in the conjectural linguistic domain of real signs.

It is obvious: we can introduce whatever we wish as the written sign of the ab-functions (i.e., truth functions), the real sign will form itself automatically. And what properties will be formed of themselves in this way? The logical scaffolding around the picture (of the proposition) determines the logical space. The proposition must reach through and grasp (durchgreifen) the entire logical space.

In the world according to logical wholism, propositions are patterns and objects are patterns; the mutuality in their natures is best conveyed by an appropriate understanding of certain sorts of variables. At this level, my claim is of a parity of sorts between objects and propositions;


and the parity is borne out in the text. The durchgreifen proposition, 3.42, is the propositional analogue to 2.0123, which is to be read in the same spirit.

If I am acquainted with the object. then I am also acquainted with the collective possibilities of its entering into states of things. (Every such possibility must lie in the nature of the object.)

It also has a companion passage in Notebooks, one which appears on page 83 of the English edition and page 178 of the German. Here I present the German in translation:

Every thing determines the entire logical world, so to say, the entire logical spacc.

5.5. There are no Special Groups of Objects

Let it not be thought that logical wholism stands entirely upon textual considerations which are negative. There are any number of passages which are difficult to reconcile with one or another of the aspects of the Hintikkas' vision of Wittgenstein's presumptive atomism. For example, there are straightforward denials of the metaphysical facet of logical atomism, the one on which the category of objects is thought to embrace not only particulars but the more expansive denizens of other logical types: properties, classes, functions and relations. I begin with the earliest antiatomistic statements, those from Notebooks.

In the German edition of Notes on Logic, 1913, in the Zweites Manuskript, we see:

Not only from a concern with [singular 1 things must logic prescind; it is as little permitted to occupy itself with predicates and relations. (Wittgenstein 1984, p. 195)

The sentiment is repeated again on the same page:

In the same way, '(1/ in 'cPx' appears to be a substantive without being one .... One reason which speaks against it(s being a substantive) is the generality of logic: logic cannot deal in any special groups of objects.

If the atomists were right about Tractatus, then Wittgenstein counted properties and relations among the "Tractarian" objects. But as properties and relations comprise special groups (in the original, "spezielle Menge") if anything does, logic, according to Wittgenstein, cannot treat of them. But it was Wittgenstein's study of logic which was supposed to create a legitimate demand for such spezielle Menge. Therefore, the metaphysical plank of atomism must be rejected.


The English version of the same, Notes on Logic, September 1913, contains a parallel remark. Wittgenstein is here diagnosing an "error" in Russell's approach:

It is easy to suppose that "individual", "particular", "complex", etc., are primitive ideas of logic. RusselI, e.g., says "individual" and "matrix' are "primitive ideas". This error is presumably to be explained by ... (N, p. 105)

In both passages, Wittgenstein is taking exception to Russell's efforts in foundations of logic. First, Wittgenstein was accusing Russell of reversing the right philosophical order of things. For Wittgenstein, Logik (with a capital 'L') was first philosophy, not only in terms of temporal or intellectual priority, but also in terms of what is philosophically definitive. Within the confines of an independent Logic were all the problems of philosophy to be resolved. And that independence was a freedom from a prior metaphysics such as Russell's theory of types or Frege's conceptual hierarchy. To Wittgenstein, Russell sought always to turn this picture around and make logic wait upon the verdicts of Russell's neo-Cartesian metaphysics. Second, Russell certainly wanted to "turn back the clock" as Wittgenstein saw it: the traditional metaphysical concepts of particular, universal, property, object, function, proposition, and symbol were absolutely defunct. Little trace of them can remain in a logical investigation. Russell believed that a version of traditional metaphysics, carried on in traditional terms, could proceed under the imprimatur of his mathematical logic. Wittgenstein believed that the only imprimatur which logic offers is interdiction.

5.6. Expression of Idealism

Tractatus 4.023 is a straightforward denial of the principal plank of atomism, that the world is, independently of actual or potential expressions of thought, a construction out of real atoms. Like atoms as envisioned in the time of Newton, these are antecedent to any speech, they are fit together in one way or another - that is how actuality is determined. Then, once we do get around to enunciating propositions, they either accord or fail to do so with a pre determinate logical cosmos, a great confabulation of atoms; concordance yields truth and discordance falsehood or, in the worst case, meaninglessness. But this is far from the way in which Wittgenstein describes it here:

Through the proposition must reality be fixed as to "yes" or "no".


Contrary to the doctrine of logical atomism, Wittgenstein seems here to be making the factual pleasure of the world wait on the prospect of the sentence for its determination. It is through the proposition that the determination occurs. Hence, it is only by creating signs that symbols are created and symbols, in turn, are the relations we demarcate among the signs of a system. It is only through the mechanism of symbols that reality is determined one way or another.

6. ANALYSIS IN TRACTATUS

Analysis in Tractatus is not Russellian. There is plenty of evidence to suggest that Wittgenstein did not endorse Russell's theory of descriptions. This conclusion stands in opposition to the Hintikkas' contention, according to which Russellian analysis is a linchpin in the formal aspect of atomism, that is, in the technical means for carrying out the logic of objects. Analysis for them forges the essential connection between an arbitrary sign and the primitive sign and, hence, brings logic and language in general into touch with the all-important objects. Ultimately, for the Hintikkas, Russell's analysis points us out of language altogether; it points us toward the objects. Analysis in Tractatus, however, aids and abets the program of linguistic idealism: we are never pointed out of the language. (In the regard, Wittgenstein's analysis is comparable to one of Frege's, a decompositional analysis which uncovers the formal patterns we need to note in order to assess inference.) To be seen as language in Tractatus is to appear to us as part of a logicallyenabling structure or pattern. The boundaries of such a pattern correspond to the linguistic area covered by the real or proper sign of which the mark (as sign) is just one manifestation. The tracing of such a pattern, or the demarcation of the pattern, is the job of one of the processes we may call "analysis" in Tractatus.

It has been taken as given that Wittgenstein's analysis is some nebulous version of Russell's. There are, however, a number of textual and doctrinal indications that this is not so. First, we have Wittgenstein's explicit endorsement of Frege's strictures on the adequacy of attempted definitions. This appears in the parenthesis of T 5.451:

In short, what Frege has said concerning the introduction of signs via definitions (in Grundgesetze) also applies, mutatis mutandis, in the same way to the introduction of primitive signs.


Wittgenstein is endorsing material that includes Grundgesetze (Volume II, Section 66), wherein Frege is explicitly refusing legitimacy to contextual definition. According to the Geach and Black translation, Frege wrote:

So we may not define a symbol or word by defining an expression in which it occurs, whose remaining terms are known .... Rather, the definition must have the character of an equation which is solved for the unknown, and on the other side of which nothing unknown occurs any longer. (Frege 1977, pp. 170-71) ,

Professor Dummett characterizes Frege's attitude toward contextual definition in his The Interpretation of Frege's Philosophy as a form of "hostility" toward them (Dummett 1981, p. 36).

Passage T 3.3442 may be construed as a reassertion of Frege's sentiments:

The sign of a complex does not dissolve via analysis arbitrarily, so that, somehow, it would have a distinct dissolution in every sentential nexus.

It is the very character of contextual definition that the resolution of the definiens depends upon context and, therefore, differs according to the sentential nexus in which it appears. Needless to say, replacement of definite descriptions is the very soul of Russell's analysis and this is a matter entirely of contextual definition.

Second, Wittgenstein's ideas on the nature of a proper Begriffsschrift allow him to skirt the semantical pitfalls to which Russell would have referred in explaining the need for a Russellian analysis, one set atop his theory of descriptions. First, Wittgenstein, unlike Russell, meets no special difficulty in accounting for the informativeness of identity statements; he avoids Frege's problem of the morning star and the evening star. This is because, for Wittgenstein, there are no identity statements at all. According to T S.S3ff, what we think of as statements of identity are not true statements but philosophically dangerous and logically superfluous commentary on the sorts of signs which we are using. As Wittgenstein wrote at T 4.242,

Expressions of the form "a = b" are, therefore, merely aids to representation; they assert nothing about the significance of the signs 'a' and 'b'.

Naturally, without identity statements, there is no worry over identity substitutions into belief contexts, the sort of problem exemplified by Russell's 'Scott is the author of Waverly'. Moreover, there is enough


in Wittgenstein's cursory discussion of the logical form of belief statements (T 5.542) to show that, even if he had allowed significant identities, the use of explicit quotation in the analysans for belief blocks possible substitutions.

Third, Wittgenstein seems to have banished the problem of empty names - the issue of the "the golden mountain" which Russell associated with Meinong - outright. As we said, the. wholist believes that the meaningfulness of an expression sets no condition to which the extralinguistic world would have to conform. As Wittgenstein wrote in T 2.0211,

Had the world no substance, then whether a sentence had sense would depend upon whether another sentence were true.

From context, it is clear that Wittgenstein intended this claim to feature in a brief modus toll ens argument with conclusion "The world has indeed substance". He also intended that the reader supply the missing premise, "Whether a sentence has sense does not depend upon whether another is true". It follows that, on a suitable view of language, 'The golden mountain does not exist' does not require for its meaningfulness that there actually be a golden mountain; according to Wittgenstein, no sentence can lay down such a requirement.

There is one caution, however. It should not be thought that Wittgenstein's extraordinary attitude toward (apparent) statements of identity and toward the independence of conditions of meaningfulness from conditions of truth is only possible or is only made plausible (to the extent that it is) by the prospect of Russellian definite descriptions analysis. It might be thought that Wittgenstein intended his ideas on identity, belief and empty names to apply only to those expressions which have been suitably analysed, which already appear in fully perspicuous form in the notation of his own Begriffsschrift. Hence, it could be (or so the putative reply would have it) that it is only by means of the familiar process of the contextual replacement of definite descriptions that we bring a statement from a linguistic state of nature into a form to which Wittgenstein's strictures will apply. This may be the only way we can get ourselves into the contortions requisite to make such ordinary statements as

Mark Twain is Samuel Clemens

conform to Wittgenstein's seemingly procrustean views on identity.


Hence - or so it might be argued - Wittgenstein needed descriptions analysis to ensure his view and, thereby, to replace statements such as the above by statements of some other form, in particular, by series of statements not containing names for Mark Twain but only "logically proper names", ones for whom Wittgenstein's mysterious views on identity and existence can be imagined to be a bit less mysterious.

A moment's thought shows that this reply is unsatisfactory. In order to apply descriptions analysis, we assume that "Mark Twain is Samuel Clemens" is to be construed as equivalent to and analyzable in terms of the descriptive statement

The author of Pudd'nhead Wilson is the same as the author of Innocents Abroad.

Now, let Px stand for 'x authored Pudd'nhead Wilson' and let Ix stand for 'x authored Innocents Abroad'. From "Mark Twain is Samuel Clemens", analysis would lead us to

3x(Px A Ix A 'Vy«Py v Iy) ~ y = x».

Now, if we put this into conformity with Wittgenstein's suggestions on identity - that identity of Bedeutungen be indicated by identity of variable names - we obtain

3x(Px A Ix) A 'Vy -, (Py v Iy).

Here, the difference in the sign for the variable - 'y' as opposed to 'x' - indicates (what we would call) disjointness in the range.

Famously, Wittgenstein did not view 3x and 'Vx as logical signs but as confused composites of generality and truth-functionality. When properly understood, they serve, in association with the remainder of the quantified statement, to stipulate a truth-function of a sequence of propositions. Therefore, when we move to a suitable notation, Wittgenstein would prefer to see the first conjunct of the above formula as replaced by an infinitary disjunction, something akin to

ViPa Ala)

where the latter is a shorthand for an actual infinitary disjunction

(Pa A Ia) v (Pb A Ib) v (Pc A Ic) v ...

wherein 'a', 'b', 'c' et aI., comprise a suitable collection of names, the


extent of the collection indicated by the form of the 'x' in the original expression.

Now, our point is clear. If you look, the move from names such as 'Mark Twain' has come full circle. On Wittgenstein's approach to the quantifiers, there is no net gain, if we measure gain in terms of the designata of names which are called for in expressing a given proposition. We may not require lexically distinct names, one for the author of Pudd'nhead Wilson and another for the author of Innocents Abroad, but we shall need some name or other which denotes Sam Clemens, the human being who wrote both works.

The contrast with Russell's views ought to be plain. For Russell, a need for ordinary names fades away into the work of the quantifiers. In their turn, quantifiers have the job of naming properties of propositional functions and make no claim about the individuals which are the designata of names. Russell says as much in the fifth of his 1917-1918 lectures on logical atomism:

Existence is essentially a property of a propositional function .... Existence-propositions do not say anything about the actual individual but only about the class or function. (Russell 1985)

In other (Russellian) words, the proposition expressed by 'an author of Innocents Abroad exists' contains no vestige of the historical individual Mark Twain. (Incidentally, Wittgenstein could hardly have accepted such a characterization of the logic of "existence-propositions" on which existence is essentially a property of propositional functions. Functions, like objects, are formal concepts; hence, there are no property statements asserting the existence of one or more of them.)

For Wittgenstein, the commitment to the name - and to its object -is inescapable. To use the jargon of the Introduction to the second edition of Principia Mathematica, we can say that Wittgenstein believed that propositional functions only enter into propositions through their values. Among other things, this means that, if we say that quantifiers do indicate second-level concepts or properties of first-level propositional functions, then all we mean by that is that quantifiers indicate patterns in (possibly infinitary) truth functions of elementary propositions, propositions whose signs are combinations of names. Notice, however, that the inescapability of naming does not arise because an appropriate theory of understanding takes its start from the relation of denotation. On Wittgenstein's view, we do not need names because,


through them, we "attach language to the world". It is not because names have to be correlated with items of a certain sort if we are to have any expression of sense. It is simply because, in order to be signs, even marks such as footprints need to be read. Wittgenstein takes whatever agreement reading requires to be captured, in large part, in our explanations of the Bedeutungen of names. As we saw earlier, names are required for the very subsistence of sense.

These considerations on the relation in Tractatus between signs of generality and names expose a third reason why Wittgenstein's conception of analysis differed from that of Russell. As we have seen, Wittgenstein would allow nothing in an ontological way, nothing in terms of metaphysical commitment, to be gained through the elimination of names by replacement with some quantified concoction. If there is a privileged class of "true" or "real" names, then they are not reached, it would seem, by some mere iteration of the procedures which Russell first set out in On Denoting. Some other form of analysis is required to make the connections between what is normally called 'a name' and whatever items form the conjectural collection of "real names".

As suggested by the remarks at T 3.23 and following, analysis in Wittgenstein is a unidirectional process of resolution (and here you may, with considerable propriety, think of the resolving of vectors). The process is triggered by the recognition of indeterminacy or generality in a sign, a generality inherent in the equivalence which Wittgenstein noted between fact and complex. As Wittgenstein indicated in his Notebooks for 28 May 1915, he thought of the terms 'complex' and 'fact' as coextensive (N, p. 52). Consider the fact (or complex) which consists in the layout of a desktop with pen lying to the left of pencil. Faced with his fact (or complex), which we might call 'pen-Ieft-ofpencil', we may take a propositional perspective on it, we may read it as having a sense - we may read it as a proposition or as comparable with a proposition. This is to treat it as a fact, as the fact that pen is to the left of pencil. When we think of it as Bedeutung, as something comparable with a name, it is treated as a complex, as, roughly "penleft-of-pencil" as is indicated by the use of this complex name. Now, when I predicate something of the complex, say "pen-left-of-pencil is to the right of the blotter", there is an indeterminacy. In fact, it is just the sort of indeterminacy which Wittgenstein examined so thoroughly in the case of "the watch is lying on the table" (N, p. 69ff). It seems perfectly clear that 'pen-Ieft-of-pencil is to the right of the blotter' is


true if the pen remains to the left of the pencil on the desktop and the whole complex lies to the right of the entire blotter. Things are not so clear, however, if, say, the pencil is to the right of the blotter but some part of the pen is not. Perhaps the pen is partially atop the blotter. Is it then true to say that the complex is to the right of the blotter?

According to Tractatus and Notebooks, such an indeterminacy is merely apparent, an artifact of our profound ignorance about the mechanism of meaning - words are like a film on deep water. To think that the logical world itself contains indeterminacy is to confuse, as the denotational semanticists did, the character of the sign with the character of its Bedeutung. First, whether we recognize it or not, the determinacy of sense requires that a reading of 'pen-Ieft-of-pencil is to the right of the blotter' associates that sentence somehow with a quite specific fact, one containing none of the indeterminacy which lodged in the sign. Second, an analysis of the sentence would eliminate the presumptive generality or indeterminacy in favor of a range of propositions. In this case, the process might result in the replacement of our original sentence,

pen-Ieft-of-pencil is to the right of the blotter

by the sentences,

pen is to the right of the blotter pencil is to the right of the blotter pen is to the left of the pencil

the last of which results from changing our perspective upon the original description of the complex and reading it as a proposition. I presume that this is, in truncated and outline form, the sort of manuever which Wittgenstein described at T 2.0201:

Every statement about complexes permits itself to be pulled apart [zerlegenJ into a statement about their constituent parts and into propositions which describe the complexes completely.

Third, the details of the analysis do not become available as the result of any investigation in pure logic; the precise nature of the situation to which 'pen-Ieft-of-pencil is to the right of the blotter' has been attached cannot be discovered by a transcendental investigation of the sign in general. Rather, Wittgenstein thinks that an investigation into psychology would be required.


One final point: as Wittgenstein makes plain at 3.24, we can also conceive of the process of analysis as the clearing-away of generality. Since a propositional variable is nothing more than a specification of a range of propositions in virtue of their structural similarities, we can think of the original sentence, 'pen-Ieft-of-pencil is to the right of the blotter', as a propositional variable for the sentences into which it is resolved. Viewed in this light then, Wittgensteinian analysis is an elimination of generality in terms of specificity.

In summary, the number of points at which Wittgenstein's analysis differs from Russell's ought to be emphasized. First, Wittgenstein's analysis is part of the empirical investigation of the sign; it is a process of displaying a sign's inner nature. Analysis reveals the way in which signs are actually formed in the mechanism which underlies reading. As it exposes logical connections, analysis stays entirely within the bounds of language. It never takes us to a place where language "points" out of itself, perhaps into a putative intentional gap between word and object. 12 All we can find before us are more words. Second, analysis proceeds not by the introduction of ever greater generality, as in Russell, but via its complete elimination. Third, as mentioned, analysis lies not in the province of the logician, but in that of the psychologist. Finally, as the word 'zerlegen' ['pull apart'] suggests, Wittgenstein's analysis is destructive in ways that Russell's is not. For one thing, analysis is not a cognitive, semantical recipe for the grasp of a sense, the indication of a process of thought by which someone (perhaps even implicitly) would come to an understanding of the analyzed expression. In Tractatus, there are no such recipes and no need for them: what we need to have before us in order to stand among signs as a reader is not constructed from below, from a semantics of simples. At T 5.526, Wittgenstein put it quite plainly: "One can describe the world completely through fully generalized propositions, that means, therefore, without correlating in advance any name whatsoever with a specific object". There is no need for a "bottom up" construction.

The distance we have marked out here between Wittgenstein's analysis and Russell's seems the same conceptual distance as that marked out by Wittgenstein himself in a passage of Notebooks:

Let us assume that every spatial object consists of endlessly many points, then it is clear that I cannot introduce all these by name if I speak of such an object. Therefore, here would be a case in which I cannot arrive at a complete analysis in the old sense at all; and perhaps this is just the normal case. (N, p. 62)


Provided that the "analysis in the old sense" is Russell's, Wittgenstein is pointing out that it could hardly be a verdict of logic, mathematics or an aprioristic conceptual investigation that every propositions admits of a complete Russellian analysis. The claim that every proposition admits of a complete Russellian analysis implies, or so Wittgenstein believed, that every object consists of at most finitely many simples. The latter could hardly be a verdict of a purely conceptual enquiry. Wittgenstein's response to this character of the "old" analysis is recorded next:

This is indeed clear: that the propositions which humanity exclusively uses will have a sense just as they stand and do not wait on a future analysis in order to acquire a sense.

So, our grasp of a sense is not constructed from cognitive units such as the objects of acquaintance which were to be revealed in Russellian analysis. The standing of understanding is always "from above", from a perspective on the whole world of signs. Nothing less will ever do.

ACKNOWLEDGMENTS

I am grateful to the members of the Logic, Language and Science Colloquium at the Ohio State University, especially Stewart Shapiro, for their comments on an earlier version of this article. Also, my thanks go to the organizers of the XIVth International Wittgenstein Symposium, Wittgenstein Centenary Celebration, especially Professor Rudolf Haller. Ellen Klein made it possible for me to present my ideas, first at Rollins College, and later at Washington College, where my claims were subjected to thorough examination by the members of her Wittgenstein seminar. The article would never have come to exist but for the persistent and insightful criticisms of members of the onetime Florida State Wittgenstein group, especially C. J. B. Macmillan, Emanuel Shargel and Anton Mikel. Finally, Jaakko Hintikka and Luise Prior McCarty deserve my special thanks for many stimulating discussions on Wittgenstein.

NOTES

* A highly condensed version of the ideas here presented will appear in the article Hintikka's Tractatus in Proceedings of the XIVth International Wittgenstein Symposium, Wittgenstein Centenary Celebration, 1991. 1 Throughout the sequel, 'T', followed by a numeral, will refer to a passage in Wittgenstein's Tractatus. References to Blackwell's edition of Notebooks, 1914-1916, will be by


'N' followed by a page number. Unless otherwise noted, translations from the German are my own. 2 My description of logical atomism is not intended to be historically accurate restatement of Russell's one-time view; principally, it is meant to fit the exposition of Investigating Wittgenstein (Hintikka & Hintikka 1986). 3 After seeing the world according to logical atomism, one is moved to exclaim "Gee, it's a good thing for us that our language fits onto the world!". Atomism does make it seem that interpreted language and the world into which it is interpreted are wholly independent fields and that their perfect logical liaison is fortuitous;. That the languageworld connection is incidental - indeed, that there is need for such connection at all - is one of the fundamental flaws in the atomistic interpretation. In Tractatus, there is an internal relation between sign and significatum; name could not be what it is without Bedeutung. 4 Since co-authoring Investigating Wittgenstein, Jaakko Hintikka has come to doubt that Tarski's theory of truth is truly a recreation of Wittgenstein's picture theory. 5 Here a "system" ought to be conceived as a network or space - on the model of a vector space - that is, a structured arrangement of articulated nodes each of which has a precise, formally determined, position relative to the others. I should not be read as relying upon the contemporary notion of a logical or formal system which is related symbiotically to the syntax/semantics distinction. A Wittgensteinian system of language would encompass far more than any conventional formal system. It will include a sign for 'the watch is lying on the table' which is the concrete circumstance in which I illustrate the words 'the watch is lying on the table' by pointing out a particular watch x lying on a particular table y. Claims such as '''the watch' refers to x" are, then, interpreted as features of such situational signs. 6 If the world in Wittgenstein is a perspective on signs, then there is, in truth, no world without language. It is here an expository device or the first rung on a ladder we ought to kick away once we have climbed it. 7 Far be it from me to suggest that particular languages such as Chinese or Frege's Begriffsschrift are extensionally distinct from the language, the system of signs, of which Wittgenstein wrote in Tractatus. We might say that they are the same things - just addressed with speech in different ways. Similarly, Bernard Ortcutt the college president and Bernie the spymaster are the same man, but get addressed in quite different ways. This distinction is to be compared with the one drawn by Wittgenstein (and redrawn by us in a section to come) between complex and proposition. 8 To say that each proposition resolves into elementary propositions or, equivalently, to say that each Tatsache resolves or divides naturally into Sachverhalten is, first, not to say the reverse, that, for example, propositions are built up or composed out of elementary propositions. Second, it is not to say that we either do or must resolve them ourselves or that, in our "cognitive processing" of propositions, we carry out such a manuever. Rather, it is Wittgenstein's contention that propositions resolve themselves. Also, it does not follow from the claim that every proposition resolves into elementary propositions that every proposition contains only finitely many elementary constituents. It is only required that the resolution process be well-founded. 9 Those familiar with Zermelo-Franekel set theory and its close relatives will notice the resemblance between this reconstruction of Wittgenstein's views on well-formedness and attempts to justify the axiom of foundation. It is unlikely that the resemblance is accidental - at least from the mathematical standpoint. (I am not asserting that there was


historical coincidence - perhaps a chance meeting between Wittgenstein and Mirimanoff on the Russian front.) In my mind, they are linked through Wittgenstein's remarks on mathematics at T 6.2ff. And the connection lies in this: the category of Wittgensteinian real signs contains an isomorphic embedding of Cantor's second number class. 10 It is noteworthy that the nature of "the world" at large and in itself never seemed to be a first concern of either Frege or Russell. The world was nothing more, in the case of the author of Der Gedanke, than the sum of the drei Reiche. The world was, however, of first concern to nineteenth century logicians of the idealist persuasion. 11 The word translated as 'linkage' here is 'Verbindung'. Wittgenstein has chosen to use it rather than 'Zusammenhang' or 'Verkettung', words which he employs on other occasions to describe the inner structures of facts. The choice is especially interesting since 'Verbindung' connotes a connection or linkage which is dependent for its existence upon our activities, in particular, some activity of bond creation or ratification. By contrast, this connotation is absent from a word such as 'Zusammenhang'. "Eine Verbindung" is a linking or binding together which has to be established or set up before it can exist. The marital bond is a sample "Verbindung" which comes readily to mind. 12 Should the reader be in any doubt about this, it might allay skepticism to consult T 3.263, where Wittgenstein makes it clear that, even if analysis were to bring us to a statement whose constituent signs were all primitive, we are not freed of the bonds of speech. He wrote the following:

The Bedeutungen of primitive signs can be clarified through elucidations. Elucidations are propositions which contain the primitive signs. Therefore, they can only be understood if the Bedeutungen of the signs are already familiar.

He thereby refused the icon of the bare ostensive association of primitive sign with object. One should note that it is not the possibility of ostensive definition which is under discussion; the main issue is its bareness, the prospect that, at the point of ostension, we leap the intentional gap between word and object. (Compare, in this regard, N, p. 70.)

REFERENCES

Anscombe, G. E. M.: 1959, An Introduction to Wittgenstein's Tractatus, 2nd ed., Harper & Row, New York.

Black, M.: 1964, A Companion to Wittgenstein's Tractatus, Cornell University Press, New York.

Dummett, M.: 1978, Preface to Truth and Other Enigmas, Harvard University Press, Cambridge, Massachusetts.

Dummett, M.: 1981, The Interpretation of Frege's Philosophy, Harvard University Press, Cambridge, Massachusetts.

Frege, G.: 1977, Translations from the Philosophical Writings, P. Geach and M. Black (trans.), Cornell University Press, New York.

Frege, G.: 1979, Posthumous Writings, Basil Blackwell, Oxford, England. G6de\, K.: 1983, 'Russell's Mathematical Logic', in P. Benacerraf and H. Putnam (eds.),

Philosophy of Mathematics. Selected Readings, 2nd edn., Cambridge University Press, pp.447-85.


Hintikka, Merrill B. and Jaakko Hintikka: 1986, Investigating Wittgenstein, Basil Blackwell, Oxford, England.

Kraus, Karl: 1987, Ober die Sprache, Suhrkamp, Frankfurt. McGuinness, B. (ed.): 1979, Wittgenstein and the Vienna Circle. Conversations Recorded

by Friedrich Waismann, J. Schulte and B. McGuinness (trans.), Basil Blackwell, Oxford, England.

McGuinness, B. (ed.): 1984, Wittgenstein und der Weiner Kreis. Gesprtiche, aufgezeichnet von Friedrich Waismann, Ludwig Wittgenstein, Werkausgabe, Band 3, Suhrkamp.

Quine, W V. 0.: 1971, Set Theory and its Logic, rev. edn., Harvard University Press, Cambridge, Massachusetts. '

Russell, B.: 1956, Logic and Knowledge. Essays 1901-1950, R. C. Marsh (ed.), London. Russell, B.: 1961, Introduction Ludwig Wittgenstein Tractatus Logico-Philosophicus,

Routledge and Kegan Paul, London. Russell, B.: 1985, The Philosophy of Logical Atomism, Open Court. Russell, B. and A. N. Whitehead: 1967, Principia Mathematica to *56, Cambridge Univer

sity Press. Wittgenstein, L.: 1953, Philosophical Investigations, G. E. M. Anscombe (trans.), Mac

millan, London and New York. Wittgenstein, L.: 1961, Notebooks 1914-1916, G. H. von Wright and G. E. M. Anscombe

(ed.), Harper and Row, London and New York. Wittgenstein, L.: 1961, Tractatus Logico-Philosophicus, D. F. Pears and B. F. McGuin

ness (trans.), Routledge and Kegan Paul, London. Wittgenstein, L.: 1982, Last Writings, G. H. von Wright and H. Nyman (eds.), University

of Chicago Press, Chicago, Illinois. Wittgenstein, L.: 1984, 'Aufzeichnungen tiber Logik, 1913', in Wittgenstein: Werkausgabe

Band I, Suhrkamp.

STEVE GERRARD

WITTGENSTEIN'S PHILOSOPHIES OF

MATHEMATICS*

ABSTRACf. Wittgenstein's philosophy of mathematics has long been notorious. Part of the problem is that it has not been recognized that Wittgenstein, in fact, had two chief post-Tractatus conceptions of mathematics. I have labelled these the calculus conception and the language-game conception. The calculus conception forms a distinct middle period. The goal of my article is to provide a new framework for examining Wittgenstein's philosophies of mathematics and the evolution of his career as a whole. I posit the Hardyian Picture, modelled on the Augustinian Picture, to provide a structure for Wittgenstein's work on the philosophy of mathematics. Wittgenstein's calculus period has not been properly recognized, so I give a detailed account of the tenets of that stage in Wittgenstein's career. Wittgenstein's notorious remarks on contradiction are the test case for my theory of his transition. I show that the bizarreness of those remarks is largely due to the calculus conception, but that Wittgenstein's later language-game account of mathematics keeps the rejection of the Hardyian Picture while correcting the calculus conception's mistakes.

1.

The philosophy of mathematics dominated Wittgenstein's philosophical middle years - from the late 1920s when he returned to philosophy until 1944 when he began revising material that eventually became Part 1 of the Philosophical Investigations. Wittgenstein's work on this subject marks his transition from the Tractatus's world of logical form and definiteness of sense to the Investigation's language-games and forms of life.

Michael Dummett represents a standard view of this work when he writes: "Wittgenstein's vision of mathematics cannot, I believe, be sustained; it was a radically faulty vision".1 Since Dummett elsewhere acknowledges an enormous debt to Wittgenstein, the standard view in effect comes down to this: Wittgenstein made great contributions to philosophy in the Tractatus and the Investigations, but in between he worked for one and one-half decades on a faulty (and even perverse) philosophy of mathematics. In other words, there is a black hole precisely in the center of Wittgenstein's career.2

The black hole theory involves looking at Wittgenstein's philosophy of mathematics as an unchanging doctrine. Remarks composed in the


126 STEVE GERRARD

early 1930s are treated in the same way as remarks from the early 1940s. This is looking at Wittgenstein's career as if there were no transition: there is the earlier Wittgenstein of the Tractatus, the later Wittgenstein of the Investigations, and in between only the unchanging darkness of his philosophy of mathematics. This view, however, cannot survive a careful examination of the texts.

Wittgenstein, in fact, had two chief post-Tractatus accounts of mathematics. I have labelled these the calculus coraception and the language-game conception. The calculus conception dominated Wittgenstein's thought from 1929 through the early 1930s, although in some areas (such as contradiction) its influence lasted longer. In the middle 1930s, his views began to change to the language-game conception, and by the early 1940s, the view of mathematical language as a nexus of language-games had completely overturned the calculus view.

In the transitional (calculus) period Wittgenstein saw mathematics as a closed, self-contained system. The rules (construed extremely narrowly) alone determine meaning, and thus become the final and only court of appeal. In the more mature (language-game) period, meaning and truth can be accounted for only in the context of a practice, and mathematics is examined by seeing what special role it plays in our lives and its special relationship to other language-games.

But not everything changed; throughout all the stages of Wittgenstein's work on the philosophy of mathematics, he remained opposed to and tried to undermine what he considered to be a misleading picture of the nature of mathematics. According to this opposing picture, mathematics is somehow transcendental: a mathematkal proposition has truth and meaning regardless of human rules or use. According to this picture there is an underlying mathematical reality which is independent of our mathematical practice and language and which adjudicates the correctness of that practice and language. This plays a similar (negative) role for Wittgenstein's philosophy of mathematics as does the Augustinian Picture for his later philosophy of language. For reasons given in the next section, I call this the "Hardyian Picture" after the mathematician G. H. Hardy.

The Hardyian Picture helps to give a structure to Wittgenstein's work on the philosophy of mathematics and to unite seemingly disparate discussions. Regardless of what else he was doing, Wittgenstein always kept this picture in mind and tried to distance himself from its temptations and confusions.

WITTGENSTEIN'S PHILOSOPHIES OF MATHEMATICS 127

The goal of this article is to challenge the black hole view, giving a new framework for examining Wittgenstein's philosophies of mathematics and the evolution of his career as a whole. The idea is not to claim that Wittgenstein never made a mist~ke - the calculus conception is certainly flawed - rather, it is to show the motivation behind the mistakes, and to demonstrate that, at least in the paradigm case of contradiction, these mistakes were made during the transitional Wittgenstein period and were corrected during the later Wittgenstein period.

The first step is to provide a structure and motivation for Wittgenstein's work on the philosophy of mathematics. This is what the Hardyian Picture does, and is the subject of Section 2. Wittgenstein's calculus period has not been properly recognized, so Section 3 gives a detailed account of the tenets of that stage in Wittgenstein's career. Wittgenstein's notorious remarks on contradiction may be taken as representative of the bizarreness of the calculus period and are often given as the main evidence for the black hole view. Section 4, concerning contradiction, is the test case for my theory of Wittgenstein's transition. There it will be shown that the bizarreness of those remarks is largely due to the calculus conception, but that Wittgenstein's later languagegame account of mathematics keeps the rejection of the Hardyian Picture while correcting the calculus conception's mistakes.

2.

A notable feature of Wittgenstein's post-Tractatus work is that he seems to spend far more time attacking opposing views than he does asserting his own. Thus, in imposing a structure on Wittgenstein's philosophies of mathematics the natural place to look is to the view Wittgenstein is rejecting. Most commentators call that view "Platonism", but this is not a happy choice. What is commonly labelled as Platonism in mathematics includes many trivialities - even truisms - and attacking these misses the force of Wittgenstein's real objections.3

The Philosophical Investigations begins with a quotation from St. Augustine describing how he learned to speak. Wittgenstein does not call this a theory, but a picture: "These words, it seems to me, give us a particular picture of the essence of human language" (PI: 1). A great deal of the Investigations concentrates on trying to undermine this picture. In addition, this picture ties together seemingly isolated discussions. On closer look, for example, we can see that what in pre-

128 STEVE GERRARD

Kripke days was considered to be the Private Language Argument, especially the S-game of a sensations diary, is really the Augustinian Picture all over again. The diary keeper is naming sensations the way the stylized Augustine named physical objects: without any background context or language.

Wittgenstein's contemporary, the Cambridge mathematician G. H. Hardy, plays a similar role for Wittgenstein's philosophies of mathematics as Augustine does for the Investigations, and ;it is helpful to posit a Hardyian Picture on the model of the Augustinian one. 4

Wittgenstein spoke of "a false idea of the role which mathematical and logical propositions play", and then identified this view with Hardy:

Consider Professor Hardy's article ('Mathematical Proof') and his remark that "to mathematical propositions there corresponds - in some sense, however sophisticated - a reality." (The fact that he said it does not matter; what is important is that it is a thing which lots of people would like to say.) (LFM [1939]: 239)

The last remark in parentheses is important. Just as it has been pointed out that St. Augustine was more sophisticated than the Augustinian Picture, it is undoubtedly true that G. H. Hardy was more sophisticated than the Hardyian Picture. What is important in each case is that in the words of Augustine and Hardy Wittgenstein found a model for the most serious temptations that he believed philosophers could fall prey to. To Wittgenstein, the most important way a philosopher of language can go wrong is by being misled by the Augustinian Picture; while the most important way a philosopher of mathematics can go wrong is by being misled by the Hardyian Picture.

What is so misleading about the Hardyian Picture? Wittgenstein is not objecting to the idea of a mathematical reality, as naive objections to Platonism do. What Wittgenstein is objecting to is a conception of mathematical reality that is independent of our practice and language and that adjudicates the correctness of that practice and language. The faulty conception is of a mathematical reality that is capable of overruling how we actually do mathematics.

If Wittgenstein had written a book on the philosophy of mathematics with a structure similar to the Investigations, that book might have begun with the following quotation from Hardy's A Mathematician's Apology:

I believe that mathematical reality lies outside us, that our function is to discover or

WITTG ENSTEIN' S PHILOSOPHIES OF MATHEMATICS 129

observe it, and that the theorems which we prove, and which we describe grandiloquently as our "creations", are simply our notes of our observations.s

Wittgenstein might have replied to this as he did in a meeting with Rush Rhees in 1938:

Certainly we may say that in our arithmetic it is a property of 3 that 3 + 3 = 6; and so that this proposition states a certain property of 3 in our arithmetic. But this would be a misleading way of speaking if it suggested that we are dealing ,here with a property which 3 has independently of any proposition in arithmetic; or that it is because of a certain property which 3 has that we say in arithmetic that 3 + 3 = 6.6

Wittgenstein's point goes beyond the context principle. What can be misleading in Hardy's words is that it makes it look as if there were two criteria for whether 3 + 3 = 6: (1) the computation or proof; and (2) the further checking of whether the results of this computation or proof match something else ("mathematical reality"). The Hardyian Picture is not only that there are two criteria, but that the second is the real one; proofs are only psychological devices to get us to see mathematical reality more clearly. The real warrant for the truth of our mathematical propositions comes not from proof, but from this reality. In fact, G. H. Hardy himself, deliberately exaggerating, comes close to saying this very thing. After drawing an analogy between a mathematician and "a man who gazes at a distant range of mountains and notes down his observations", Hardy writes:

The analogy is a rough one, but I am sure that it is not altogether misleading. If we were to push it to its extreme we should be led to a rather paradoxical conclusion; that there is, strictly, no such thing as mathematical proof; that we can, in the last analysis, do nothing but point; that proofs are what Littlewood and I call gas, rhetorical flourishes designed to affect psychology, pictures on the board in the lecture, devices to stimulate the imagination of pupils. 7

Thus, just as in the Augustinian Picture the sentence "that is a desk" points to a desk, in the Hardyian Picture a proof points to a mathematical reality. If that object is not a desk, then the sentence is wrong; if mathematical reality is different, then the proof is wrong. But to Wittgenstein this account is no more satisfactory for mathematics than it is for our ordinary talk of desks and tables.

The issue here is whether sense can be made of anything overruling our mathematical language and practice, our proofs and computations. The picture is that contrary to our computation, it could be false that 3 + 3 = 6, or that contrary to our proof it could be false that there is

130 STEVE GERRARD

not a largest prime - false not in the sense of a slip of the pen or an arithmetical error or the use of an invalid inference, but false in the sense that the computation or proof has failed to accurately represent mathematical reality.

This might be considered a skepticism about the truth of mathematics on the analogy of the familiar skepticism about the truth of our ordinary talk of objects. 8 We believe there is a desk here, but physical reality is different (perhaps there is only a Cartesian demon making us believe there is a desk); we believe that 3 + 3 = 6, but mathematical reality is different (perhaps a demon has misled us about our mathematical rules).

But such skepticism about the truth of our mathematical propositions would consistently lead to skepticism about the meaning of our mathematical propositions. It is part of the meaning of our mathematical terms '3' and '+' that 3 + 3 = 6. We would not have good reason to translate foreign terms as "3", "6', "+", and "=" unless such a translation kept the truth of the equation. But how could a demon mislead us about the meaning of our terms?

Let us review the situation. The Hardyian Picture holds that the real criterion for the truth of our mathematical propositions is the nature of a mathematical reality independent from our practice and language, and that our proofs only point to that reality. (Notice that unlike some traditional attacks on Platonism, the issue here is not whether we can perceive this reality, but whether this reality can serve as a warrant for our proofs.) But this implies that the meaning of our mathematical terms is also independent of our practice and language. But, contra the Hardyian Picture, our terms and proofs are only meaningful (in other words, are only terms and proofs as opposed to ink marks or grunts) in the context of our language.

Much of the attack on the Augustinian Picture in the Investigations seeks to establish the importance of the point that expressions are expressions only in the context of a language. In this case there is nothing special about mathematical language: just as "3 + 3 = 6' is meaningful only in the context of our language; my pointing to a desk is only pointing to a desk within our language-game; and my statement "the cat is on the desk" is only about animals and furniture in the background of our language.

If meaning is a function of practice, then there is no room for any determinations of meaning that are not part of our practice. The mis-


take is not in talking of a mathematical reality, the mistake is to think: that the meaning of this reality can be independent of our practice; that we can say something more than the proof; and that mathematical reality can be opposed to proof. Thus the Hardyian Picture of a mathematical reality adjudicating our practice has become, in a phrase Wittgenstein sometimes used, a wheel turning idly. As Wittgenstein wrote: "Even God can determine something mathematical only by mathemat-ics" (RFM [1941]: VII.41). .

The Hardyian Picture is the constant in Wittgenstein's philosophies of mathematics; as different as the calculus and language-game conceptions are, they are both motivated by an opposition to the Hardyian Picture's view that there is an underlying mathematical reality which our language and practice must mirror or· be responsible to. In the calculus period Wittgenstein's point can be put this way: there are no criteria for mathematical correctness outside of the rules of individual calculi. In the language-game period the point becomes: there are no critieria for mathematical correctness outside of mathematical practice.

It is one thing, however, for Wittgenstein to say that the Hardyian Picture is wrong; it is another to give a positive account of mathematics in terms of language and language-games. This is what the calculus and language-game conceptions are each designed to do, and we turn to these very different positive accounts next.

3.

As is well known, the earlier Wittgenstein looked at meaning and language in terms of logical form and definiteness of sense, while the later Wittgenstein looked to language-games and forms of life. In between, however, there was a distinct transitional theory of language -the calculus conception.

The transitional Wittgenstein wrote:

Grammar is not accountable to any reality. It is grammatical rules that determine meaning (constitute it) and so they themselves are not answerable to any meaning and to that extent are arbitrary. (PG [1932-34): 184)9

This is obviously part of Wittgenstein's rejection of the Hardyian Picture's external criteria which judge language. However, the calculus conception is itself an incorrect account, failing to capture the openended character of mathematics. Godel's theorem, by showing that any

132 STEVE GERRARD

formal axiomization of arithmetic will be incomplete, demonstrates conclusively that any conception of mathematics as simply a calculus fails. In addition to this problem, the calculus conception fails to give a correct account of mathematical language. The conception unnecessarily restricts the scope of mathematical language, reducing it to mere syntactical rules. Furthermore, as heavily as the conception depends on the notion of rules, there is here no analysis of that notion: any account of the application of a calculus or a critique of what it means to follow a rule is pushed aside only to be ignored. No account of the change or growth of mathematics can be given; the rules are all we have and that is all we can say. The result is a conception of mathematical language that is, whatever Wittgenstein's intentions, divorced from human use or purpose.

The language-game conception overturns this. There meaning and truth can be accounted for only in the context of a practice, and mathematics is examined by seeing what special role it plays in our lives and its special relationship to our other language-games. The calculus conception was unable to account for the change and growth of mathematics, while the language-game conception emphasizes this. The bizarre views that have earned many commentators' derision drop out.

It is not that Wittgenstein's calculus period was a complete disaster, nor is our point simply that at one time Wittgenstein's views were confused but he later corrected them. Rather, the language-game conception is an extension and revision of the earlier view and not a complete rejection of it. The mistakes of the calculus period were not haphazard, but had a point; a point that could not reach complete fruition until the language-game period.

Wittgenstein said at the beginning of the transition that "[c]ontradiction is between one rule and another, not between rule and reality" (CAM I [1931-32]: 92). Wittgenstein's transition is characterized in many ways by his working out of this theme. What he is doing is trying to account for the meaning and objectivity of mathematical language (and indeed of all language) without the Hardyian Picture's misleading notion of a transcendental mirroring of reality. In seeing that Wittgenstein is expounding this theme, we can rationalize many of the mistakes of the calculus period. Many of those mistakes come from reaching too far and from unnecessarily restricting the scope of language.


From the texts of the transitional period we can abstract four interrelated principles that characterize Wittgenstein's calculus conception:

a) the autonomy principle: each individual calculus is a closed, selfcontained system, having no external critique;

b) there is a sharp separation between a calculus and its application or use;

c) any revision of the rules, no matter how minor, means an entirely new calculus; and

d) we can only discuss individual calculi, we can assert no requirements of calculi in general.

These four principles (and their corollaries) ripple throughout the transitional works. Wittgenstein's changing philosophies of mathematics is the story of how each of these principles is modified or discarded as the notions of language-games and forms of life come to the fore.

The autonomy principle (a) is never completely discarded; properly modified it will play an important part in Wittgenstein's later philosophy. At first look it seems little more than a restatement of the context principle.

A name has meaning, a proposition has sense in the calculus to which it belongs. The calculus is as it were autonomous. - Language must speak for itself ....

The meaning is the role of the word in the calculus. (PG [1932-34]: 63)

There is more here than the context principle, however. At this stage the autonomy principle denies the possibility of any critique of language. Wittgenstein often makes this point rather bluntly:

A mathematical system, e.g., the system of ordinary multiplication, is completely closed. I can look for something only within a given system, not for the system. (WWK [1929]: 35).

I might as well question the laws of logic as the laws of chess. If I change the rules it is a different game and there is an end of it. (CAM I [1930]: 19)10

This is part of Wittgenstein's opposition to the Hardyian Picture, a preliminary step in the rejection of the view that in some transcendental sense language must mirror the world.

The emphasis at this stage is on rules, but although the rules bear the entire brunt of meaning there is no critique of them here. Rules are seen as meaningful (indeed as the sole criterion for meaning) totally apart from their use or a background practice. This will obviously change in the language-game conception.

Part of the problem of a lack of critique of rule following involves

134 STEVE GERRARD

principle (b) where there is a sharp separation between the calculus and its application. In his transitional years, what Wittgenstein usually means by "calculus" is an uninterpreted logical or mathematical language - the syntax alonell (see WWK [1930]: 106). "If I am asked, then", Wittgenstein says, "what it is that distinguishes the syntax of a language from the game of chess, I answer: It is its application and nothing else" (WWK [1930]: 104). He continues later: "Detached from its applications and considered by itself it [syntax] is a game, just like chess" (WWK [1930]: 105).

It is not very clear (and that is a part of the problem with the calculus conception) what Wittgenstein means by application here. As it is commonly used, "application" can have two different meanings in the context of mathematics; the distinction is between the application of the calculus and the application of the rules. In the former, call it (1), we can speak of applying a calculus to something else. An example would be using arithmetic to say that if there are two apples in the refrigerator and two apples on the table, then there are four apples in the kitchen. In the latter, call it (2), it is an application of the rules of arithmetic that the series n + 2 is continued 1000, 1002, 1004. It appears that at this stage of his thought Wittgenstein was not concerned with the difference between (1) and (2), but usually thought of application as meaning practical use (the application of a calculus as a whole, not the application of the rules).

One reason for the lack of clarity here is that it is not just that calculus and application (in any sense) are completely separated, but just as in the Tractatus; where problems of epistemology and application are shunted aside as not germane to philosophy, here application is separated from the calculus only to be ignored. "Mathematics is always a machine, a calculus", Wittgenstein said, "[t]he calculus does not describe anything. It can be applied to everything that allows of its application" (WWK [1930]: 106).12 The motivation for this view is the rejection of the Hardyian Picture's correspondence of mathematics with reality. But the (unnecessary) price Wittgenstein pays here for that rejection is to separate mathematical language not only from this reality, but from human use or practice as well. Here we see the separation without any further account of application or the relationship between calculus and application. Both the examination of the application of a calculus and the examination of following a rule belong to a later Wittgensteinean stage. Indeed, once Wittgenstein saw that rules have


no meaning apart from a practice he had to reject the calculus conception.

Principle (c) causes more trouble. It claims that any revision of the rules means an entirely new calculus. 13 This peculiar view can be explained with reference to Wittgenstein's favorite example of chess. At one time the rules of chess were different from the modern ones. Pawns could only be advanced one square at a time - even the first time they were moved. This slowed the opening of the game considerably, as usually in the opening a player advanced a pawn once and then on the very next move advanced it again. In order to remedy this a new rule was added: the first time a pawn was moved it could be moved either one or two squares. The en passant rule was then added so no pawn could be promoted without the possibility of it being captured by another pawn. All this seems very reasonable, as do the following judgments: modern chess is a faster game than old chess; modern chess is a better game than old chess; and modern chess without the en passant rule would result in some "cheap" victories. In addition, certain middle and endgame positions from old chess are the same as in modern chess, and we can compare how different players handled similar situations. Many themes present in old chess are useful for modern chess. Again, all this seems reasonable, but under Wittgenstein's calculus view the above judgments would be completely senseless. There can be no such thing as the evolution of a game; a game is completely characterized by its rules alone, and if any rule is different, then all that can be said is that they are different games. There can be no such thing as an improved chess; there is only chessl and chess2 and chess3' Since all we can appeal to is the rules, when the rules are at all different there is no more basis for saying chessl and chess2 have anything in common than saying that cat and cattle have anything in common.

Wittgenstein explicitly compares the situation in chess with the situation in mathematics.

We cannot reduce mathematics; we can only make a new one. The size of a proof can be reduced, but not the body of mathematics. The same point can be made about chess. Suppose chess is defined by the way we move pieces, and that a new way of producing a certain move is discovered. This is not to reduce the old game; it is to make a new game. (CAM II [1933-34]: 71)

Again, this is the autonomy principle gone too far. The number system with irrationals is obviously different from the number system with only

136 STEVE GERRARD

rationals. But it is an extension of the old system, not something completely new and different. This is what the transitional Wittgenstein explicitly denies (see WWK [1929]: 35-36) and is what the later Wittgenstein explicitly asserts in the Investigations (see PI: 67).

Principle (d) emphasizes this sharp separation between different calculi. 14 Since there can be no reference to anything outside of the rules (including their purpose), and since there is no basis to assert that calculi have anything in common, then all that we can do is discuss individual calculi: we can assert nothing about calculi in general. Under this principle it makes no sense to require that for something to be a calculus at all it must be consistent, nor do we have a basis for saying that one calculus is more complete than another.

4.

The test case for my theory of Wittgenstein's transition is his notorious remarks on contradiction. Those remarks have puzzled and even irritated many commentators. In 1931 Wittgenstein said:

I want to object to the bugbear of contradiction, the superstititious fear that takes the discovery of a contradiction to mean the destruction of the calculus. (WWK [1931]: 196)

This typical quotation seems to justify one commentator's statement that "[n]ow on the face of it, the views Wittgenstein puts forward here are absurd. ,.15 In remark after remark from 1929 through the 1930s, Wittgenstein seems to be doubting the harm of contradiction. 16 It is almost as if he was following the Walt Whitman school of contradiction: "Do I contradict myself? / Very well, then, I contradict myself. / (I am large, I contain multitudes).,,17

But more than a decade later, what Wittgenstein decides to include on the subject of contradiction in the Investigations is perfectly reasonable.

The fundamental fact here is that we lay down rules, a technique, for a game, and then when we follow the rules, things do not turn out as we had assumed. That we are therefore as it were entangled in our own rules.

This entanglement in our rules is what we want to understand (i.e. get a clear view of) ....

The civil status of a contradiction, or its status in civil life: there is the philosophical problem. (PI: 125)

Here, far from debunking the problem of contradiction, Wittgenstein


is trying to get a clear view of why a contradiction does mean the destruction of a calculus, of what it means to be entangled in our own rules.

What we see here is Wittgenstein's two different philosophies of mathematics, both partly motivated by an opposition to the Hardyian Picture. The crucial fact is that Wittgenstein's Walt Whitman theory of contradiction follows directly from the calculus conception's principles, but the language-game conception rejects that theory' by overturning those principles.

The autonomy principle (a) quickly leads to the transitional Wittgenstein's views on the harmlessness of a contradiction in a calculus. Our syntactical rules may allow us to produce a sentence of the form 'F & - F', but since under the calculus conception the rules of the calculus itself are the only criteria for the meaning of the calculus's expressions, then there is no standpoint from which to judge such sentences a problem. The rules are not about anything, so they cannot come into conflict with anything. ("[M]athematics is a calculus and hence isn't really about anything" (PG [1932-34]: 290).) It cannot even be claimed that the rules come into conflict with each other, for if all we have is the syntax (the rules of the calculus), then the rules themselves are the final court of appeal. The rules determine what the calculus is, and if the rules produce F & -F then that is all there is to it: we have a calculus with F & -F just as there are calculi with P v -Po

If you change the rules to disallow sentences of the form F & -F, then according to principle (c) you have changed the meaning and moved to a new calculus; you have not corrected the old one (just as chessz is a different - not a better - game than chessl)' And principle (d) rejects the requirement that all calculi be consistent, and indeed, holds that any such requirement for all calculi would be senseless.

The calculus principles, while opposing the Hardyian Picture, have restricted too much and resulted in seeing the fear of contradiction as a superstition.

But when considered from the language-game conception consistency is not an optional characteristic of calculi, nor is it a superstitution. The point, once again, can be made with reference to chess. In the Investigations Wittgenstein writes: "Let us say that the meaning of a piece is its role in the game" (PI: 563). (Note that without further interpretation of "role" this sentence would be accurate for both the calculus and language-game periods.) But Wittgenstein then imagines

138 STEVE GERRARD

that the rules of chess state that the king will be used at the beginning of the game to determine which player gets white: "To this end one player holds a king in each closed fist while the other chooses one of the two hands at random." Is this rule on the same level as the rule that the chess game is won when the opponent's king cannot escape capture? Wittgenstein implicitly denies this, and then writes: "The game, one would like to say, has not only rules but also a point" (PI: 564). This last sentence is crucial. It keeps the calculus conception's emphasis on rules, but adds the new theme that the rules must be placed in a context of human activity.

Take three games. The first is our chess, the second is chess with Wittgenstein's white-choosing rule, and the third is like our chess except that the winner is the one who first moves her queen rook. Compare this to three calculi. The first is a standard predicate calculus. The second is like the first, but all variables must be underlined. The third, like Frege's, can produce Russell's paradox. Assuming standard human characteristics and goals, one would say that the white-choosing rule is an inessential modification of our chess, while the queen-rook rule destroys the point of the game, preventing it from serving all the purposes we now use chess for. (White would always win in two moves.) Similarly, the variable underlining rule changes nothing essential, whereas the inconsistency of the third calculus destroys the point of the calculus. For, under Wittgenstein's later conception, calculi are not seen as isolated systems of rules, but are systems of rules which have a role - and a point - in our lives.

This returns us to principle (b). In Wittgenstein's later conception one cannot separate a calculus from at least one sense of application. Being a calculus already implies an application, namely, to calculate. We may get truths from falsehoods or falsehoods from falsehoods, but the absolute minimum requirement of a calculus is that it not yield falsehoods from true premises. IS If we had such a calculus we might just as well consult the entrails of a bull. And this, of course, is what happens with inconsistent calculi: from true premises one can deduce falsehoods; indeed, one can deduce anything at all. 19

Looked at from the calculus conception, an inconsistent calculus is just another calculus. In order to oppose the Hardyian Picture Wittgenstein had stripped away any constraint on meaning not due to syntactical rules. In so doing Wittgenstein denied the harm of contradiction and was led to bizarre bugbear statements. But under the language-


game conception the opposition to the Hardyian Picture remains without paying the calculus conception's unnecessary price. The new goal is to describe the harm without falling prey to the misleading picture.

What is wrong with an inconsistent calculus is not that it somehow misrepresents mathematical reality (as in the Hardyian Picture), but that in producing falsehoods from truths and thus allowing anything to follow, it fails to do what we want our calculi to do, namely, to calculate. The situation is like the strange tribe

who used money in transactions; that is to say coins, looking like our coins, which are made of gold and silver and stamped and are also handed over for goods - but each person gives just what he pleases for the goods, and the merchant does not give the customer more or less according to what he pays. In short this money, or what looks like money, has among them a quite different role from among us. (RFM [1937-38]: 1.153; emphasis added)

Money has a special role in our lives, and this is what justifies translating foreign terms as "money". Mathematics has a special role in our lives and special characteristics, 20 and these are what justify calling alien practices "mathematics." An inconsistent calculus cannot serve this role. Wittgenstein's mature philosophy of mathematics saves objectivity without paying the Hardyian Picture's price of meaningless external criteria or paying the calculus conception's price of too restricted internal criteria. Mathematical objectivity and necessity are due to the special role of the mathematical language-game.

The general lesson of this specific look at contradiction is that an account of Wittgenstein's mature philosophy of mathematics should not saddle the language-game conception with the mistakes due to the calculus conception's principles. The Investigations (and some later sections of Remarks on the Foundations of Mathematics) emphasize and examine the change and growth in the language-games of mathematics. Rather than neglecting application, they concentrate on it. Instead of seeing mathematics as isolated calculi, they conceive it as a nexus of language-games, related to each other and embedded in our form of life. No longer is it forbidden to say anything about calculi other than give the rules - calculi have roles, and they can serve them more or less successfully.

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5.

The conception of language in general as a nexus of language-games is the view of the Investigations, and is, to say the least, well known. For too long, however, it has not been recognized that Wittgenstein has a coherent language-game conception of mathematics. This is partly due to the failure to recognize the calculus period and its demise. Most commentators have either felt obligated to defend the bizarre remarks of the calculus period, or alternatively, have ~ttacked those remarks without recognizing that Wittgenstein himself later saw the problems. Coupled with the Hardyian Picture, the recognition of Wittgenstein's two philosophies of mathematics should help overturn the black hole view of Wittgenstein's career. Stripped of the calculus conception, Wittgenstein's language-game conception of mathematics can now be examined unencumbered by the earlier conception's mistakes. 21

NOTES

* The following abbreviations are used in this article to refer to Wittgenstein's works: WWK: Ludwig Wittgenstein and the Vienna Circle: Conversations Recorded by Friedrich Waismann, ed. B. F. McGuinness, trans. J. Schulte and B. F. McGuinness, Oxford: Basil Blackwell, 1979; CAM I: Wittgenstein's Lectures: Cambridge, 1930-32, ed. D. Lee, Chicago: University of Chicago Press, 1982; CAM II: Wittgenstein's Lectures: Cambridge, 1932-35; ed. A. Ambrose, Chicago: University of Chicago Press, 1982; PG: Philosophical Grammar, ed. R. Rhees, trans. A. Kenny, Oxford: Basil Blackwell, 1974; BIB: The Blue and Brown Books, Oxford: Basil Blackwell, 1958; LFM: Wittgenstein's Lectures on the Foundations of Mathematics: Cambridge, 1939, ed. C. Diamond, Ithaca: Cornell University Press, 1976; RFM: Remarks on the Foundations of Mathematics, ed. G. H. von Wright, R. Rhees, G. E. M. Anscombe, trans. G. E. M. Anscombe, revised ed., Cambridge: MIT Press, 1978; PI: Philosophical Investigations, ed. G. E. M. Anscombe, R. Rhees, trans. G. E. M. Anscombe, New York: Macmillan Company, 1953; Z: Zettel, ed. G. E. M. Anscombe, G. H. von Wright, trans. G. E. M. Anscombe, Berkeley and Los Angeles: University of California Press, 1970.

References to PI and Z are to remark number; references to RFM are to part number (Roman numerals) and remark number (Arabic numerals); and references to the other works are to page numbers. As the evolutionary nature of Wittgenstein's work is an important theme of this article, following the abbreviation for the book in the text I have put in brackets the date of the book or the part of the book from which the quotation comes. 1 Michael Dummett, 'Wittgenstein on Mathematics', Encounter 50, (March 1978), 68. 2 Calling the black hole view a "standard view" does not, of course, mean it is the only view. There are those who, like Dummett, read Wittgenstein as a radical in the philosophy of mathematics, but, unlike Dummett, think Wittgenstein is right. They dissent from the black hole theory for different reasons than I do. Two notable examples are Crispin


Wright, Wittgenstein on the Foundations of Mathematics, Cambridge: Harvard University Press, 1980; and S. G. Shanker, Wittgenstein and the Turning-Point in the Philosophy of Mathematics, State University of New York Press, Albany, 1987. 3 W. W. Tait writes that, properly examined and freed of confusions, "Platonism will appear, not as a substantive philosophy or foundation of mathematics, but as a truism" ('Truth and Proof: The Platonism of Mathematics', Synthese 68, (1986), 342). In this section I am heavily indebted to this article. 4 There is ample evidence that Wittgenstein was familiar with both Hardy and his works. See John King, 'Recollections of Wittgenstein', in Rush Rhees (ed.), Recollections of Wittgenstein, Oxford University Press, Oxford, 1984, p. 73; G. H. 'von Wright, A Biographical Sketch, in Norman Malcom, Ludwig Wittgenstein: A Memoir, Oxford University Press, Oxford, 1958, p. 6; Wolfe Mays, 'Recollections of Wittgenstein', in K. T. Fann (ed.), Ludwig Wittgenstein: The Man and the Philosopher, Humanities Press, New Jersey, 1967, p. 82; and Garth Hallett, A Companion to Wittgenstein's 'Philosophical Investigations', Cornell University Press, Ithaca, 1977, p. 766. References to Hardy in LFM are listed in that book's index. Wittgenstein also mentions Hardy in CAM II [1932-33]: 215-20, 222, and 224-25; in BIB [1933-34]: 11; and quotes from 'Mathematical Proof' in Z [1945-48]: 273. 5 G. H. Hardy, A Mathematician's Apology, Cambridge University Press, Cambridge, 1967, pp. 123-24. 6 Rush Rhees, 'On Continuity: Wittgenstein's Ideas, 1938', in Discussions of Wittgenstein, Routledge & Kegan Paul, London, 1970, p. 109. 7 G. H. Hardy, 'Mathematical Proof', Mind 38, (January 1929), 18. Hardy continues: "This is plainly not the whole truth, but there is a good deal in it." 8 See W. W. Tait, op. cit., 343-45. Once again I am heavily indebted to this article. 9 See also PG [1932-34]: 89: "[L]anguage is not something that is first given a structure and then fitted onto reality", and even more simply PG [1932-34]: 143: "It is in language that it's all done." 10 For more on the early transition's comparison between the rules of chess and language see WWK [1930]: 134: "[I]t is only the rules of the game that define this [chess] piece. A pawn is the sum of the rules according to which it moves (a square is a piece too), just as in language the rules of syntax define the logical element of a word." 11 There are troubles here from the very beginning. How is something logical, mathematical, or even a language if it is uninterpreted? 12 See also WWK [1930]: 114: "The calculus can be applied to anything that admits of such application. (And you cannot say anything that goes beyond this.)" 13 For representative statements see PG [1932-34]: 374-75 and WWK [1929]: 35-36. 14 See WWK [1930]: 133; WWK [1931]: 149 and 202; and PG [1932-34]: 369. 15 Charles S. Chihara, 'Wittgenstein's Analysis of the Paradoxes in his Lectures on the Foundations of Mathematics', Philosophical Review 86 (1977), 369. 16 See also WWK [1930]: 120, 131; WWK [1931]: 174,208; PG [1932-34]: 303-05; CAM II [1933-34]: 71; LFM [1939]: 206-07, 211, 224-25; and RFM [1937-38]: App. III. 17. 17 Leaves of Grass, "Song of Myself", verse 51. 18 Wittgenstein was late in seeing the implications of this point. (The calculus conception held sway the longest in the area of contradiction.) In LFM [1939]: p. 230, Wittgenstein writes: "You could say that if we allow a contradiction, in the sense that we allow anything to follow from it, then we have given up any idea of a calculus at all." This is right (and, indeed, is my point), but at the time Wittgenstein mistakenly thought that it

142 STEVE GERRARD

was false that one may be able to derive any sentence from a calculus which contains a contradiction without actually going through the contradiction. (Chihara, op. cit., takes Wittgenstein to task for this.) Thus he thought he could have an ad hoc solution to contradiction: when a contradiction is discovered, simply add an ad hoc rule prohibiting the drawing of any conclusions from the contradiction. Even this serious mistake was partly motivated by opposition to the Hardyian Picture. Wittgenstein was trying to say that it is we who are in charge llere; we are not being pushed from the outside. The community of language users makes the rules, and if things do not turn out as they intended (e.g., they get F & -F), then they can simply change the rules. 19 My colleague Sahotra Sarkar advises me that I need only to assume that the logical system is of such a type and has such a notion of derivability that it permits all that goes on in classical mathematics. 20 Chief among these special characteristics is that the statements of mathematics are non-revisable by sensory experience. This partly separates a proof from an experiment. A full account of Wittgenstein's language-game conception of mathematics would examine this more fully. 21 It would be impossible to exaggerate the help I received on an ancestor of this article from Leonard Linsky and especially W. W. Tait. I am also grateful to Lydia Goehr for her helpful criticisms.

Dept. of Philosophy Boston University Boston, MA 02215 U.S.A.

JULIET FLOYD

WITTGENSTEIN ON 2,2,2 ... : THE OPENING OF

REMARKS ON THE FOUNDATIONS

OF MA THEMA TICS!

l.

If we consider Wittgenstein's career as a whole, it is clear that he wrote more on philosophy of logic and mathematics than on any other subject. Yet his writings on these topics have exerted little influence. Indeed, the tide of response to Remarks on the Foundations of Mathematics -which contains the bulk of his later views of mathematics - has been for the most part negative, and many able readers have concluded that Wittgenstein was simply out of his depth in the fields of mathematics and logic. 2 Thus the most pressing question with regard to Wittgenstein's discussion of mathematics - addressed as yet by relatively few commentators - is, Does it offer anything at all?

The opening sections of Remarks on the Foundations of Mathematics are, I shall argue, the beginnings of a powerful and total reworking of a traditional philosophical picture of logic and mathematics. Wittgenstein is out to question whether the hallowed earmarks of logical and mathematical truth - its necessity, a prioricity, self-evidence and certainty - may serve as the appropriate starting point for philosophizing, or even whether these notions, in the end, make sense. Even more, he will question the very applicability of the notion of truth to socalled logical and mathematical "statements". The later Wittgenstein's conception of philosophy has long been a stumbling block for his readers. But the very strangeness of the opening questions of Remarks on the Foundations of Mathematics is highly revealing of Wittgenstein's aims: these questions are intended to slow up the too facile reasoning of the philosopher who fastens on the necessity of mathematical and logical inference as a peculiar philosophical datum. He challenges his interlocutor to explain precisely what it is he is trying to account for and what it is he is seeking. Wittgenstein's ultimate aim is to test the limits of idealized conceptions of logic in the doing of philosophy. He attacks the construal of formal logic as the overarching standard for clarity, as the basic model for the functioning of language in general, and as the key tool in the resolution of philosophical problems. (Such


144 JULIET FLOYD

a construal was central to the work of Frege, Russell and Wittgenstein, himself, in Tractatus.)

Wittgenstein is out to undercut the notion that particular claims must be made from within an over arching general philosophical conception or systematic logical structure. This means that he will continually question the urge to construe his own statements in general philosophical terms, that is, as part of a systematic a priori theorizing about language, or logic, or thought. Wittgenstein writes in dialectical form in order to expose the character of philosophical debate over the nature of logic and mathematics. The philosopher's task, according to Wittgenstein, consists in "assembling reminders for a particular purpose,,3 -that is, at a particular juncture in the philosophical discussion - in order to give us insight into the workings of our language. The profundity and impressiveness of philosophy retreats from purported answers to the nature and character of the questions themselves. 4

There is an impression, held by many readers of Philosophical Investigations, that Wittgenstein's interlocutor is a straw character whose queries, assertions and claims are those of no serious philosopher. I believe that no amount of argument or methodological clarity can totally lay such objections to rest. However, Wittgenstein seems to have been acutely aware of this. As I read him, the dialectical style of his later writing - and its seemingly interminable character - reflects his conception of the problems under discussion. We are left in the end with dispensable comments, for purposes of linguistics, empirical psychology or mathematical practice, but the point of the investigation is to show that what the essentialist says about language, thought and mathematics is equally dispensable.s This is not supposed to be demonstrated by a linear argument from fixed premises. The tone and manner in which Wittgenstein's own considerations emerge - which so many of his readers find frustrating and tortuous - is internal to the claims being made.

Wittgenstein's interlocutor reacts in an unguarded way, without refinement. He does not begin with a metaphysical conception. But as the interlocutor refuses, over and over again, to accept Wittgenstein's countersuggestions about the uses of various expressions, his words about "justification", "knowledge", "compulsion", "truth" and "proof" begin to take on a metaphysical cast. This is Wittgenstein's way of attempting to depict the move into a philosophical worry, i.e.,

WITTGENSTEIN ON 2, 2, ... 145

the origin of both particular philosophical accounts and the need for them. 6 Clearly, if there is such a stage in philosophizing to be unearthed, it cannot itself be made out in systematic or general terms; if someone (including himself) tried to do so, Wittgenstein would no doubt have subjected these terms themselves to the same sort of scrutiny. The roots of philosophy's demands for systematic accounts are divergent and multifarious. Wittgenstein's continued sparring with the interlocutor is meant to show this, and at the same time to portray the task of clarification as never definitively completed. The interlocutory voice is not meant to be silenced; illumination comes from the shifts and modulations of its tone and through the connections drawn between questions in the course of the conversation. The simplicity and naiVete of the interlocutor (whose remarks, at the same time, are never foolish or off the point) is also intended to get us to ask the question, How much more sophisticated and explanatory are the full-blown theories which so attract us (including Wittgenstein himself)? It is an open question how much distance lies between a given, more refined view and the utterances of the interlocutor. And Wittgenstein intends to get us to see that this distance is always less than we might have initially supposed.

The force of Wittgenstein's method - insofar as it attempts to depict the roots and seeds of philosophical puzzlement -lies in the details, the inner gropings of the exchanges between the interlocutor and Wittgenstein. Too few of Wittgenstein's commentators (whether interpreters or critics) have been willing to offer detailed exegesis of his interlocutory debates (especially in the case of Remarks on the Foundations of Mathematics). But engagement with the text is the only way to see what the method in the end amounts to. The remainder of this paper will attempt to show, by way of example, the value of such interpretive scrutiny. My focus, after a brief discussion of the textual context of Part I of Remarks on the Foundations of Mathematics, will be the first three sections of that book. In these sections, Wittgenstein attempts to unearth the roots of philosophical wonder about the nature and necessity oflogical and mathematical inference. He constantly challenges the interlocutor to rethink his (pre )conceptions of necessity, knowledge and truth so as to reflect our actual use of these notions. The intended result is to shock us into asking ourselves whether we are as clear as we might have supposed about what inference and necessity really involve.

146 JULIET FLOYD

2.

The first sections of Remarks on the Foundations of Mathematics were not originally intended by Wittgenstein to stand on their own. They form the initial paragraphs of the second part of the so-called "early version" of Philosophical Investigations, composed between 1936 and 1937. This "Friih version" is a typescript consisting of two parts.7 The first part corresponds to a substantial draft of th,e first 188 sections of the final published version of Philosophical Investigations, while the second focuses on the philosophy of logic and mathematics. In 1938 Wittgenstein wrote a preface to the entire typescript and submitted it to the Cambridge University Press. Though the Press agreed to its publication, Wittgenstein never allowed the book to come to print. 8

Von Wright hypothesizes that Wittgenstein's hesitation "was connected with his continued work on the second part of the book dealing with the philosophy of mathematics". 9 This work Wittgenstein never lived to complete. He set aside the second part of the manuscript, reworked it,1O and finally abandoned it in 1944. It has been published posthumously as Part I of Remarks on the Foundations of Mathematics. 11 Thus it is clear that the text of Remarks on the Foundations of Mathem~tics lacks some of the historical authority and integrity of Philosophical Investigations and must be used with care. Nevertheless, I believe it can fruitfully sustain detailed scrutiny. Its first three sections are especially noteworthy because they form the branching point of Wittgenstein's earlier and later drafts of Philosophical Investigations. We may think of Remarks on the Foundations of Mathematics, Part I, Section 1, as initiating an alternate trajectory for the first 188 remarks of Philosophical Investigations. 12

The first two sections of Remarks on the Foundations of Mathematics are almost identical with Sections 189-90 of Philosophical Investigations, and, as I have just said, the whole of part I of Remarks on the Foundations of Mathematics originally followed (a draft of) Philosophical Investigations Sections 1-188. This explains its rather abrupt beginning, which examines, as if out of nowhere, the notion of the "steps ... determined" by an algebraic formula. 13 In the framing discussion (i.e., the earlier sections of Philosophical Investigations and the "Fruhversion") Wittgenstein had embarked on a lengthy investigation into the notions of understanding, meaning and thinking in connection with our command of language. At issue is the nature of the logic of


our language, and in what sense our use of language may be regarded as the operation of a calculus of definite rules. Wittgenstein writes:

F. P. Ramsey once emphasized in conversation with me that logic was a 'normative science'. I do not know exactly what he had in mind, but it was doubtless closely related to what only dawned on me later: namely, that in philosophy we often compare the use of words with games, calculi which have fixed rules, but cannot say that someone who is using language must be playing such a game. - But if one says that our linguistic expression only approximates to such calculi, one thereby immediately stands on the very brink of a misunderstanding. For then it may look as if what we were talking about in logic were an ideal language. As if our logic were, so to speak, a logic for a vacuum. -Whereas logic does not treat of language - or of thought - in the sense in which a natural science treats of a natural phenomenon, and the most that can be said is that we construct ideal languages. But here the word "ideal" would be misleading, for it sounds as if these languages were better, more perfect, than our everyday language; and as if the logician were needed to show people at last what a proper sentence looked like.

All this, however, can only appear in the right light when one has attained greater clarity about the concepts of understanding, meaning, and thinking. For it will then also become clear what can lead us (and did lead me)14 to think that if anyone utters a sentence and means or understands it he is thereby operating a calculus according to definite rules. 15

Among central questions examined in Philosophical Investigations are: What is it that we learn when we learn language?; What is it to understand a word, or a sentence?; How is it that words, sentences, have meaning at all?; And, is the command of language itself a special kind of knowledge? These are for Wittgenstein simultaneously part of an investigation of the scope and nature of what he views as logic, that is, the logic of our language. Evidently, in Philosophical Investigations Section 81, Wittgenstein is revealing a plan to investigate the limits and presuppositions of philosophical uses of "ideal languages", including formalizations of what we have come to think of as logic, i.e., formalized languages whose grammatical structures are the truth-functional and quantificational structures developed by Frege and Russell. In Wittgenstein's later philosophy, logical structure is not conceived of as lying behind language awaiting discovery through analysis of the proposition, the concept, or the nature of logical inference. Instead, structure is to be exhibited and elicited by "comparing" our uses of language to games with fixed rules (the simplified "language games" of, e.g., Philosophical Investigations). But this indicates that for Wittgenstein our language is not itself a game with fixed rules; that is, our language is not itself a "language game". 16

148 JULIET FLOYD

The example of an algebraic formula is brought into Wittgenstein's discussion in Philosophical Investigations Section 146 as a paradigm of what it is to operate in accordance with a definite rule. In the simplified "language game" of Section 143, we are asked to imagine that "when A gives an order, B has to write down series of signs according to a certain formation rule [Bildungsgesetz]".17 And now we imagine teaching a pupil to write out the series of numbers from zero to nine. But then "the possibility of getting him to understllfld will depend on his going on to write it down independently,,18 - that is, in his being able to follow a rule. What enables him to follow the rule? We can imagine that the pupil is unable to grasp the rule of the series; that no matter how we encourage, blame, or play with him, he simply continues on differently, all the while calling his way "going on in the same way". 19 Wittgenstein emphasizes that we may imagine this,20 but imagining a scenario is not for Wittgenstein the same as understanding or making sense of it. Having a picture is not the same as using or applying it. Hence it is not clear that Wittgenstein wishes to say that we could make sense of such a case. Still, our capacity to picture it may allow us to reflect on the extent to which understanding may be fruitfully viewed as an activity governed by fixed rules - or even on the notion of what it is to operate with a definite rule in mind.

The rule of an arithmetic series expressed by an algebraic formula is a paradigmatic case of something we feel we need to grasp before we are to be capable of carrying out the correct development of a series. By analogy, the understanding of a word may be thought of as the grasping of a rule for its use. Is the rule itself then a Platonic entity? How do we reach or follow out its "extension", i.e., the things or situations to which it correctly applies? According to Wittgenstein's figure of speech, the rule for use of a word must be grasped before correct responses and utterances are possible?1 What the recalcitrant pupil shows, however, is that the framing of such rules alone will not make sense of our uses of language. For even in very simple cases (like 0,1,2,3,4,5,6,7,8,9) it is clear that an algebraic formula will not carry within itself the understanding of its application.22 We may be tempted at this point to draw a distinction between the expression of a rule (the algebraic formula) and the rule itself.23 But then, having drawn a systematic distinction between the two, we may begin to suspect that the rule, not the rule's expression, compels and makes possible an individual's correct responses. The analogy with understanding a linguistic expression may then incline us to think that the understanding


of the word, the rule, or concept grasped, is something other and more fundamental than any expression of the rule we can provide. The rule itself - or the understanding - determines something ahead of our applications of particular linguistic expressions. But since it is difficult to imagine what a self-interpreting rule would be, we are faced with a puzzle about how and in what sense a rule may determine its applications in advance. 24

Wittgenstein's framing of the problem of rule-following in terms of an analogy between the use of an algebraic formula and the use of a linguistic expression is no accident, as Investigations Section 81 shows. But the analogy is more complex than either the background of Tractatus or the text of Investigations straightforwardly indicate. For Wittgenstein pushes the analogy in several different directions. In Investigations the question of a rule's "determining the steps" ahead of time is examined as part of an effort to show the limits of conceiving of the meaningfulness of language as constituted by a set of definite rules. Various purported criteria of understanding are put forward as possible candidates for the role of "that which constitutes grasping a rule (or understanding a word)": an image (Vorstellung] (PI Sections 6,396), a picture [Bild] (PI Sections 6, 425-6), a text (PI Section 156ff), a sound (PI Sections 6, 156ff), a sensation (PI Sections 159-60, 243ff), a feeling (PI Section 184), an act or way of meaning (PI Sections 188, 190), an act of intuition or insight (PI Sections 186, 213-4), an intention (PI Sections 197, 337). None of these seem to be able to constitute or explain the application of a linguistic expression on their own.

But the analogy between a rule for the use of a word and the rule expressed by an algebraic formula has two sides, as the alternate trajectory of Investigations sections 1-188, in Remarks on the Foundations of Mathematics Part I, indicates. And in fact Wittgenstein's investigation of the notion of what it is to grasp a rule for the use of a word is meant to shed light in the other direction: on our understanding of what it is for an algebraic formula to "determine" the algebraic "steps". The Tractatus notion that the necessity of logic and mathematics could be in some way illuminated by means of the (linguistic) notion of grammar ("logical syntax") is still in play, though it has been substantially transformed. Now the notion of grammar is itself to be given content by way of an examination of our uses of language in particular contexts - including logical and mathematical contexts. How do we actually operate with algebraic formulas?

In Remarks on the Foundations of Mathematics the determination of

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algebraic steps by a formula is an example of the necessity of mathematical truth and logical inference. (In Tractatus it was intrinsic to Wittgenstein's attack on Frege's and Russell's conceptions of logical truth to view "proof" in logic in an algebraic way, as a purely mechanical transformation of symbols. 25 ) In Remarks on the Foundations of Mathematics Wittgenstein views the "steps" determined by an algebraic formula, the necessity governing the development of a mathematical series, and the inferential transitions determined bo/ the rules of logic as exactly parallel. (The same German word "Ubergang" is used for all three cases.) In Part I, Section 4, Wittgenstein writes:

"But then what does the peculiar inexorability of mathematics consist in?" - Would not the inexorability with which two follows one and three two be a good example?

and in Section 5:

"But doesn't it follow with logical necessity that you get two when you add one to one, and three when you add one to two? and isn't this inexorability the same as that of logical inference?" - Yes! it is the same ...

In the initial sections of Remarks on the Foundations of Mathematics, Wittgenstein seeks to "get clear what inferring consists in". 26 But he seeks to undermine the idea of locating necessity in one place, that is, in a fixed structure or grammar that may be delineated a priori. Remarks on the Foundations of Mathematics begins with an examination of our uses of the notion of algebraic determination in order to question the idea that we can make any general sense of what following an algebraic rule consists in. By analogy, Wittgenstein is thereby questioning whether we can make general sense of what inferring, understanding, or using a word in accordance with its grammar or meaning consist in. His attack on a fixed sense of "determination" is an attack on the idea of necessity as a clear phenomenon, and so, a fortiori, a challenge to the idea that logic has an interesting and unique characterization.

3.

In the original manuscript (the Fruhversion) and in Philosophical Investigations's version of the first section of Remarks on the Foundations of Mathematics Part I, Wittgenstein is responding to the interlocutor's charge that in the preceding discussion Wittgenstein has in some way wished to deny, in a skeptical vein, that there is an appropriate sense


in which an algebraic formula may be said to "determine the steps". The interlocutor objects,

"[But] are the steps then not determined by the algebraic formula?,,27

to which Wittgenstein responds,

- The question contains a mistake.28

Clearly Wittgenstein wishes to fend off the interlocutor's attribution of skepticism. We need to ask what sort of "mistake" the interlocutor has made. Wittgenstein's response (with which Remarks on the Foundations of Mathematics opens) makes this only partially clear.

We use the expression: "The steps are determined by the formula ... " How is it used?,,23

Wittgenstein's question insinuates that the interlocutor's misunderstanding is about this, i.e., the use of an expression. How is calling attention to the use of an expression intended to unmask the interlocutor's mistake? In a sense, my entire reading of Section 1 will be required to show how this might happen. There is no simple "mistake" or misuse of language involved in the interlocutor's question, and Wittgenstein invokes no theory of meaning (e.g., of meaning as use) to refute some independent interlocutory thesis. Instead, Wittgenstein immediately goes on to respond to his own question in what I shall view as six different ways. He fully knows that much of what he says will seem off the point to those who would ask the interlocutor's question. But once these responses to his own question are assembled Wittgenstein has succeeded, at least for the moment, in shifting the burden of explication onto the interlocutor, in effect making a (reasonable?) demand that the interlocutor specify what more he wants from the notion of determination and what more is left out to be accounted for.

The first response Wittgenstein offers to the question "How is the expression used?" sounds quite behavioristic:

We may perhaps refer to the fact that people are brought by their education (training) so to use the formula y = x 2 , that they all work out the same value for y when they substitute the same number for X. 3D

Wittgenstein's response suggests that the interlocutor who took Wittgenstein's earlier words to deny that the steps are determined by

152 JULIET FLOYD

the formula has misunderstood; for Wittgenstein can certainly find a use (so he seems to be saying) for the expression "the steps are determined by the algebraic formula". But was that all that was in question? Surely what bothered the interlocutor was not merely finding a sense for this series of eight words, but a concern that something essential to the notion of determination (perhaps its "compulsion", its "necessity", or its "rule-governedness") was being denied. Simply finding a use for an expression - particularly a use appealing so prominently to the notions of training, education and sameness of response - cannot touch that worry we may feel. So the interlocutor is bound to find Wittgenstein's answer here grossly irrelevant. Of course, this objection cannot rule out Wittgenstein's answer to the question about how the expression is used as false, or even inappropriate; and Wittgenstein's suggestion certainly raises a question about what more the interlocutor is after. Nevertheless, there are grave difficulties facing any attempt to align Wittgenstein's answer with the interlocutor's concerns. Viewed as a direct response, it seems crudely behaviorist. In fact, Wittgenstein's use of "Abrichtung", translated as "training", is bound to invite this reading; "abrichten" is the verb for training or breaking in an animal, or coaching or drilling someone, as if by rote?1 Is Wittgenstein then denying that there is any sense of what Kant called "inward necessity" for the people computing the square of x? No. (See my discussion of this point in Section 4 below.)

The behavioristic reading of Wittgenstein's suggestion is equally well invited by his second response:

Or we may say: "These people are so trained that they all take the same step at the same point when they receive the order "Add 3"." We might express this by saying: for these people the order "Add 3" completely determines every step from one number to the next. (In contrast with other people who do not know what they are to do on receiving this order, or who react to it with perfect certainty, but each one in a different way. )32

Here Wittgenstein puts the notion of a command or order in the place of a formula. 33 The comparison or shift from "y = x2" to the imperative "Add 3" is reminiscent of the language game of Investigations Section 143, and is intended to offer the interlocutor a kind of anthropomorphic source of compulsion which might give countenance to the idea of determination the interlocutor wishes to secure. As in Investigations Section 143, it also places the notion of truth in the background, since imperatives (like rules) are either followed or not followed, but are

WITTG ENSTEIN ON 2, 2, ... 153

neither true nor false. "Determines" now means that educated people use the formula (and react to the order) as they were taught to, thereby always reacting in the same way, "with perfect certainty" at each stage.

As Wittgenstein says, however, "we might" have been inclined to express the idea differently, in terms of the notion of "complete determination". Why might this way seem to better express the necessity or compulsion the interlocutor feels in the steps taken with an algebraic formula? Since this use of "complete determination" goes along with a reference to "every step from one number to the next", we may at first be tempted to read "complete determination" as making implicit appeal to the notion of a function. The generality of the function (i.e., its being defined for all natural numbers), coupled with its being a function (i.e., its uniquely "associating" a single "output" with a "given" "input"), then seems to provide us with an explanation of what lies behind the "determination" in the cases described. It would be natural to take the first formula, y = x 2 , to express the squaring function, and to use it as a representation of the computation of a function at a (given) point. For someone educated in elementary arithmetic, the ability to respond correctly to arbitrary inputs is then a test of their grasp of the function. Similarly, the command to "Add 3" determines our steps because the function expressed by, e.g., y = x + 3 determines a unique answer as correct. The root of our idea would be this: since a function "determines" a value for a given input (in virtue of being a function), may we not better explain how the formula "determines the steps" by saying that it expresses or denotes a function, which then does the work of "determining the steps"?

In fact the word "function" [Funktion] appears nowhere in the passage.34 Wittgenstein's parenthetical remark wards off this Platonistic idea of "complete" determination, making clear that he means by it "complete determination of behavior", i.e., all people in this group react in the same way when asked to "Add 3,,?5 Although we may feel deprived of an essential concept, namely, that of a function, Wittgenstein is not recommending that we substitute the notion of "having received appropriate training" for the idea of "grasping a function". Rather, he is suggesting that an ambiguity lies in the notion of determination. In order to be justified in postulating the existence of a function we need more than a mere formula: we need a determinate mathematical system within which to work.

This interpretation is confirmed in the remainder of the section. In

154 JULIET FLOYD

Wittgenstein's third response, he suggests an alternative way to find a use for the expression "The steps are determined by the formula ... ":

On the other hand we can contrast different kinds of formula, and the different kinds of use (different kinds of training) appropriate to them. Then we call formulae of a particular kind (with the appropriate methods of use) "formulae which determine a number y for a given value of x", and formulae of another kind, ones which "do not determine the number y for a given value of x". (y = x2 + 1 would be of the first kind, y > x2 + 1, y = x 2 ± 1, y = x 2 + z of the second.) The proposition "The formula ... determines a number y" will then be a statement about the form of the formulae. 36

Once again, Wittgenstein resists appeal to the notion of a "function". The italicized "Then we call" is meant to shift our focus from thinking about what the formulas denote (those of the first kind, as we might say, denote or express total functions on the integers; those of the second kind denote non-functional relations) to what we do, viz., define a notion of "determination" by way of our classificatory system. "The formula y = x 2 determines the number y for a given value of x" becomes an expression of how we have decided to classify the formula; it is a statement about the "form" of the formula. Not, however, literally its mere shape. The activity of "sorting shapes" usually requires something like putting circles with circles and squares with squares, or like outlines with like outlines. But there is little, spatiotemporally speaking, which the shapes of formulas of the same kind in this system of classification have in common.37 The "form" of a formula is not for Wittgenstein merely its syntactic form; it is instead its kind relative to a practice in which we are trained. In this case, assuming our training in the use of particular formulas (as, e.g., in the first two of Wittgenstein's responses), we can reflect, in turn, on this use of these formulas and thereby be able to further sort given formulas into kinds, according to the sort of reactions trained persons (including, presumably, ourselves) have to them.

Wittgenstein's fourth response, at first difficult to fathom, strikingly reveals the character and motives of his criticisms. Wittgenstein writes:

- and now distinguish such a proposition as 'The formula which I have written down determines y", or "Here is a formula which determines y", from one of the following kind: "The formula y = x2 determines the number y for a given value of x". The question "Is the formula written down there one that determines y?" will then mean the same as "Is what is there a formula of this kind or that?" - but it is not clear off-hand what we are to make of the question "Is y = x 2 a formula which determines y for a given value of x?" .38


In Wittgenstein's example of a classification system, particular statements such as "This formula is of the first kind" represent elements of our (use of the) classificatory system itself. But now Wittgenstein wants us to distinguish such sentences from those such as "The formula y =

x2 determines the number y for a given value of x". But on what basis are we to distinguish them? In the first case I point or call attention to a formula written somewhere; in the second I write "The formula y = x 2 determines the number y for a given value of x' l - But this does not seem to involve anything logically or semantically different. Both sentences are, as we would say, "metalinguistic", about a formula ("y =

x 2 ,,). The suspicion may arise here that Wittgenstein is involved in a use/mention confusion. But I think the distinction he asks us to draw, though subtle, is real. (It also illustrates the sort of distinction Wittgenstein often urges us to draw in philosophy.) Wittgenstein is still bearing in mind the interlocutor's "mistake" about determination. The problem with the second sentence ("The formula y = x 2 determines the number y for a given value of x") is that it is more likely to lead to the kind of philosophical worries about necessity which spawned the interlocutor's objection in the first place.39 Wittgenstein says that it is "not clear off-hand" what we are to make of the question "Is y = x 2 a formula which determines y for a given value of x?". He has given us several ways in which to respond to his question about use (and there are others, e.g., appealing to the notion of a function). These ways differ in emphasizing, on the one hand, the determination (through training) of a group of people, hence their uniformity of response; and, on the other, their training in a practice of sorting formulas into those which "determine" and those which do not. In the first cases, it is the people who are (said to be) determined; in the second, the formulas (are said to) determine values; but in each of Wittgenstein's examples education (or rote training) in a practice bears crucially on the "determination". Thus, if the question "Is y = x 2 a formula which determines y for a given value of x?" is unclear without something further ["ohne Weiteres"], namely, a choice among alternative scenarios, how much more equivocal must be the expression, "The steps are determined by the formula ... "! And this ambiguity bears crucially on the interlocutory question which originally prompted the whole remark, namely, "But are the steps then not determined by the algebraic formula?". Wittgenstein has not denied that there is any sense in which a formula can be said to determine the steps. (By analogy, he has not denied that

156 JULIET FLOYD

we are able to grasp rules for the use of a word.) He has instead suggested that there is not a single notion of determination (or rulegoverning, or rule-grasping) one could negate (or, presumably, affirm) unambiguously. Without something further the question "Is y = x 2 a formula which determines y for a given value of x?" is simply unclear; it has no reference to anyone essential thing. And this indicates the root of what was "mistaken" in the objection the interlocutor voiced.

The last two of Wittgenstein's six responses 'are meant to indicate that although the sentence "The formula y = x 2 determines the number y for a given value of x" is (as we have just seen) off-hand misleading and unclear, it is not meaningless. For, in a particular setting, the question may have an answer, e.g.,

[0 ]ne might address this question to a pupil in order to test whether he understands the use of the word "to determine"; or it might be a mathematical problem to work out whether there was only one variable on the right-hand side of the formula, as e.g. in the case: y = (x2 + Z)2 - z(2x2 + Z).40

In the first example we are to imagine a pupil who has been trained, like the people in Wittgenstein's first two responses, to calculate with individual formulas, and now we are trying to teach the pupil to use the system of classification outlined in Wittgenstein's third response. We may "test" whether he understands how to use the system of classification, and in this case there would be nothing misleading in asking the question, "Is y = x 2 a formula which determines y for a given value of x?". We would simply be asking the student to classify the formula according the system we are trying to teach.

Wittgenstein's final response sets a "mathematical problem" to work out. A calculation shows that the variable "z" can be eliminated from the (simplified) fromula. 41 In carrying out this calculation (or indeed, in using formulas like "y = x 2" , or classifying formulas in the previously described way) we do not need to be clear about what the notions of necessity, compulsion, or determination consist in. Rather, we know what to do when asked.

The entire Section 1, in examining the expression "the formula determines the steps", investigates the concept of "determination" ["Bestimmung"]. But I have interpreted Wittgenstein's use of the expression, and the examples he gives, to indicate an indeterminateness in the interlocutor's use of this notion. So there is a tremendous irony here, a play on the word "Bestimmung".42 On its own, Wittgenstein suggests,


the notion of "determination" makes no sense, and so offhand it is not clear what to do with either the question "Is y = x 2 a formula which determines y for a given value of x?", or the question "What sort of determination is the determination of steps by a formula?". To sum up, the interlocutor's "mistake" was to think that we have a determinate sense of determination (or a determinate absolute notion of a function). But then the idea that their is an univocal (metaphysical?) quality, logical or mathematical necessity, which may be said, to compel us to assent to a mathematical sentence (such as "4 = 22,,) on penalty of absurdity - a quality whose character is independent of our ability to partake in particular mathematical practices - begins to crumble. The example of an algebraic formula fails to exhibit a special kind of determination except in particular mathematical contexts. Similarly, reverting to Wittgenstein's governing analogy between an algebraic formula and a rule for the use of an expression, we may begin to suspect that the "determination" of our linguistic steps by our understanding, if conceived of as the grasping of a rule for the use of an expression, may not be the monolithic or clear phenomenon we are tempted to treat it as being when we wonder how it is that we can follow any rule at all. The logical necessity we think of as inhering, in traditional terminology, in the relation between a concept and its instances, and indeed, in the unity of a judgment itself, begins to slip from our grasp.43

4.

Neither of Wittgenstein's final examples of uses of the expression "the formula determines the steps" seems to secure what the interlocutor was after. So, taken collectively, all six of Wittgenstein's responses to his own question about use fail to give content to the interlocutor's objection. This is Wittgenstein's point: the problem of necessity does not seem to lie in either our uses of the word "determines" or the carrying out of a solution to a particular mathematical problem. So there is a difficulty in getting a general problem about logical compulsion or necessity off the ground. But the interlocutor tries again in Section 2. Note, however, that in the opening question of Section 2 the interlocutor now uses "meinen", translated here as "to mean"; that is, how a speaker intends or means to use an expression. This contrasts with the discussion in Section 1, where one was tempted to talk about the meaning (in the Fregean sense of Bedeutung, or Sinn) of the formula

158 JULIET FLOYD

itself. In German a formula [Formel] cannot, grammatically speaking, "mean" [meinen], just as in English a formula cannot, literally "intend". The interlocutor responds to Wittgenstein's play on the ambiguity of "determines" as follows:

'The way the formula is meant [gemeintJ determines which steps are to be taken,.44

The interlocutor's idea here is this: the determination of each of my particular steps, and, indeed, of the "mathematical" steps from input to output, is secured or constituted by the particular intention I have to use the formula and the particular meaning I endow or associate the formula with. This is a natural suggestion. As a description or (beginning) explanation of how the formula "determines the steps", it has the appeal of seeming less crudely behaviorist than Wittgenstein's previous suggestions about how we are trained to use the expression "The formula determines the steps". "Rule" is, apparently, an intentional notion insofar as it plays the role of a guide for action. But Wittgenstein quickly presses the interlocutor on what it is to mean or intend the formula "in a particular way". He asks

What is the criterion for the way the formula is meant? Presumably the way we always use it, the way we were taught to use it. 45

The suggestion is that "meaning" or "intending" a formula "in a particular way" is itself an activity or feat accomplished by being able to use the formula, having been trained in its use. Our "criterion" for determining whether or not someone means the formula in a particular way is what they do. Wittgenstein makes his point by looking at how we incorporate into our language a sign unknown to us, but used by someone who speaks our language. Thus he says:

We say, for instance, to someone who uses a sign unknown to us: "If by "x!2" you mean x 2 , then you get this value for y, if you mean x, that one". - Now ask yourself: how does one mean [meinenJ the one thing or the other by "X!2,,?46

Since the natural home of the notion of intending a formula in a particular way is just the intention to use it in a particular way, the answer to Wittgenstein's question presumably lies, so far as my view of the person using the symbol "x!2" goes, in what he does, and for me, in how I go on to use the symbol myself. I have no special experience of "meaning 'x!2' the first way" when I do mean it; and I do not attribute

WITTG EN STEIN ON 2, 2, ... 159

such experiences to the other simply in virtue of interpreting his or her actions in one way or the other. Wittgenstein emphatically declares:

That is how meaning it [das Meinen] can determine the steps in advance. 47

So once again the use, the training, come to the fore. Wittgenstein is happy to give the interlocutor, at least for the moment, the notion of "intention" or meaning. Insofar as he compares the "truths" of mathematics and logic with rules of grammar, Wi'ttgenstein himself assimilates questions about the special necessity of mathematics and logic to broader questions involving the relation of intention, expectation, and desire to their (particular) fulfillments. This is indeed part of his challenge to the traditional picture of the a priori as a category of knowledge designed to account for our knowledge of necessary truth, for traditionally the relation of intention to action was hardly deemed one of a priori knowledge. 48 So in addition to attempting to show the unclarity of the notions of logical and mathematical necessity, Wittgenstein's discussion restructures and broadens the field of concepts to be investigated in connection with the apparent necessity and full-blooded truthfulness of logic. This shifts the traditional epistemological framework for discussing the character of mathematics and logic. For Wittgenstein, Platonism in mathematics makes no more and no less sense than Platonism about meaning, desire, or intention. This is borne out in Investigations Section 437, where he writes:

A wish seems already to know what will or would satisfy it; a proposition, a thought, what makes it true - even when that thing is not there at all! Whence this determining [Bestimmen] of what is not yet there? This despotic demand? ("The hardness of the logical must. ,,)49

My reading of the first two sections of Remarks on the Foundations of Mathematics indicates at least the beginnings of an answer to the question whether Wittgenstein is ultimately offering a behaviorist or conventionalist account of logical inference and mathematical necessity. 50 The answer he would give to such a question would be another question, viz., "Convention (or behavior) as opposed to what?". The opposed notion ("nature", "mind", "inner" "feeling", etc.) may be seen, with appropriate scrutiny, to suffer from the same unclarity as the notions of "conventional" and "behavior" themselves. The other side of absolute arbitrariness is absolute necessity, absolute determination or compulsion. And these are the notions I have argued Wittgenstein is trying to

160 JULIET FLOYD

unmask as unclear in the first two sections of Remarks on the Foundations of Mathematics.

5.

Wittgenstein's emphasis on our criteria for ascribing intentions and his example of the introduction of an unknown symbol into our language fail to unearth what has struck the interlocutor. Obviously we can define or find a meaning for the sign "x!2" in particular cases like the one described. But this does not get at the peculiar compulsion, the sense of what must happen, the idea that something must be fixed ahead of our particular steps in virtue of the ways in which we mean, or intend to mean, the formulas (or, for that matter, the words) we are now operating with. 51 Wittgenstein's emphatic remark that "That is how meaning it can determine the steps in advance" was intended to call attention to the fact that our criteria for determining "the way" someone intends or means an expression lie in what they (and we) do. But now a natural response to this is to ask How is it that he (or J) know what to do? Is Wittgenstein denying that we may say that someone who understands an expression knows what to do with it ahead of time? This is the kind of worry which prompts Wittgenstein to suggest, in Section 3, that the interlocutor pose the following question to himself:

How do I know [Wie weiss ich] that in working out the series +2 I must write

and not "20004,20006"

"20004,20008,,?52

Unlike the questions Wittgenstein posed to the interlocutor in Section 2, this first-person question is inflicted on a sign I already know how to use ("+2"). Thus it may seem to demand a different sort of answer than the one about "x!2". Indeed, in the course of the ensuing passage Wittgenstein will try to elicit from his reader a sense that this is not the straightforward question it might appear to be: construed in the most natural way it is empty, that is, "How do I know ... " is out of place here. What sort of "emptiness" is in question? In this case Wittgenstein does not, nor do I for him, appeal to an absolute standard of emptiness. (Wittgenstein had invoked something like such a standard in Tractatus in connection with the doctrine of a "formal", or "internal", relation holding between the members of a "formal" series. )53


Still, the relation(s) between the members of a series such as +2 is thought of by the later Wittgenstein as in some sense or another "grammatical".54 Our question is, What does this idea amount to in Remarks on the Foundations of Mathematics?

One can, upon reflection, imagine circumstances in which "How do I know to write ... ?" might have a point. For example, it might arise in the writing of a step in an algebraic series whose generating principle was especially complex or difficult (e.g., if I found myself computing differently each time I tried to determine the correct next step). In this case, "How do I know that in working out this series that this is the correct next step?" might be answered with several calculations worked out on paper. Similarly, a child learning arithmetic might reasonably pose this question. On the other hand, the rule or law of the series considered here (+2) is familiar and easy. I seem to be so certain that "20004,20006" is the correct thing to write that a calculation would seem superfluous, ad hoc - hardly informative about this particular step. This is part of Wittgenstein's point.

The interlocutor continues to feel that Wittgenstein is denying something. He responds to the question "How do I know that in working out the series +2 I must write "20004 ,20006" ?" , as if Wittgenstein is endorsing a skeptical view.

But you surely know for example that you must always write the same sequence of numbers in the digits: 2,4,6,8,0,2,4, etc.

The interlocutor seeks to find some basis or justification for writing "20006" at the 1O,003d step of the series. He locates his confidence in the repeating pattern of right-most digits of numerals in the series, thus hoping to circumvent worries about the infinite length of the series and his (apparently) unlimited capacity to continue writing different numerals in the correct order. Wittgenstein accepts this response as "Quite true!" ("Ganz richtig!", "Completely correct!"), and then, pushing the interlocutor's idea one step further, turns the purported answer against him:

The problem must already appear in this sequence, and even in this one: 2,2,2,2, etc. -For how do I know that I am to write "2" after the five hundredth "2"? And if I know it in advance, what use is this knowledge to me later on? I mean: how do I know what to do with this earlier knowledge when the step actually has to be taken?

What is "the problem"? A regress arises because the interlocutor

162 JULIET FLOYD

supposes that he knows something in advance of the step's being taken, something different from the taking of the step itself. He supposes that he holds a belief which leads him to act. The case of the recalcitrant pupil (PI Sections 143, 185) is brought home to the first person: Wittgenstein's question places a seeming gap between my knowledge of a general principle and its application, thus inviting a "Third Man" argument which asks, each time I try to apply my knowledge, how I know that this application is correct. At each particular step, when I try to say how I know that this is the next correct step in the series, my answers seem thinner than my conviction. And if there is trouble with the series 2,2,2 ... , then will there not be trouble, i.e., trouble in saying how I know, in every case? Wittgenstein's new question ("How do I know that I am to write "2" after the SOOth "2"?") seems to raise a general wonder about how knowing the principle of any series tells me what to do in the particular case. How can I follow any rule at all?55

In fact, however, the example seems to just as easily cut the other way. Just because there is no problem (other than boredom or exhaustion or pointlessness) with my writing the SOOth "2" in the series 2, 2, 2 ... , it seems foolish to allow such worries to creep in about the 1O,003d step in the series +2 - or at least, to view such questions as carrying the same force with them as grammatically analogous "How do I know ... ?" questions raised about matters of genuine arithmetic or empirical difficulty. Admittedly, Wittgenstein's reduction of "the problem" to the case of 2, 2, 2 . .. draws a somewhat daring analogy between the series +2 and the series +0 - if that is how we want to view my writing of 500 "2s". The series + 0 is a limiting case, requiring, as we should ordinarily say, no calculation at all from step to step. In fact, it appears that nothing specifically mathematical is required to continue; i.e., no special kind of knowledge that, say, my writing out of a series of repeating color hues, or shapes, or repeating letter a's (a, a, a, a ... ) does not require. I have an idea in such cases that I write "the simplest" or "the most natural" pattern,56 but this does not provide me with knowledge of something specific which compels me at this particular step. The interlocutor's attempt to answer the original question about "20004,20006" directly by insisting that I ought to do "the same" (writing digits in the pattern 2,4,6,8,2,4 ... ) evidently presupposes the knowledge or capacity in question. Thus it yields no independently informative answer. This is because knowing that


"20006" is the numeral to write in order to "go on in the same way" at the 1O,003d place is just (part of) what it is to know that this is the series "+2" starting with 0.57 Suppose 1 exhibited confusion at the 10,003d step. To get this far successfully and then hesitate would probably look most like exhaustion, not error. But if it did not seem to be a mental seizure of some kind (e.g., 1 cheerfully chew on my pencil, giving every indication of thinking hard) 1 would, barring special circumstances, (be said to) not understand the series. ;So far as other people's views of me goes, my knowledge of the general and knowledge of the particular go hand in hand here. And even for myself, my wondering how 1 know what to do in the particular case is inseparable from wondering whether 1 grasp the series itself. But the "How do 1 know ... ?" question, as phrased, makes it look like my knowledge of the series has to hook up with, or fit into, my knowledge of the particular step. It is as if what the rule actually consists in is two things: the general principle and the atomic points in reality which fit its demands. However, while 1 can memorize a formula and call it "the formula of a series", 1 am not without further ado said to understand the formula unless 1 can operate with it. And if 1 operate with the series well enough to convince myself, my teachers and other speakers that 1 have grasped the principle, what more is needed? The question about what to do at the 1O,003d (or the SOOth) step, if viewed as opening up a doubt of some kind, begins to look absurd, like the question "How do 1 know that this thing is identical with itself?". One is tempted to say that this is simply what working out the series +2 (or what identity) is, amounts to, or comes to. This will not give me an informative answer to the question or a justification for taking this particular step in the way 1 do - much less a general defense of the practice of calculating with ruleS.58 Nothing (in particular) does. But so far, nothing is needed. "How do 1 know that in writing out 500 "2s" 1 should write "2" at the SOOth step?". The question is empty - unless it is taken as a neurophysiological question, or a question about purported "mental machinery". (I shall discuss this way of giving the question content below.) Hence Wittgenstein's parenthetical remark,

(If intuition is needed to continue the series + 1, then it is also needed to continue the series +0.)59

Wittgenstein wants to undermine both the idea that a justification is required for each particular step in the number series and that in the

164 JULIET FLOYD

absence of such justification a special appeal to intuition is the only recourse.60

But the interlocutor reacts to Wittgenstein's move to 2,2,2 ... as if Wittgenstein is denying that he knows what to write at the 1O,OO3d step of the series + 2:

But do you mean to say that the expression "+2" leaves you in doubt what you are to do e.g. after 2004?61

Wittgenstein reacts sharply:

- No; I answer "2006" without hesitation. But just for that reason [aber darum] it is superfluous [ilbellilssig] to suppose that this was determined earlier on. My having no doubt in face of the question does not mean that it has been answered in advance.

We need to get to the bottom of this "superfluousness". Wittgensteinsays that he answers "2006" "without hesitation", "ahne Bedenken", without thinking over or considering anything. The analogy between the step to "2004" from "2002" and the SOOth 2 in the series 2, 2, 2 ... helps make Wittgenstein's point clearer. In the case of 500 2s, there is a real sense in which no thought can be brought to bear at the SOOth step. Something rote governs the process. Unlike an initial segment of a series whose principle requires some kind of calculation, 2, 2, 2 ... requires no guess, no inference, no thought at all between steps. My actions may become mechanical and they may remain mechanical. So Wittgenstein seems to be saying, with the writing of "20006" at the 1O,OO3d step of working out the series +2.

Of course my certainty that "20004" is the correct thing to write at this point is supposed by the interlocutor to reflect the fact that something was "answered in advance" of the steps actually being taken. He objects, still supposing that Wittgenstein is denying that he knows what to write:

But I surely also know that whatever number I am given I shall be able, straight off and with certainty, to give the next one.

to which Wittgenstein responds,

- Certainly my dying first is excluded, and a lot of other things too. But my being so certain that I will be able to go on is naturally very important.62

Wittgenstein does not deem it irrelevant, much less false, for the interlocutor to fix on the certainty with which I develop the series under

WITTG ENSTEIN ON 2, 2, ... 165

certain circumstances.63 But the certainty, Wittgenstein says, is a certainty that I shall be able to do something.64 I have been trained to react with confidence, without doubt, to such rules as +2. This is indeed of the utmost importance, this rote ness of response, but the need for further attempts to justify it on independent and specific grounds ("grounds" more specific than "I have learned arithmetic") has not yet been made clear. 65

The interlocutor's idea is that something is known; "in advance" of the actual writing of the step. His reaction to Wittgenstein's remarks is that something is being denied, some kind of knowledge it seems to make sense to say we possess, knowledge that explains how it is we know what to do. However, it is not yet clear what the notion of "in advance" adds to the idea of being "determined". If our steps are "determined", it is natural to suppose something has fixed them ahead of time; this is just what being "determined", presumably, comes to. Wittgenstein is interested in the idea that something is "known ahead of time" insofar as it expresses the a priori. But Wittgenstein's earlier investigations of "determination" and his suggestion that "knowledge" is out of place (or anyway playing an idiosyncratic role) in the opening question of Section 3 serve to undermine the traditional category of the a priori entirely - at least insofar as it is viewed, in Kant's manner, as the epistemic companion to necessity. If "knowing" is out of place at the 1O,003d step of working out the series +2, then (as the reductio ad absurdum of Section 3 shows) the urge to say that I (know to) write "20006" because it is a mathematical fact (or: mathematically true) that 20006 follows 20004 in the series + 2 is undercut. There is no question of anything known here - it is rather a question of what is done. 66

Having no doubt and being able to say how I know in this sort of case pull in opposite directions, in part because my having no doubt is seen (by the interlocutor) to be a matter of my being "determined". The "determination" must be determination, in this case, of a very particular sort. Let us try to make out a sense of genuine determination in advance.

I have said that something "mechanical" emerges in "2, 2, 2 ... ". In what sense might we think of a machine determining the steps of this series in advance? Consider, by way of analogy, a computer, programmed to both add 2 and to write a sequence of repeating "2s" indefinitely. In a sense, the program (plus the machine's hardware) "determines" the steps it will take "in advance". Now we could ask,

166 JULIET FLOYD

"How does the machine know to write "2" at the SOOth step?" An answer would presumably specify the program and the details of how the hardware implements the program. (The computer might even be programmed to "answer" the (first person) question "How do I know to "write" ... ?") But granted the program and the specification of the hardware's implementation of it, there is no further question to ask about this machine's taking this step at this point. The analogy with Wittgenstein's suggestion in Section 3 is this: once my program (my training in arithmetic) and the implementation of my hardware (by my neurophysiological nature) have been specified, it seems absurd to think that there could be more to ask about why I write "20006" (or "2") here. Thus, although it may be an interesting neurophysiological or psychological question what it is, e.g., that allows me to write "2" at the 1st, the 10th, and the SOOth step of 2, 2, 2, ... , or what the state of my retina and brain are when I watch a series of "2s" go by, one after the other, first in this sort of light, then after food deprivation, etc., these are still very particular and difficult questions with (if they make scientific sense) very particular answers, answers which would yield no general conclusions about the kind of determination the interlocutor is interested in.67

Wittgenstein offers the interlocutor other examples of epistemic compulsion, or genuine knowing in advance in Sections 21 and 22 of Remarks on the Foundations of Mathematics. These sections are especially concerned with the Platonism of Frege and Russell, as the remark of Section 21 makes clear.

21. In his fundamental law68 Russell seems to be saying of a proposition: "It already follows - all I still have to do is, to infer it". Thus Frege somewhere says that the straight line which connects any two points is really already there before we draw it; and it is the same when we say that the transitions, say in the series + 2, have really already been made before we make them orally or in writing - as it were tracing them. 69

Wittgenstein now replies to this patent Platonism by giving several further examples of "determination".

22. One might reply to someone who said this: Here you are using a picture. One can determine [bestimmen] the transitions [Ubergiinge] which someone is to make in a series, by doing them for him first. E.g. by writing down in another notation the series which he is to write, so that all that remains for him to do is to translate it; or by actually writing it down very faint, and he has to trace it. In the first case we can also say that we don't write down the series that he has to write, and so that we do not ourselves make the transitions of that series; but in the second case we shall certainly say that the


series which he is to write is already there. We should also say this if we dictate what he has to write down, although then we are producing a series of sounds and he a series of written signs. It is at any rate a sure way of determining [bestimmen] the transitions [Obergiinge] that someone has to make, if we in some sense make them first. 70

Thus Wittgenstein has given us several ways to determine the transitions "in advance". But he immediately returns to the lessons of Sections 1, 2 and 3, writing:

, If, therefore, we determine [bestimmen] these transitions [Obergiinge] in a quite different sense, namely, by subjecting our pupil to such a transition as e.g. children get in the multiplication tables and in multiplying, so that all who are so trained do random multiplications (not previously done in the course of being taught) in the same way and with results that agree - if, that is, the transitions which someone is to make on the order "Add 2! " are so determined by training that we can predict with certainty how he will go, even when he has never up to now taken this step [Obergang]- then it may be natural to us to use this as a picture of the situation: the steps [Obergiinge] are all already taken and he is just writing them down.71

But now our picture - the Platonist picture - is no longer literally true. Relative to these examples, it is only a metaphor. In the case of our actually writing out the series faintly, and then asking the pupil to trace what we have already marked out, there is a perfectly good sense in which the pupil, may make a mistake (perhaps by a slip of the pen). As the pupil copies, we can see the transitions or steps that are made, from faint numeral to darker numeral. If we ask the pupil to ask him or herself, "How do I know to write "20004,20006"?" there is a perfectly good answer the pupil can give: simply point to the faint marks that look just like this ("20004,20006"). But in the cases we were imagining earlier in Section 3, there was nothing to point to. The "picture" the interlocutor is operating with is that the case we described is just like the pupil's tracing of the faint numerals, only the numerals are very, very faint - in fact so faint they cannot be seen. But now the notion of a "transition" or "step" is metaphorical, a Platonic entity of some kind, or a whispering of the entity to us to take this step. 72

Wittgenstein indicates in Section 3 that in order to be "answered in advance" there must be some question, some possible mistake, some particular way of getting it wrong. But rote learning - like the kind of drills lying behind our "training" in arithmetic - is a kind of memorization ahead of time. This is not a matter of "answering questions in advance", but of practicing so as to not have to think. As we have seen, something "mechanical" is happening by the SOOth step of

168 JULIET FLOYD

2, 2, 2 ... This is what leads to our not being sure whether to call the step at that point calculation, or inference, or even whether I may be said to have "intended" this step (or not intended it). It is no longer clear what sort of "necessity" is in question, or how we are to demarcate the role and scope of the notions of logical or mathematical inference.

Let me back up for a moment and discuss a parenthetical analogy Wittgenstein draws in Section 3. After the posing of the original question ("How do I know that in working out the series +2 I must write "20004,20006" and not "20004,20008"?"), Wittgenstein writes:

- (The question: "How do I know [Wie weiss ich] that this color is "red"?" is similar.)

Now in Philosophical Investigations Section 381 we read the following:

How do I recognize [erkenne] that this color is red? - It would be an answer to say: "I have learned English". 73

Wittgenstein's response in Philosophical Investigations that "I have learned English" is, it may seem, hardly an answer at all. In fact, it is tantamount to a rejection of the question, at least as an intended articulation of the interlocutor's sense of the mystery and uniqueness of the meaning of "red". For the interlocutor did not doubt that he spoke English. If he had, he would have pictured himself as a foreigner or a child; but this is part of Wittgenstein's point: what the foreigner and the child lack is the training, the practice that we have engaged in. Posing the question in the way the interlocutor does can make it seem as if there is something special going on when I recognize that this color is "red", some particular understanding that is manifested, some knowledge of a particular and unique meaning relation between the word and the thing. Yet when I ask myself how I know ... , there seems nothing particular to pinpoint in virtue of which I may claim to know. The result may be a kind of skeptical giddiness about meaning, but Wittgenstein offers instead the fact that I speak English. This squares with our untutored reactions: if I ask myself the question, "How do I now this color is "red"?" I am tempted to respond, "Because it's red!,,74

These may seem to be irrelevant and impoverished responses if taken on their own. Certainly they are "circular" if taken as direct answers to the questions, but viciously so? From what standpoint could we find a better sort of response?

Thus, using Wittgenstein's parenthetical analogy, we may rethink the


opening question of Section 3. An analogous response to the question about my compulsion to write "20004,20006" would not be that I speak English; it would presumably be something like "I have learned basic arithmetic" or "I have learned to count". This response hardly informs me about this particular step (from "20004" to "20006"). In a real sense, it rejects the question. But it serves as a kind of reminder (cf. PI Section 127). Wittgenstein wishes to call attention to the interlocutor's inclination to view as irrelevant the fact that I have learned arithmetic. Why does this seem irrelevant? What more could the interlocutor want by way of a justification?75

NOTES

1 Eds. G. H. von Wright, R. Rhees and G. E. M. Anscombe; trans. G. E. M. Anscombe (revised edition, Cambridge: M.LT. Press, 1978). Hereafter cited as RFM. Subsequent references to Wittgenstein's other works will be as follows: Tractatus Logico-Philosophicus, trans. C. K. Ogden (London: Routledge & Kegan Paul, 1933) is cited as TLP; Philosophical Investigations, trans. G. E. M. Anscombe (Oxford, Basil Blackwell, 1958) as PI; the "Frilhversion" of Philosophical Investigations (discussed below in Section III) as FV; the "Mittelversion" of Philosophical Investigations (discussed below in Section III) as MV; Wittgenstein's 1939 Lectures on the Foundations of Mathematics, ed. Cora Diamond (Ithaca: Cornell University Press, 1976) as LFM; Remarks on Color, ed. G. E. M. Anscombe, trans. Linda L. McAlister and Margarete Schiittle (Berkeley: University of California Press, 1977) as ROC; On Certainty, eds. G. E. M. Anscombe and G. H. von Wright, trans. G. E. M. Anscombe and Denis Paul (New York: Harper & Row, 1972) as OC; Philosophical Grammar, ed. Rush Rhees, trans. Anthony Kenny (Oxford: Basil Blackwell, 1974) as PG; Wittgenstein and the Vienna Circle, ed. Brian McGuinness, trans. Joachim Schulte and Brian McGuinness, (Oxford: Basil Blackwell, 1979) as WVC; and Zettel, eds. G. E. M. Anscombe and G. H. von Wright, trans. G. E. M. Anscombe (Berkeley: University of California Press 1967) as Z. 2 The early reviews of RFM were particularly scathing. See, e.g., A. R. Anderson, 'Mathematics and the "Language Game''', Review of Metaphysics 11, 446-58; G. Kreisel, 'Wittgenstein's Remarks on the Foundations of Mathematics', British Journal of the Philosophy of Science 9, 135-58; Paul Bernays, 'Comments on Ludwig Wittgenstein's Remarks on the Foundations of Mathematics', Ratio 2, 1-22.

More recently there has been more willingness to countenance Wittgenstein's views, though little consensus on what those views are or even how ignorant Wittgenstein was of certain central technical results. See, e.g., Michael Dummett, 'Wittgenstein's Philosophy of Mathematics', in Truth and Other Enigmas (Cambridge, MA: Harvard University Press, 1978), pp. 166-85; Charles Chihara, 'Wittgenstein's Analysis of the Paradoxes in his Lectures on the Foundations of Mathematics', Philo~phical Review 86, 365-81; Crispin Wright, Wittgenstein on the Foundations of Mathe'inatics (London: Duckworth, 1980); V. H. Klenk, Wittgenstein's Philosophy of Mathematics (The Hague: Martinus Nijhoff, 1976); Saul Kripke, Wittgenstein on Rules and Private Language (Cambridge,

170 JULIET FLOYD

MA: Harvard University Press, 1982); S. G. Shanker, Wittgenstein and the Turning Point in the Philosophy of Mathematics (Albany, NY: State University of New York Press, 1987); and G. P. Baker and P. M. S. Hacker, Wittgenstein: Rules, Grammar and Necessity, Vol. 2 of an Analytical Commentary on the Philosophical Investigations (Oxford: Basil Blackwell, 1985). I have learned from all these authors, but none of them seems to see Wittgenstein's later dialectical style of writing as internal to his conception of logic and grammar in the way I outline in this essay. 3 PI Section 127. 4 PI Section 110:

"Language (or thought) is something unique" - this proves to be a superstition (not a mistake!), itself produced by grammatical illusions.

And now the impressiveness retreats to these illusions, to the problems.

5 See LFM, Lecture I (p. 14):

Mathematicians tend to think that interpretations of mathematical symbols are a lot of jaw - some kind of gas which surrounds the real process, the essential mathematical kernel. A philosopher provides gas, or decoration - like squiggles on a wall of a room.

I may occasionally produce new interpretations, not in order to suggest they are right, but in order to show that the old interpretation and the new are equally arbitrary. I will only invent a new interpretation to put side by side with an old one and say "Here, choose, take your pick." I will only make gas to expel old gas.

6 Cf. Warren Goldfarb, 'I Want You to Bring Me A Slab: Remarks on the Opening Sections of the Philosophical Investigations', Synthese 56 (1983): 265-82, especially pp. 266-7. 7 A critical edition of both parts of this so-called "Friihversion" (hereafter FV), has been prepared by G. H. von Wright and Heikki Nyman. The first part of FV was composed during 1936; the second during the fall of 1937 (see pp. 113-4 of von Wright, 'The Origin and Composition of Philosophical Investigations' (in his Wittgenstein, (University of Minnesota Press, 1983, pp. 111-36». The parts are of equal page length and form a consecutive typescript (see Ibid., p. 117). The so-called "intermediate version", or "Mittelversion" of PI (MV) was compiled by von Wright, who conjectures that it was completed by Wittgenstein some time in 1945 (see von Wright, The Origin and Composition of Philosophical Investigations', pp. 125ff). 8 von Wright, The Origin and Composition of Philosophical Investigations', pp. 120ff. 9 von Wright, 'The Origin and Composition of the Investigations', p. 121. 10 In the typescript from which RFM, I was printed (TS 222) approximately 50 passages were deleted and the order of others rearranged from the FV version (TS 221). Anhang III of von Wright's critical edition gives a list of the correspondences and alterations between TS 221 and TS 222. 11 See von Wright, 'The Origin and Composition of the Investigations', pp. 114-19. According to von Wright, there were originally three copies of the second part of the typescript. One contained a few revisions in Wittgenstein's hand; the second was entirely clean; the third Wittgenstein cut up into pieces which he "clipped together in a large number of bunches" many of which are annotated and changed (Ibid., p. 118). Part I of


RFM was printed from this third copy, entitled TS 222 in von Wright's catalogue. In the editors' preface to the revised edition of RFM, p. 30, we read that "in a notebook as late as 1944 [Wittgenstein) proposed a few alterations to this typescript". 12 In Volume II of their Analytical Commentary on the Philosophical Investigations (Chapter I), Baker and Hacker emphasize the manuscript basis of PI and view PI Sections 1-189 as a tree which bore "two fruits": in the original sequel (FV) Wittgenstein focussed on the philosophy of mathematics and logic; in the intermediate and final versions (MV and PI) on the philosophy of mind. Developing this metaphor, Baker and Hacker suggest several interesting similarities between Wittgenstein's discussions of mathematics and his discussions of mind. But the complexity of the i'llterweaving I find among Wittgenstein's remarks in RFM I and later sections of PI does not seem to me to bear out the metaphor of "two fruits", which suggests that there are two distinct yet comparable realms of Wittgenstein's later philosophy, distinguished by rali\ge of topic. 13 RFM I Section 1. 14 In an earlier draft of PI Section 81 (FV Section 78.(80.», Wittgenstein explicitly mentions Tractatus, writing in the final sentence:

Denn dan wird auch klar werden, was dazu verleiten kann - und mich verleitet hat (Log.Phil.Abh.) - zu denken, dass, wer einen Satz ausspricht und meint, oder versteht, damit einen Kalkiil betreibt, nach bestimmten Regeln.

15 PI Section 81. I have altered Anscombe's translation in the fifth, ninth and final lines of the published English text. Her translation suggests that games and calculi which have fixed rules must be different, and leaves out the word "logic" at one point altogether. 16 Despite occasional remarks which suggest otherwise (e.g., PI Section 7, RFM VI Section 28, RFM VII Section 35), my interpretation is reinforced by PI Sections 130-1:

130. Our clear and simple language-games are not preparatory studies for a future regularization of language - as it were first approximations, ignoring friction and airresistance. The language-games are rather set up as objects of comparison which are meant to throw light on the facts of our language by way not only of similarities, but also of dissimilarities.

131. For we can avoid ineptness or emptiness in our assertions only by presenting the model as what it is, as an object of comparison - as, so to speak, a measutingrod; not as a preconceived idea to which reality must correspond. (The dogmatism into which we fall so easily in doing philosophy.)

17 PI Section 143. 18 Ibid. 19 See PI Sections 143, 185. 20 PI Section 144:

144. What do I mean when I say "the pupil's capacity to learn may come to an end here"? Do I say this from my own experience? Of course not. (Even 'if I have had such experience.) Then what am I doing with that proposition? Well, I should like you to say: "Yes, it's true, you can imagine that too, that might happen too!" - But was I trying to draw someone's attention to the fact that he is 'capable of imagining that? - I wanted to put that picture befote hiIJI, and his acceptance of

172 JULIET FLOYD

the picture consists in his now being inclined to regard a given case differently: that is, to compare it with this rather than that set of pictures. I have changed his way of looking at things. (Indian mathematicians: "Look at this".)

The FV basis for this section (FV Section 126 (128», identical with Z Section 461, draws a connection between geometrical figure construction, Wittgenstein's own philosophical method, and discussions of the convincingness of proof in RFM. 21 Stanley Cavell emphasizes the quality of the analogy as a "figure of speech" in The Claim of Reason (New York: Oxford University Press, 1979). In discussing the function of mathematical examples in PI he writes (pp. 121-2):

Their general background is an idea that the primitive abilities of mathematics (e.g., counting, grouping, adding, continuing a series, finding quantities equal or smaller) are as natural as any (other) region of a natural tongue, and as natural as the primitive abilities of logic (e.g., drawing an inference, following a rule of substitution). The implication is that ordinary language no more needs a foundation in logic than mathematics does. More specifically, he uses the picture of "continuing a series" as a kind of figure of speech for an idea of the meaning of a word, or rather an idea of the possession of a concept: to know the meaning of a word, to have the concept titled by the word, is to be able to go on with it into new contexts - ones we accept as correct for it; and you can do this without knowing, so to speak, the formula which determines the fresh occurrence, i.e., without being able to articulate the criteria in terms of which it is applied. If somebody could actually produce a formula, or a form for one, which generated the schematism of a word's occurrences, then Wittgenstein's idea here would be more than a figure of speech; it would be replaced by, or summarize, something we might wish to call the science of semantics.

22 PI Sections 146, 152. 23 Elsewhere, however, Wittgenstein plays on the fact that it is usual in mathematical contexts to speak of the formula (e.g., (a + b) + c = a + (b + c» and the rule (e.g., of associativity of addition) interchangeably. This comes out strikingly in his discussion of recursive proof, Skolem primitive recursive arithmetic and mathematical induction in PG Part II, Chapter IV. 24 Viewing concepts as rules, Kant raised a similar problem in the Critique of Pure Reason (A 133/B 172-A 136/B 175) and attempted to resolve it in the schematism and in the introduction to the Critique of Judgment. 2S See Tractatus 6.126ff. Compare Frege's critical discussion of Schroder in his review of Schroder's Algebra der Logik, translated in Translations from the Philosophical Writings of Gottlob Frege, eds. Peter Geach and Max Black (Totowna, NJ: Rowman & Littlefield, 1980) pp. 86-106. See also Russell's implicit criticisms of the algebra of logic tradition in his Principles of Mathematics (New York: W. W. Norton & Co., 1938), Chapter II. 26 RFM I Section 6. 27 See both the Friihversion (FV, p. 162.(168.» and PI Section 189. 28 Ibid. 29 This portion of the passage is identical in FV Section 162.(168.) and RFM I, 1. In PI Section 189 the first word of the question is italicized: "How is it used?". 30 RFM I Section 1. 31 Wittgenstein's play on the ideas of instruction ("unterrichten"), training ("abrichten"),


teaching ("lehren") and education, or up-bringing ("erziehen") in. connection with the learning of language are of course familiar themes in the opening sections of PI, especially Sections 6, 7 and 9. 32 RFM I Section 1. 33 PI Section 206 uses a similar analogy in a different context to make a somewhat different point:

206. Following a rule is analogous to obeying an order. We are trained to do so; we react to an order in a particular way. But what if one person reacts in one way and another in another to the order and the training? Which ooe is right?

Suppose you came as an explorer into an unknown country with a language quite strange to you. In what circumstances would you say that the people there gave orders, understood them, obeyed them, rebelled against them, and so on?

The common behavior of mankind [Die gemeinsame menschliche Handlungsweise] is the system of reference [das Bezugssystem] by means of which we interpret an unknown language.

34 Nor does it appear in the final version PI Section 189. 35 All people, every time? Human frailty, such as it is, would eventually bring errors or exhaustion to falsify this claim. The possibility of mistakes in calculation versus uses of alternative "arithmetics" is a related and complex topic investigated by Wittgenstein at length in RFM and elsewhere. See, e.g., RFM I Section 136; RFM III Section 81; RFM IV Section 26, and ROC III, Section 293.

Kripke offers an especially incisive criticism of dispositionalist accounts of meaning by focussing on the difficulty of stating non-question-begging ceteris paribus clauses to pinpoint an explanation of behavior. See Kripke, Wittgenstein on Rules and Private Language, pp. 25ff. 36 RFM I Section 1. 37 One might have dismissed the conversation between the interlocutor and Wittgenstein from the beginning by dismissing the interlocutor's initial objection as rooted in a (rather obvious) confusion of use and mention. But such a dismissal would skirt the philosophical interest of Wittgenstein's writing: to plumb the sources of the interlocutor's interest in the necessity of logical inference. 38 RFM I Section 1. I have altered Anscombe's translation of the first clause quoted. 39 Here I am differing in point of emphasis with both Garth Hallett (A Companion to Wittgenstein's Philosophical Investigations, (Ithaca: Cornell University Press, 1977), pp. 278-9), and Baker and Hacker (Wittgenstein, Rules, Grammar and Necessity, An Analytical Commentary on the Philosophical Investigations, Vol. II, pp. 107ff). These commentators label the latter kind of statement "grammatical". 40 RFM I Section 1. 41 Strangely, the simplified formula is y = X4, rather than y = x 2 , which would have made better sense. Perhaps Wittgenstein made an algebraic error, or there was a typographical error in transcnptlOn. If the formula to be simplified were instead y = (x + Z)2 - z(2x + z), the simplification would be y = x 2. Compare PI Section 189, where the altered passage reads in part:

or it might be a mathematical problem to prove in a particular [bestimmten] system that x has only one square.

174 JULIET FLOYD

Note the substitution of the notion of proof for calculation in PI Section 189. 42 This is borne out in the revision of the section's final sentence Wittgenstein made in PI, quoted in the previous footnote. 43 RFM VII Section 42:

When I said that the propositions of mathematics determine rbi/den] concepts, that is vague; for "2 + 2 = 4" forms a concept in a different sense from "p J p". "(x).fx :::> fa", or Dedekind's Theorem. The point is, there is a family of cases.

And again, at RFM VII Section 45:

The word "concept" is too vague by far.

Cf. RFM VII Section 70 and RFM VII Section 71: "'Concept' is a vague concept". Wittgenstein's discussion in RFM I Section 1 should be compared with the "indetermi

nateness" [Unbestimmtheit] of our notion of sameness of color in ROC I Sections 17, 56 and 59; and ROC III Section 251. 44 RFM I Section 2. See the corresponding PI Section 190. 45 RFM I Section 2. 46 Ibid. 47 Ibid. I have altered Anscombe's translation of this sentence. 48 The tradition, of course, tended not to think of the relation as primarily epistemic. If it is thought of as an epistemic relation at all, such a relation would not presumably be known by means of the senses. (Compare G. E. M. Anscombe's idea of "non-observational knowledge" in her Intention (Ithaca: Cornell University Press, 1963) pp. 12ff.) Kant, who viewed the will as a kind of causality, would have discerned a (causally) "necessary connection" between an intention and an action, hence a relation with an a priori element. But the intention itself would not have been deemed knowledge a priori of the effect (the action); rather, the (regulative) category of causality would give us a priori knowledge that the effect (the movement of my body, say) had some cause or other in the realm of appearance. 49 The entire surrounding discussion in PI is relevant, especially Sections 435 and 437 where Wittgenstein says:

457. Yes: meaning [meinen] something is like going up to someone.

(This section was drafted much earlier in Wittgenstein's life. See PG p. 157.) In PI Section 439 Wittgenstein explicitly speaks in terms of "metaphor". 50 Wittgenstein does his best to explicitly avoid being read this way. See, e.g., RFM II Section 61, LFM, p. 111 and PI Sections 307-8:

307. "Are you not really a behaviorist in disguise? Aren't you at bottom really saying that everything except human behavior is a fiction?" - if I do speak of a fiction, then it is of a grammatical fiction.

308. How does the philosophical problem about mental processes and states and about behaviorism arise? - The first step is the one that altogether escapes notice. We talk of processes and states and leave their nature undecided. Sometime perhaps we shall know more about them - we think. But that is just what commits us to a particular way of looking at the matter. For we have a definite concept of what it


means to learn to know a process better. (The decisive movement in the conjuring trick has been made, and it was the very one that we thought quite innocent.) -And now the analogy which was to make us understand our thoughts falls to pieces. So we have to deny the yet uncomprehended process in the yet unexplored medium. And now it looks as if we had denied mental processes. And naturally we don't want to deny them.

51 Cf. PI Section 188:

Here I should first of all like to say; your idea was that that act of meaning the order [Meinen des Befehls] had in its own way already traversed all 'those steps: that when you meant it your mind as it were flew ahead and took all the steps before you physically arrived at this or that one.

Thus you were inclined to use such expressions as: "The steps are really already taken, even before I take them in writing or orally or in thought". And it seemed as if they were in some unique way predetermined, anticipated - as only the act of meaning [das Meinen] can anticipate reality.

52 RFM I Section 3. At PI Section 211 the question finds an analog:

211. How can he know how he is to continue a pattern by himself - whatever instruction you give him? - Well how do I know? - if that means "Have I reasons?" the answer is: my reasons will soon give out. And then I shall act, without reasons.

53 See TLP 4.1252,4.1273, 6.02ff. 54 See, e.g., RFM I Section 128, RFM 1I Section 27, RFM III Sections 26,39, RFM VI Section 27. 55 This is, essentially, the interpretive route taken by Kripke, whose much discussed Wittgenstein on Rules and Private Language outlines an interpretation of Wittgenstein as a skeptic about the notion of meaning a word in a particular way. Kripke regards RFM I Section 3 as a vivid statement of the paradox he attributes to Wittgenstein. Says Kripke (p. 20):

The passage strikingly illustrates a central thesis of this [i.e., Kripke's] essay: that Wittgenstein regards the fundamental problems of the philosophy of mathematics and of the "private language argument" - the problem of sensation language - as at root identical, stemming from his paradox. The whole of Section 3 is a succinct and beautiful statement of the Wittgensteinian paradox; indeed the whole initial section of Part I of Remarks on the Foundations of Mathematics is a development of the problem with special reference to mathematics and logical inference.

I cannot take up my systematic differences with Kripke in this essay. Reasonable doubts about his argument as interpretation of Wittgenstein seem to me to have already been raised by several commentators, including G. E. M. Anscombe, 'Critical Notice of Saul Kripke's Wittgenstein on Rules and Private Language', Canadian Journal of Philosophy, 15 (March 1985), 103-9; G. E. M. Anscombe, 'Review of Wittgenstein on Rules and Private Language', Ethics 95 (January 1985), 342-52; Baker and Hacker, Scepticism, Rules and Language, (Oxford: Basil Blackwell, 1984); Stanley Cavell's second Carus Lecture, 1988; Warren Goldfarb, 'Kripke on Wittgenstein on Rules', Journal of Philo-

176 JULIET FLOYD

sophy 82 (1985), 471-8; and William Tait, 'Wittgenstein and the "Skeptical Paradoxes"', Journal of Philosophy 81 (1984), 759-78. 56 RFM IV Section 9 suggests that the appeal to "same" occurs most naturally when trying to explain a rule to someone:

How could one explain to anybody what you have to do if you are to follow a rule? One is tempted to explain [Man ist versucht, zu erkliiren]: first and foremost do

the simplest thing (if the rule e.g. is always to repeat the same thing). And there is of course something in this. It is significant that we can say that it is simpler to write down a sequence of numbers in which each number is full same as its predecessor than a sequence in which each number is greater by 1 than its predecessor. And again that this is a simpler law than that of alternately adding 1 and 2.

57 Compare Baker and Hacker's discussion in their Scepticism, Rules & Language, (Oxford: Basil Blackwell, 1984), pp. 82ff. I have some hesitations about Baker and Hacker's rather free use of the notion of an "internal relation" to expound the later Wittgenstein, hesitations I elaborate in my dissertation, 'The Rule of the Mathematical: Wittgenstein's Later Discussions' (Harvard PhD Dissertation, 1990). 58 Compare PI Sections 215-6. 59 RFM I Section 3. See also PI Sections 213-4 where we read:

213. "But this initial segment of a series obviously admitted of various interpretations (e.g. by means of algebraic expressions) and so you must first have chosen one such interpretation". - Not at all. A doubt was possible in certain circumstances. But that is not to say that I did doubt, or even could doubt. (There is something to be said, which is connected with this, about the psychological 'atmosphere' of a process.)

So it must have been intuition that removed this doubt? - If intuition is an inner voice - how do I know how I am to obey it? And how do I know that it doesn't mislead me? For if it can guide me right, it can also guide me wrong.

«Intuition an unnecessary shuffle.»

214. If you have to have an intuition in order to develop the series 1 2 3 4 ... you must also have one in order to develop the series 2 2 2 ...

60 Cf. Frege's Gmndgesetze der Arithmetik, p. vii:

Of course the pronouncement is often made that arithmetic is merely a more highly developed logic; yet that remains disputable so long as transitions occur in the proofs that are not made according to acknowledged laws of logic, but seem rather to be based upon something known by intuition.

Wittgenstein is also indirectly attempting to undermine the kind of debate which took place between Russell and Poincare over "intuition". See Russell's review of Science and Hypothesis, reprinted from Mind, July 1905, in Russell's Philosophical Essays (New York: George Allen and Unwin, 1966). 61 RFM I Section 3. Wittgenstein moved the final two paragraphs from a different place in the manuscript, which may explain his switch to "2006" from "20006". See FV, Section 310.(316.). 62 RFM I Section 3. I have altered Anscombe's translation of the last sentence.


63 Cf. RFM IV Section 52:

Now can it be said that the concepts which mathematics produces are a convenience, that essentially we could do without them?

First and foremost the adoption of these concepts expresses the sure expectation of certain experiences.

We do not accept e.g. a multiplication's not yielding the same result every time. And what we expect with certainty is essential to our whole life.

64 See PI Section 211. 65 Cf. DC Sections 448-9. 66 PI p. 211:

"I know what I want, wish, believe, feel, .... " (and so on through all the psychological verbs) is either philosophers' nonsense, or any rate not a judgment a priori.

67 What would count as a relevant specification of my physiological state - whether, e.g., it would have to be similar in different environments for the same computation, whether it could vary from step to step of the same series, whether there would have to be any similarity between my state for the SOOth step of 2,2,2 ... and the 20003d step of +2 beginning with 0, whether it would be similar to other humans' physiologies for the same computation, or even "related" computations, etc. - all this is, at present, unknown. An informative physiological specification of my state at the 20003d step of the series + 2 would be considerably more difficult than our explanation of the computer's hardware, since after all, we built the computer. Warren Goldfarb, 'Wittgenstein, Mind, and Scientism', (Journal of Philosophy 86 (Nov. 1989),635-42) explores such difficulties in connection with Wittgenstein's discussions in PI of intentional mental notions (understanding, believing, remembering, thinking, etc.) and the question of whether Wittgenstein is standing in the way of empirical inquiry on the basis of an a priori argument. The care with which Wittgenstein asks us to treat (and distinguish) specific questions serves, it seems to me, as a reasonable philosophical lesson for the psychologist, who may jump too quickly into glossing the aim of particular experiments to be the support of a general psychological hypothesis about, say, inference in general. 68 Wittgenstein is referring to the law of Russell and Whitehead expressed in Principia Mathematica (Press Syndicate of the University of Cambridge, 1910; reprinted paperback version 1962), pp. 131-2:

We have next two propositions concerned with inference to or from propositions containing apparent variables, as opposed to implication. First, we have, for the new meaning of implication resulting from the above definitions of negation and disjunction, the analogue of *1·1, namely

*9·12. What is implied by a true premiss is true. Pp.

That is to say, given "~.p" and "~.p:J q", we may proceed to "~. q", even when the propositions p and q are not elementary. Also, as in *1·11, we may proceed from "~. 4>x" and "~ . 4>x:J !/Ix" to "~ . 1jJx", where x is a real variable, and 4> and !/I are not necessarily elementary functions. It is in this latter form that the axiom is usually needed. It is to be assumed for functions of several variables as well as for functions of one variable.

178 JULIET FLOYD

See RFM I Section 19ff. 69 RFM I Section 21. 70 RFM I Section 22. 71 Ibid. 72 Cf. PI Section 223:

One does not feel that one has always got to wait upon the nod (the whisper) next, but it always tells us the same, and we do what it tells us.

One might say to the person one was training: "Look I; always do the same thing: I ... "

73 PI Section 381:

Wie erkenne ich, dass diese Farbe Rot ist? - Eine Antwort ware: "Ich habe Deutsch gelernt".

In the above translation, I have altered Anscombe's translation of "erkenne". The context of this remark is different from that in RFM I, 3. In PI Wittgenstein is engaged in a discussion of the notion of a private ostensive definition and interlocutor's notion that such a definition might be secured by way of an image. The primary focus of the discussion in the opening sections of RFM I is, by contrast, the character of logical inference. Cf. Baker and Hacker, Scepticism, Rules & Language, p. 26. 74 Compare RFM VI Section 28:

Someone asks me: What is the color of this flower? I answer: "Red". - Are you absolutely sure? Yes, absolutely sure! But may I not have been deceived and called the wrong color "red"? No. The certainty with which I call the color "red" is the rigidity of my measuring-rod, it is the rigidity from which I start. When I give descriptions, that is not to be brought into doubt. This simply characterizes what we call describing.

(I may of course even here assume a slip of the tongue, but nothing else.)

75 I have many intellectual debts. My emphasis on the importance of Wittgenstein's style of writing derives from several years of courses, lectures, and reading of the works of Stanley Cavell, Burton Dreben, Warren Goldfarb and Hilary Putnam. My first debt is to Dreben, who urged me to work on Wittgenstein's discussions of mathematics and logic and whose wit and acuity have been a constant source of encouragement and stimulation. Conversation with Cavell on an earlier draft of Part 3 helped me to articulate my outlook on Wittgenstein's notions of grammar and logic and to rethink Baker and Hacker's metaphorical description of the manuscript basis of Wittgenstein's text. Goldfarb offered numerous helpful criticisms of earlier drafts of Parts 1-4. Thomas Scanlon's detailed comments on my characterization of Platonism helped me to clarify what I see at stake in Wittgenstein's writing. William Flesch's reading of an early draft of Parts 4-6 kept me focussed on Wittgenstein's text, while the thoughtful responses of Gary Ebbs and Charles Parsons made me better appreciate the importance of placing an emphasis on Wittgenstein's philosophical method in defending my interpretation. Susan Austrian's willing ear provided me with strong support in the early phrases of writing, and David Stern was kind enough to provide me with a copy of the critical edition of FV and MV compiled


by G. H. von Wright and Heikki Nyman. Judson Webb and Cora Diamond offered supportive criticism of the paper's final draft.

REFERENCES

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Anscombe, G. E. M.: 1985a, 'Review of Wittgenstein on Rules and Private Language', Ethics 95, 342-52. '

Anscombe, G. E. M.: 1985b, 'Critical Notice of Saul Kripke's Wittgenstein on Rules and Private Language', Canadian Journal of Philosophy 15, 103-9.

Baker, G. P. and P. M. S. Hacker: 1984, Scepticism, Rules and Language, Basil Blackwell, Oxford.

Baker, G. P. and P. M. S. Hacker: 1985, Wittgenstein: Rules, Grammar and Necessity: (An Analytical Commentary on the Philosophical Investigations, Volume II), Blackwell, Oxford.

Bernays, P.: 1959, 'Comments on Ludwig Wittgenstein's Remarks on the Foundations of Mathematics', Ratio 2, 1-22.

Cavell, S.: 1979, The Claim of Reason: Wittgenstein, Skepticism, Morality, and Tragedy, Oxford University Press.

Cavell, S.: 1988, The Carus Lectures, 1988. Chihara, C.: 1977, 'Wittgenstein's Analysis of the Paradoxes in his Lectures on the

Foundations of Mathematics', Philosophical Review 86, 365,..81. Dummett, M.: 1959, 'Wittgenstein's Philosophy of Mathematics', in M. Dummett: 1978,

Truth and Other Enigmas, Harvard University Press, Cambridge, MA, pp. 166-85. Floyd, J.: 1990, The Rule of The Mathematical: Wittgenstein's Later Discussions, PhD

Dissertation, Harvard University. Frege, G.: 1893, Grundgesetze der Arithmetik, originally published at Jena; republished

by George Olms Verlagsbuchhandlung, 1966, Hildesheim; English translation (which I cite), 1969, The Basic Laws of Arithmetic: Exposition of the System, Montgomery Furth (trans.), University of California Press.

Frege, G.: 1980, Translations from the Philosophical Writings of Gottlob Frege, P. Geach and M. Black (eds.), third edition, Rowman & Littlefield, Totowna, NJ.

Goldfarb, W.: 1983, 'I Want You to Bring Me a Slab',. Synthese 56, 26S-82. Goldfarb, W.: 1989, 'Wittgenstein, Mind, and Scientism', Journal of Philosophy 86,635-

42. Kant, 1.: 1790, The Critique of Judgment, James Creed Meredith (trans.), Oxford Univer

sity Press, 1952. Klenk, V.: 1976, Wittgenstein's Philosophy of Mathematics, Martinus Nihjoff, The Hague. Kreisel, G.: 1958, 'Wittgenstein's Remarks on the Foundations of Mathematics', British

Journal for the Philosophy of Science, 9, 135-58. Kripke, S.: 1982, Wittgenstein on Rules and Private Language, Harvard University Press,

Cambridge, MA. Kripke, S.: 1985, 'Kripke on Wittgenstein on Rules', Journal of Philosophy 82, 471-8. Russell, B.: 1903, The Principles of Mathematics, Cambridge University Press, Cam

bridge; reprinted with a new introduction, 1938.

180 JULIET FLOYD

Russell, B.: 1905, 'Review of Science and Hypothesis', Mind; reprinted in Russell's Philosophical Essays, George Allen and Unwin, New York, 1966: 70-8.

Russell, B. and A. N. Whitehead: 1910, Principia Mathematica, Cambridge University Press, Cambridge; second ed. (1927) reprinted in paperback to 56, 1962.

Shanker, S. G.: 1987, Wittgenstein and the Turning Point in the Philosophy of Mathematics, State University Press of New York, Albany, NY.

Tait, W. W.: 1984, 'Wittgenstein and the "Skeptical Paradoxes''', Journal of Philosophy 81,759-78.

Von Wright, G. H.: 1969, The Wittgenstein Papers', in vol\ Wright, (1983), pp. 35-62. Von Wright, G. H.: 1979, 'The Origin and Composition of the Philosophical Investi

gations', in von Wright (1983), pp. 111-36. Von Wright, G. H.: 1983, Wittgenstein, University of Minnesota Press, Minneapolis. Wittgenstein, L.: 1921. Tractatus Logico-Philosophicus, originally published in the final

number of Ostwald's Annalen der Naturphilosophie under the title Logische-Philosophische Abhandlung (1921); English translation, C. K. Ogden (trans.) Routledge & Kegan Paul, London, 1933 (first published in English, without corrections, 1922).

Wittgenstein, L.: 1937, The "Friihversion", or Early Version of Philosophical Investigations, compiled by G. H. von Wright and Heikki Nyman (unpublished).

Wittgenstein, L.: 1945, The "Mittelversion", or Intermediate Version of Philosophical Investigations, compiled by G. H. von Wright and Heikki Nyman (unpublished).

Wittgenstein, L.: 1958, Philosophical Investigations, G. E. M. Anscombe and R. Rhees (eds.), G. E. M. Anscombe (trans.), second edition, Blackwell, Oxford.

Wittgenstein, L.: 1967, Zettel, G. E. M. Anscombe (ed.) and G. H. von Wright (trans.), Blackwell, Oxford.

Wittgenstein, L.: 1969, On Certainty, G. E. M. Anscombe (ed.), Blackwell, Oxford. Wittgenstein, L.: 1974, Philosophical Grammar, R. Rhees (ed.), A. J. P. Kenny (trans.),

Blackwell, Oxford. Wittgenstein, L.: 1976, Wittgenstein's Lectures 011 the Foundations of Mathematics, Cam

bridge 1939, Cora Diamond (ed.), University of Chicago Press; originally published by Cornell University Press, Ithaca, NY. 1976.

Wittgenstein, L.: 1977, Remarks on Color, G. E. M. Anscombe (ed.), L. L. McAlister and M. Schiittle (trans.), University of California Press.

Wittgenstein, L.: 1978, Remarks 011 the Foundations of Mathematics, G. H. von Wright (ed.), R. Rhees and G. E. M. Anscombe (trans.), revised edition, Blackwell, Oxford.

Wittgenstein, L.: 1979, Wittgellstein and the Vienna Circle, Brian McGuinness (ed.), Joachim Schulte and Brian McGuinness (trans.), Basil Blackwell, Oxford.

Wright, C.: 1980, Wittgellstein on the Foulldations of Mathematics, Duckworth, London.

Dept. of Philosophy The City College of New York New York, New York 10031 U.S.A.

ANNOUNCEMENT

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The Department of Philosophy, Logic and Scientific Method announces a new one-year M.Sc. degree. The degree is designed specifically for students with either a first degree in philosophy, or a science degree, who are interested in philosophical questions that arise in scientific inquiry in general, and physics in particular. Applications from students for October 1991 are now welcome.

The core course is Philosophical Foundations of Physics:- An introduction to some fundamental ideas in physics and the methodological and philosophical issues they raise.

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Synthese 87: 181, 1991.

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LAKATOS AWARD

No Lakatos Award was awarded in 1990. (Professor John Earrnan won it in 1989, not 1990 as appeared in the last announcement.)

Synthese 87: 182, 1991.

JAAKKO HINTIKKA

AN IMPATIENT MAN AND HIS PAPERS*

Ludwig Wittgenstein died in 1951. At the time, the i,deas he had developed after his return to philosophy in 1928 were known only to a handful of people through his lectures and conversations and through the typescripts which he had dictated and which were circulating among friends and colleagues. The wider philosophical community was eagerly waiting for Wittgenstein's ideas to become effectively available.

Since 1953, no fewer than twelve volumes of Wittgenstein's writings dealing with his later philosophy have seen the light of printer's ink. In addition to them, posthumous material has been published in several jourrials, and at least six volumes of Wittgenstein's recorded lectures and conversations as well as five volumes of letters have found their way into print. This might very well seem to constitute an adequate basis for understanding Wittgenstein's later philosophy. Indeed, the great majority of philosophers writing on him have obviously been working on that assumption. Why, in view of these prima facie reasons to the contrary, is there an urgent need to make all of Wittgenstein's Nachlass available in print?

The reasons are deeply rooted in Wittgenstein's character and temperament. A revealing glimpse is offered by Fania Pascal's perceptive reminiscences in "Wittgenstein: A Personal Memoir" (in Rhees, R. (ed.): 1981, Ludwig Wittgenstein: Personal Recollections, Basil Blackwell, Oxford, pp. 26-62, esp. pp. 48, 60). She recounts the strange incident of Wittgenstein's confession in 1937.

"I have come to make a confession". He had just been to Professor Moore for the same purpose. "What did Professor Moore say?" He smiled. "He said, 'You are an impatient man, Wittgenstein' .... " "Well, did you not know you were?" Wittgenstein, with disdain: "I did not know".

Later in her memoir Fania Pascal sums up some of her observations as follows:

He was an aggressive and explosive man, but this too in a very peculiar, naive way of his own. At 48 he did not know the simplest thing about himself, namely, that he was impatient. 1 have several times mentioned the forbidding severity he directed at himself.


184 JAAKKO HINTIKKA

But he never saw himself through the eyes of others, and he had no other standards than his own.

No one who ever came in contact with Wittgenstein is likely to challenge Ms. Pascal's observations. Not long ago, I was asked by a younger philosopher whether I had some insight into, or knowledge of, why Wittgenstein and Carnap could not g~t along. The implied expectation obviously was of some dark moral secret casting its shadow over the relationship of the two men. For a brief moment I was astounded, but only until I realized that the questioner was too young to have met either philosopher in person. If he had, I doubt that he would have raised the question. Wittgenstein was the most impatient of human beings; Carnap was one of the most patient of men. Carnap was wont to ponder what this or that philosopher meant by what he had said, and to ask repeatedly questions about them. Wittgenstein hated having to explain himself. Carnap's patient and persistent questioning must have driven him up the wall.

Wittgenstein's impatience offers a clue to the significance of his Nachlass. As a philosophical expositor, he exhibited the same qualities as he did as a person. He directed a "forbidding severity" at Wittgenstein the philosophical writer; but he did not see his writings through the eyes of others, only in the light of his tremendous impatience.

What this implies for the reader of Wittgenstein's writings is clear. He was struggling heroically to reach the clarity which would have satisfied his own high standards, and anxious to express the ideas that he had been able to reach. But he was frequently too impatient to explain adequately what the problems were that his ideas were supposed to be solutions to, partly because he did not realize that his problem background was not always familiar to his readers.

Of course his problems were not traditional "philosophical problems", such as the reality of the exte~nal world, the mind-body problem, etc. Such questions were regarded by him as hopeless muddles. But this does not affect the fact that Wittgenstein's entire thought was problem-driven, even though the solution to his problems consisted typically of the elimination of a confusion or some other "mental cramp".

Sometimes Wittgenstein was impatient even in presenting his own solutions. After having moved on to new problems, he no longer felt the need of expounding his solutions to the old ones again at any length,

AN IMPATIENT MAN AND HIS PAPERS 185

and expressed them only through shorthand references. For instance, in Philosophical Investigations the name-object relation is explained in a couple of sentences:

What is the relation between name and thing named? - Well, what is it? Look at language-game or at another one; there you see what his relation can consist in.

(My reasons for departing from the standard translatipn are indicated in Merrill B. Hintikka and Jaakko Hintikka: 1986, Investigating Wittgenstein, Basil Blackwell, p. 209.) Yet when Wittgenstein had first come upon the idea that language-games mediate the name-object relation, viz., in the Brown Book, pp. 171-73, he had spent two entire pages for the purpose of explaining the idea, and also had signalled unmistakably its connection to his other problems.

This is an excellent illustration of what Fania Pascal meant by saying that Wittgenstein never saw himself (or in this case, his ideas and writings) through the eyes of others. This impatience affects different parts of Wittenstein's oeuvre differently. His pre-World War I problems were by and large the same as those of Russell and the other Cambridge philosophers. Yet even there, in understanding Tractatus, Wittgenstein's impatience has made the task of later interpreters needlessly difficult. As David Pears has convincingly shown, an important part of Wittgenstein's background was Russell's theory of acquaintance. Tractatus was in effect an Aufhebung of certain aspects of Russell's theory, especially of the idea that logical forms can be objects of acquaintance. Yet Russell's theory, which Wittgenstein takes to be known to the reader, was never spelled out fully in print in Russell's lifetime. It is developed most explicitly in the 1913 manuscript Theory of Knowledge whose relevant parts were first published only in 1984 in vol. VII of Russell's Collected Papers (Russell, B.: 1984, Collected Papers, ed. by Elizabeth R. Eames in collaboration with Kenneth Blackwell, Allen & Unwin, London).

Later, the members of the Vienna Circle shared most of Wittgenstein's central problems. However, subsequent generations of philosophers, beginning with Wittgenstein's own students in the thirties, have not always been aware of where Wittgenstein was coming from and what path his work on his problems took. For this reason, Wittgenstein's former students are not necessarily in a better position to understand his writings than others. Not all of them have realized that they, too, can reach an adequate understanding of Wittgenstein's problems

186 JAAKKO HINTIKKA

and hence a deeper understanding of Wittgenstein's philosophy onl through a careful study of the posthumous materials, especially of th notebooks.

These insights into Wittgenstein as an expositor of his own ideas pl the entire project of publishing his Nachlass into a new perspectiv~ The early publication efforts seem to have aimed at publishing Wittger stein's later philosophical ideas in the way he himself intended. Thi aim, understandable though it is, is not the appropriate one, for tw different reasons. First, Wittgenstein's ideas were constantly changin~ It is far from clear that there is anything like the later philosophy c Ludwig Wittgenstein, much less that it is codified in anyone manuscrir or typescript (or sets thereof) that he left behind. It is for instance monstrous oversimplification to try to view The Blue and the Brow, Books as "Preliminary Studies of the Philosophical Investigations", t, quo~e the subtitle Rush Rhees gave to the volume.

Second, in view of what has been said, the relatively finished writing of Wittgenstein's require as a necessary complement, needed to enabl, us to understand their problem background, the availability of th, notebook materials.

The emphasis in Wittgenstein editing has in fact shifted, at leas ostensively, from the publication of individual volumes to the produc tion of a Gesamtausgabe.

Before discussing the complete works projects, it is in order to notl the serious problems that beset some of the piecemeal publications For instance, the only halfway conventional book Wittgenstein lef behind is TS 213 in von Wright's catalogue, commonly referred to a The Big Typescript. (It even has chapters, chapter titles, sections, sec tion titles, etc.) Rhees was supposed to edit it, but as Anthony Kenn: has shown, he ended up doing something quite different. (See Kenny 1984, 'From the Big Typescript to the Philosophical Grammar', in Th, Legacy of Wittgenstein, Basil Blackwell.) Rhees assembled a medley 0

materials, from different sources, which was never intended by Witt genstein to go together and which are sometimes lifted out of an impor tant context.

Likewise, Rhees's 1968 edition of Wittgenstein's highly import an "Notes for Lectures on 'Private Experience' and 'Sense Data'" (1968 Philosophical Review 77, 274-320) omits without any indications abou 30 percent of Wittgenstein's actual text, including what I consider somt of the most important passages Wittgenstein ever wrote. The onl~


warning Rush Rhees issues is to say that "(f)or special reasons, I have not included the sections on mathematics". This is entirely misleading, because most of the omitted material has nothing to do with mathematics. Rhees's omissions frequently take place in the midst of Wittgenstein's text, thus destroying any hope of grasping the continuity of Wittgenstein's thought on the basis of his "edition".

Furthermore, the volume entitled Remarks on the·, Foundations of Mathematics is a mixture of materials from ten different manuscripts of typescripts, of which five are merely excerpted. These MSS were written over a period of several years. There is little reason to expect that the different parts of the volume reflect one and the same set of views or that these parts show faithfully Wittgenstein's line of thought.

Most importantly, there are serious questions also about Philosophical Investigations, especially about Part II. It is supposed to have been intended by Wittgenstein to be a part of the same work as Part I, but no documentary evidence to that effect has ever been made public. This problem needs a separate study, but in view of its importance, a few words may be in order here, even though I have little to add to the facts of the case as presented by von Wright. The final version of Part I of Philosophical Investigations was essentially finished in 1946, even though Wittgenstein kept on polishing it. The preface to the published book was dated in January 1945. Between 1946 and 1949 Wittgenstein wrote down his further ideas in notebooks 130-138. On their basis he dictated two TSS, nos. 229 and 232, most of which were subsequently published as Remarks on the Philosophy of Psychology I-II. He also used these notebooks to compose carefully and selectively a further MS, viz., MS 144. Out of this MS, somehow a typed version (TS 234) was produced. This TS is the text Part II of Philosophical Investigations was actually printed from. Professor Rhees has claimed that Wittgenstein dictated it. There is some - admittedly inconclusive - evidence to suggest that this claim is mistaken. By and large, the published version (Philosophical Investigations II) and MS 144 are very close together. There are a number of discrepancies, however, and in a few of them MS 144 is apparently better in line with Wittgenstein's intentions than the printed text. Moreover, five fragments which are included in MS 144 are missing in Philosophical Investigations. It would be of some interest to know precisely why these remarks were omitted from the printed version, especially as some of the omissions seem to exhibit a philosophical bias. Unfortunately, the situation is made even

188 JAAKKO HINTIKKA

more difficult by the fact that TS 234 has meanwhile disappeared and no copy of it is known to survive. (Further information is nonetheless forthcoming in a new, so far unpublished paper by G. H. von Wright, whose perspective differs somewhat from my own.)

Whatever the details are or may be, it is clear that Philosophical Investigations cannot automatically be assumed to be Wittgenstein's definitive statement of his own settled philosopi;lical views.

The upshot of this list of problems is the importance of the rest of Wittgenstein's literary remains. They provide, in fact, an ideal antidote to philosophers' exclusive and misdirected preoccupation with the postulated end product of Wittgenstein's literary and philosophical labors. In order to see this, it is useful to recall Wittgenstein's working method. He kept a series of notebooks of which about thirty have survived from the post-1928 period. In them, he wrote his ideas as they came to him, sometimes dating the entries. These notebooks constitute a highly unusual and fascinating document. Historically, psychologically, and philosophically they offer a rare opportunity to witness a major philosopher in the very act of coming upon new ideas, developing them, revising them, and so on. Sometimes Wittgenstein even comments on his own changes of mind. Reading the notebooks attentively and in awareness of their ancestors and descendants almost gives one a feeling of peeking over his shoulder.

When Wittgenstein had reached something like an equilibrium in his thinking, he typically hired a typist and, using the notebooks as raw material, dictated a typescript which he often hoped would eventually become a publishable book. In dictating the typescript, he of course omitted liberally old material and added new text. Thus, if the notebooks show what Wittgenstein's spontaneous new ideas were and how he developed them before he was satisfied with them, the typescripts show what solutions eventually satisfied him, if only for the time being. Above all, the notebooks show what Wittgenstein's problems were, what questions he was raising and where he was looking for answers to them.

Publishing only the typescripts, or some of them, as Wittgenstein's editors have mostly done so far, will give an incomplete picture of the development of his ideas and consequently of these ideas themselves.

It would perhaps be an exaggeration to say that Wittgenstein's later philosophy cannot be understood without a thorough knowledge of his development such as it is reflected in his notebooks. It is extremely


difficult to do so, however, and it can only be done by someone who is attuned to the philosophical problems which occupied Wittgenstein. And even so, I doubt that an interpretation which is not based on the notebooks can be fully detailed and accurate. Even more, I doubt whether it can be convincingly proved to be correct. More than once I have myself (alone, or in cooperation with Merrill B. Hintikka) first came upon an interpretation on the basis of Wittgenstein's published writings only to find subsequently the "smoking gun" 'that clinched the case in Wittgenstein's notebooks or in other unpublished materials.

One of the many invaluable clues which the unpublished materials yield to Wittgenstein's thought and to its development are the several explicit statements that Wittgenstein makes as to what his own previous views had been on this or that matter. Thus in MS 105, p. 251, Wittgenstein offers an explanation of what he had earlier thought of the color incompatibility problem. And in TS 213, as well as in MS 166, he makes an extraordinary statement which shows to what extent his discussion of rule-following in Philosophical Investigations was directed against his own earlier views of what it takes to understand a rule.

And even apart from their role in showing us the development of Wittgenstein's thought, his notebooks are a rare document in the entire field of human thought. I doubt that there is any other major thinker who has provided us with a more direct access to his own thought processes.

Hence there are ample reasons for making Wittgenstein's Nachlass available to the philosophical community in its entirety and in a form in which it can be used by active philosophers who want to understand his thought, evaluate it, and use his insights in their own work.

Thus we are led to the crucial question: What has been done to make available the full story of Wittgenstein's philosophical efforts, such as they are reflected in his literary remains?

The stage was set for these efforts by Wittgenstein's will. Its relevant parts read as follows (I follow the original spelling and punctuation):

I give to Mr. R. Rhees, Miss G. E. M. Anscombe and Professor G. H. von Wright of Trinity College Cambridge All the copyright in all my unpublished writings; and also the manuscripts and typescripts thereof to dispose of as they think best but subject to any claim by anybody else to the custody of the manuscripts and typescripts. I intend and desire that Mr. Rhees, Miss Anscombe and Professor von Wright shall publish as many of my unpublished writings as they think fit ...

190 JAAKKO HINTIKKA

The frequently used term "literary executors" for the three original copyright owners does not occur in Wittgenstein's will. For convenience, I shall nevertheless use it here.

The three literary heirs mentioned in the will donated in 1969 all the MSS and TSS to Trinity College, Cambridge. According to the terms of the agreement between the literary heirs and Trinity College, two committees were created to serve the two functions mentioned in Wittgenstein's will. There is a Board of Trustees who administer the copyrights and a Committee of Editors managing the publication of the posthumous material. So far, both of these legally separate bodies have had the same members. Originally, both of them consisted of the three literary heirs. After Rush Rhees's death in 1989, Professor Peter Winch was co-opted to serve on both committees, and in January 1990 Dr. Anthony Kenny was likewise added to both boards.

There is another curious fact about the copyrights to the bulk of Wittgenstein's Nachlass. In a sense, the bulk of Wittgenstein's literary remains has been made available to the general philosophical public. Since 1967, it has been possible to purchase a microfilm copy of most of the unpublished materials through the Cornell University library system. This has greatly facilitated scholars' work on Wittgenstein. However, it has complicated the legal situation. In U.S. copyright law, making these microfilms available for purchase (with the consent of the copyright owners) constitutes publication. Therefore, the microfilmed material is subject to the same provisions of the law as ordinary published material, including the normal fair use provisions. Among other things, this means that bona fide scholars have the right to quote short passages from the Cornell material without an explicit permission from the copyright owners.

Furthermore, it appears that the copyrights to the entire Cornell material, which amounts to the bulk of Wittgenstein's Nachlass, are in the public domain. The reason is that U.S. copyright law, at the time of the Cornell "publication", required that, in order to retain exclusive rights, the publisher register the copyrights and indicate them on the publication itself. Apparently, neither of these things was done.

The availability of the Cornell microfilms means that most of Wittgenstein's literary remains are in a sense accessible to interested scholars. This does not close the issue, however. For all practical purpose the microfilm version is unusable, unless one is willing to devote one's entire professional life to the study of Wittgenstein's development. This


is because much of the material exists only in the form of Wittgenstein's longhand untranslated, unedited and untranscribed. Admittedly, as German longhand goes, Wittgenstein's is mostly relatively easy to read. (Personally I find myself temporarily stymied every couple of pages or so, but only until I realize that Wittgenstein, in his impatience, has run two German words together.) But what is impossible is to have any quick overview of what Wittgenstein is saying on anyone page. In order to see what he is as much as writing about, you have to read his words one by one. This makes it extremely hard to get any sense of the continuity of Wittgenstein's thought. For he seldom pursues the same line of thought uninterruptedly for very long. He is usually thinking about several different topics at the same time, and records his ideas on all of them one after the other. After dropping temporarily one line of thought, it may be hours, days, weeks, months or years before he takes it up again. Hence the use of his notebooks requires a constant series of comparisons between different pages of the same notebook and between different notebooks, which is agonizingly difficult on a microfilm machine. Furthermore, the recognition of the continuity of Wittgenstein's thought is made difficult by the habit of his that Waismann complained so bitterly about, viz., his as it were constantly beginning from the beginning, as if he had never thought about the topic before.

Hence the Cornell microfilms cannot serve the purpose of making Wittgenstein's literary remains effectively accessible to serious professional philosophers trying to understand his thought. In view of the complexity of Wittgenstein's surviving writings and of their interrelations with each other, it is tempting to try to use computer technology for the purpose. If an accurate, readable machine database is created of the Nachlass, one is tempted to think that it could be used as a basis of a printed edition of some or all of the materials, and, in any case, could be used by scholars to follow the continuity of Wittgenstein's thought (with the help of suitable global search programs) in less time than the months and years of hard work presently required. It is therefore not surprising that the use of computers has been the leading idea in the three major projects aimed at making Wittgenstein's entire Nachlass available to scholars.

Before discussing these projects, it is in order to spell out what is involved. When Wittgenstein died, no one, including his literary executors, had a realistic idea of what he was leaving behind. Gradually,

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a surprisingly large and complex Nachlass has emerged, compnsmg somewhere between twenty and thirty thousand manuscript or typescript pages. Initially, it was virtually impossible to find one's way among them. The philosophical community owes an enormous debt to Professor G. H. von Wright whose work now enables us to have an overview of the Nachlass. He has written an annotated, critical catalogue of the posthumous material, whose num~ering of the MSS and TSS I am following in this article. He has also related the Nachlass to Wittgenstein's most influential works, Tractatus and Philosophical Investigations. Professor von Wright's papers on all these subjects are most easily available in his volume Wittgenstein (Basil Blackwell, 1982).

The first attempt to edit a complete edition of Wittgenstein's writings was launched around 1975. It involved a team working at the University of Tiibingen in what was known as the Tiibingen Wittgenstein Archive. The team was led by Mr. Michael Nedo and Professor H. J. Heringer. The other scholars involved were Drs. R. Nowak, M. Rosso and J. Schulte. The legal basis of their work was an agreement between the three literary executors and the Wittgenstein-Archiv Tiibingen which was signed on 19 October 1974. The project was supported mostly by Fritz Thyssen Stiftung.

For a variety of reasons, the work on this project was never carried out to its intended conclusion. The team members quarrelled with each other, and work on this project came to an end sometime in 1980-81. Not a single volume of Wittgenstein's posthumous manuscripts or typescripts was published as a result of this project or has been subsequently published. The Tiibingen Wittgenstein-Archive which was to host the project was also dissolved. Some insight into the reasons for the collapse of the Tiibingen project is perhaps provided by the closing report of the project. In it Professor Heringer complained that Mr. Nedo "was incapable of directing such a project in an organizationally serious or personally responsible manner" ("der ein solches Projekt weder organisatorisch serios noch menschlich verantwortlich leiten konnte") and that eventually "there arose with all the collaborators considerable doubts concerning Mr. Nedo's scholarly competence".

On a later occasion, Mr. Nedo listed as his contributions to this project only the organization (together with H. J. Heringer) of two international symposia whose proceedings were published by Suhrkamp and the editing (together with Michele Ranchetti) of a pictorial biog-


raphy of Wittgenstein. Neither enterprise furthered in any way the Gesamtausgabe project.

In reality the Tiibingen project had nevertheless accomplished a fair amount. Among other things, more than a half of the Nachlass was transcribed into a database; a search program for textual similarities was developed; and a prototype text segment was produced to serve (it was hoped) as a basis for further development and for scholarly discussion of the different forms which a definitive ect'ition might take. Because of disagreement between the different persons involved, these results could not be utilized by the second editing project, however.

After the Tiibingen project had come to an end, a new one was launched. On 16 October 1981, the three literary executors applied for support from Fonds zur Forderung der wissenschaftlichen Forschung, which is the main Austrian governmental research foundation. The project was to be directed this time by Mr. Nedo alone, and the project description was written by him. The project was to involve Mr. Nedo as Projektleiter, Ms. Isabelle Weiss plus short-term technical and secretarial help. The aim of the project included a "complete transcription of the posthumous writings into a database and especially developed computer programs". As far as the timetable was concerned, Mr. Nedo wrote that

given appropriate working conditions a complete edition of Ludwig Wittgenstein's works can be available by his hundredth birthday in April 1989.

Curiously, there is no indication in the grant application that the proposed work would, to a considerable extent, merely repeat what had already been accomplished by the Tiibingen group, or that Mr. Nedo would not have access to those fruits of the Tiibingen group's labors, even though such information would clearly have been highly pertinent to the evaluation of the scholarly significance of the new project.

The Fonds (as I shall here abbreviate the name) undertook to support the project. On 27 September 1982, its Kuratorium decided to fund its first stage as a pilot program which was to last twelve months and was to be continued if successful. The Fonds awarded 633,000 Austrian shillings for the purpose. At the same time, IBM Wien donated the necessary computer time to the project.

The subsequent history of the project is not easy to chronicle, one

194 JAAKKO HINTIKKA

reason being Mr. Nedo's failure to keep his own sponsors apprised of what he had done and what he had not done. The following is at least part of the story. On 5 November 1983, Nedo submitted an annual report to the Fonds. This report was approved of by Professor Anscombe on the behalf of the literary executors without actually consulting all of them. On the basis of her Aussage, the grant from the Fonds was renewed in March 1984. It was apparently renewed again in 1985.

In spite of the renewals, the project was not proceeding very well. Mr. Nedo had promised the literary executors to produce for their inspection a transcript of MSS 105-108 and TSS 208-210 as evidence of his progress by October 1984. Because Nedo had not fulfilled any of this promise by November 1987, Professor G. H. von Wright informed the Fonds that he was withdrawing any further support of Mr. Nedo) Without his knowledge, Professor Anscombe had meanwhile submitted a renewal application on behalf of all the literary executors, dated on 19 September 1987. As a consequence of Professor von Wright's letter, the Fonds postponed its decision on the renewal application.

Early in 1988 Mr. Nedo produced a transcript of MSS 105-106. Although this represents only about one quarter of his initial task, a compromise was reached among the literary executors in October 1988 to the effect that a new application should be made to the Fonds for a grant which would enable Nedo to complete the assignment. On 24 April 1989, the Kuratorium of the Fonds awarded the sum of 1,690,000 Austrian shillings for the project, which is the sum applied for in 1987.

What all this amounts to is a nearly total failure of the project so far. Mr. Nedo has yet to fulfill most of the work he promised to have ready in 1984. In general, the documented progress of the project has been minimal. Several disturbing questions are prompted by Mr. Nedo's record. For instance, in a report of his activities in 1983, Nedo claimed that the first notebook volume had been typeset in 1983. If this information is correct, much of the material which Nedo finally produced as evidence of his activities in 1988 was in effect ready in 1983. If so, there is precious little that the project accomplished between 1983 and 1986. The very same picture book that Nedo had, in 1981, listed as a product of the Tiibingen project is now listed as a result of the 1981 project. In reality, this book has nothing to do with the collected works project. In the earlier project descriptions, several interesting results


were promised by Nedo, including the following: In the 1981 project description, Nedo claimed to have reconstructed two MSS, MS 126 and MS 127 (which have disappeared), and promised to edit and publish them. Not only has this promise remained unfulfilled, it has been dropped completely from the new project. Likewise, in the original project Nedo undertook to publish "an extensive bibliographical description of the entire Wittgenstein Nachlass". Nothing has come about this plan either. In 1981 Mr. Nedo was thinking about having the entire Nachlass published by the Wittgenstein centennial in April 1989. In 1987 he claimed that, with appropriate support, he would have four volumes in print by April 1989 containing MSS 105-108 and TSS 208-210. Needless to say, nothing like that was ever accomplished.

In view of this string of unfulfilled promises, it does not seem advisable to let Mr. Nedo continue the editing of Wittgenstein's Nachlass. His track record shows amply that he is not a suitable person to carry out the Gesamtausgabe project.

Why has the Gesamtausgabe project failed so far? How should it be continued, if it will be? There is not enough evidence available to give a definitive answer to these questions, but a few educated guesses are possible. According to the information supplied by Mr. Nedo to his sponsors, by 1985 he and his collaborators had 15,000 pages, that is, about a half of the Nachlass, transcribed in a database. How is it conceivable, assuming that this information is correct, that by 1990 no single volume has appeared and that a decent hard copy is available only of a tiny fragment of the total material? Several explanations are possible, but they all point to the same direction. The transcribed material might have been coded in a way that makes its utilization for editing purposes difficult. Furthermore, it seems obvious that Mr. Nedo and his aides have not managed to develop software that would enable them to move effectively from the transcribed text material to an edited text. This is undoubtedly the gist of the problem. The alleged coding problems are also likely to be but consequences of the same fact: it is hard to know what kind of coding is appropriate when you do not have an adequate idea of the software to be used to handle the inputted text.

It is in fact embarassingly obvious that the entire editing project was launched before the people responsible for it had a realistic conception of the software needed for the purpose, or even a conception of how such software could be developed. What is amazing is nevertheless not

196 JAAKKO HINTIKKA

this overoptimism which the project undoubtedly shares with several others. What is astounding is the failure, as far as the available record above, of Mr. Nedo to use any of the available resources for the purpose of software development. The industrial companies he has tried to befriend have been big computer manufacturers like IBM and Olivetti, not software companies, even though such companies have meanwhile actually developed all kinds of software for the very purpose of text editing. There is no evidence available that Mr. Nedo has consulted any software expert, and no evidence that he has availed himself of the experience of other computer-based editing projects. His excuse has been the alleged special difficulty of the Wittgenstein manuscripts. Yet there are successful computer-based editing projects where the technical problems, however different, are of an even greater complexity, such as the Leibniz project. Mr. Nedo's comments on other recent editing projects, such as the new Holderlin edition, merely show that he has no grasp of where his real problems lie. It looks as if Mr. Nedo has been waiting for a solution to fall into his lap as a gift from the heavens, perhaps simply in the form of increasingly powerful computers, without realizing that you need appropriate software for them, too.

I for one do not see any reason for continuing the Gesamtausgabe project before a suitable software has been developed and successfully tested. And the most efficient way of doing so is probably a close cooperation with a suitable ambitious software company.

Other important questions concern the rationale of the entire project. The edition of MSS 105-106 which Mr. Nedo has finally made available to others does not yield to a philosophical reader any information which a conventional critical edition would not. Yet such a conventional edition, even the most ambitious editio diplomatica, could have been produced in a few months at a fraction of the cost. It is also hard to see what the decisive advantages are supposed to be of Mr. Nedo's so far unpublished edition of the two notebooks over the prototype printout which was produced by the Ttibingen project.

It is hard to avoid the impression that the total plan of the Gesamtausgabe project has never been clearly thought out. If the aim has been simply to edit Wittgenstein's complete writings, it could have probably been done in fifteen years with the resources that have actually been available for the purpose, while maintaining the highest editorial standards.


The advantage which can be claimed for a computer-based edition is that, after a database has been created out of the total material, suitable software will enable scholars do research on Wittgenstein in a way which is now either impossible or else extremely tedious. However, it is obvious that the fundamental questions have not been asked here. How important would, e.g., the availability of computerized search programs be for Wittgenstein research? Having u~ed unpublished Wittgenstein materials in my own work, I am keenly aware of the tremendous convenience promised by search programs and other similar automated research tools. I am also keenly aware how very important the precise form of Wittgenstein's words can be, including the variants he himself penned in the text. Yet I cannot help asking: How crucial are such automated research tools as compared with the availability of a decent critical text? If, for instance, I look back on the insights into Wittgenstein's terminology and choice of words that have recently been achieved, such as the force of his term Aspekt or the crucial contrast between Name and Bezeichnung, would they have been easier to reach by means of computerized methods of dealing with the database? Scarcely. What is required for such insights is a sensitivity to the philosophical and conceptual issues involved such more than extensive comparative evidence, whose main role perhaps lies in verifying results rather than in reaching them. There is, in my judgment, even a clear danger that Wittgenstein research, or part of it, will be directed by the increased reliance on computers into philosophically unimportant directions.

Be such fears justified or not, the fact remains that decisions concerning editorial priorities cannot be detached from judgments concerning the philosophical interest of the different aspects of Wittgenstein's literary remains. I am very uneasy to see such decisions entrusted to Mr. Nedo, who has no formal philosophical training and whose expressed views on the content of Wittgenstein's Nachlass seem to me superficial and arbitrary. For instance, in the 1981 grant application to the Fonds, Mr. Nedo discusses Wittgenstein's ideas about mathematics in a way which shows that he has no sense of what is essential and inessential in Wittgenstein's views.

And even if I am underestimating the importance of computerized text processing, a very serious priority question arises here. Which would have been easier, quicker, and more economical, producing a conventional critical text first and then inputting it into a database or

198 JAAKKO HINTIKKA

the other way round, as in the two Gesamtausgabe projects? Would anything have been lost in the former procedure? Maybe the answer is that something would have been lost, but it seems to me that the question has not been raised. And the moral of the story of the two Gesamtausgaben projects surely is that the editing could have been done much more quickly in the old-fashioned way.

It may also turn out that the bottom line on tpe balance sheet of the Gesamtausgabe project is in a sense not even zero, but negative. Not only is it the case that the project has not produced any publications so far. Because of Mr. Nedo's work, the majority of the literary executors has disallowed certain other Wittgenstein editions. For instance, there exist several fully edited volumes, virtually ready for the printer, in Helsinki which have been edited by Professor von Wright and his assistants. They include most of the unpublished materials that are crucially important for our understanding of the genesis of Philosophical Investigations, including MSS 116 and 144 as well as TSS 220, 221, 227, and 239.

Ironically, Mr. Nedo's partial monopoly of editing Wittgenstein seems to have, at this moment, no legal basis, if it ever had one. In 1979, the literary executors wrote a letter to the Tiibingen group promising that they would not give permission for any competing edition in the next ten years. However, this promise was given to the Tiibingen group, which came to an end in 1981, not to Mr. Nedo. In any case, the monopoly expired in 1989. But even before it, Nedo had little claim to any preferential treatment, for he had consistently failed to fulfill the terms of the 1981 application to the Austrian Fonds. In particular, he had failed to keep all the literary executors informed about his work.

The efforts to publish a Gesamtausgabe are thus after some fifteen years without any definitive product, even though there is some hope for the future. This has created an unfortunate situation in several respects. There is a veritable scholarly industry of books and papers on Wittgenstein going on unremittingly, oblivious to the critical importance of the notebooks and other unpublished materials for the interpretation of Wittgenstein, which will be subject to a sharp re-evaluation in the light of the literary remains.

What may be worse, an unhealthy climate has been created among those who are aware of the importance of the Nachlass but are without easy access to them. The main reasons for the failure of the major editing projects have been the judgments and decisions of the literary


executors. Yet some of the very same persons responsible for the editing of Wittgenstein have also been engaged in interpreting his philosophy. They have therefore placed themselves in the precarious position of being in control of other scholars' access to materials in the light of which their own interpretations are to be judged and which could conceivably prove some of these interpretations wrong. For their own sake, it is to be hoped that the present untenaple situation will soon be resolved so as to clear up unnecessary suspicions and rumors of their motivation and comportment.

The third project designated to make Wittgenstein's Nachlass more easily available to scholars is of an entirely different kind. There is a detailed account of this project available in the form of mimeoed report by Claus Huitfeldt and Viggo Rossvaer entitled The Norwegian Wittgenstein Project Report 1988 (The Norwegian Computing Centre for the Humanities, October 1989, 282 pp., ISBN 82-7283-052-3). Because of the public availability of this report, I shall restrict my description of this Norwegian Wittgenstein Project to a minimum.

The project began in 1981 as a joint venture of a number of Norwegian Wittgenstein scholars who formed a committee representing all the philosophy departments of Norwegian universities. The aim was not a published edition, but a computer-readable text which would be able to yield to scholars all the necessary information about Wittgenstein's own textual changes, corrections, alternatives, etc. The project was funded exclusively from Norwegian sources, to wit, by the Norwegian Research Council, the Nansen Foundation, and different Norwegian universities.

Approximately 3250 pages had been transcribed under the auspices of the Norwegian project by the time the report was written. Over and above that, transcribed material from the Tilbingen project was transferred to Norway, resulting in machine-readable text totalling somewhere between 700 and 8400 pages. Software to facilitate machine reading was also developed. At least one non-Norwegian scholar has actually used the material in question and found it useful. The Tilbingen material has not yet been properly converted, however, because of disputes concerning its legal status. These disputes go back to the quarrels within the Tilbingen group.

The Norwegians unfortunately did not realize that in order to make the Nachlass generally available even in a machine-readable form they needed the permission of Wittgenstein's literary executors. After a long

200 JAAKKO HINTIKKA

series of negotiations, that permission turned out not to be available. In the absence of a permission, no continued financial support was available, and effective work on the project came to a standstill in December 1987.

Recently, however, the Norwegian Wittgenstein Project has been reorganized and revived. The University of Bergen has assumed the responsibility for the project. On 3 May 1990, a, decision was made by the committee controlling the Nachlass to grant the Norwegian project the permission to create a machine-readable database Gesamtausgabe for the use by Wittgenstein scholars. I do not know whether or not this welcome development will actually help the production of a printed Gesamtausgabe.

A secondary, but not unimportant subplot in the story of Wittgenstein's literary remains, concerns the publishers of the remains. The original text material published so far in book form has been mostly brought out by Suhrkamp or by Basil Blackwell. Alas, Mr. Nedo has had a bitter quarrel with Suhrkamp, and there has been friction between Professor Anscombe and Basil Blackwell. Perhaps because of these problems, probably for other reasons as well, the Gesamtausgabe project does not have a publisher for the products of their labors.

Another subordinate issue concerning Wittgenstein's notebooks is due to his double use of them. Besides writing in them his philosophical ideas as they came to him, Wittgenstein used the very same notebooks to record a number of other observations. In order to make it impossible for any casual reader to have access to his private thoughts, he used in these observations a code, which is, nevertheless, easy to decipher. The coded passages have in fact been deciphered. In 1985, a pirated edition of the coded parts of the 1914-1916 notebooks was published in Spanish, in the magazine Saber in Barcelona.

In principle, however, access to the coded passage is strictly controlled by the literary executors. They are supposed to be censored from the microfilms distributed hy the Cornell University library, although at least one major university library has mistakenly received an unexpurgated copy.

Once again, the issues surrounding the coded passages are too complex to be resolved in a single essay. I cannot pass judgment here on what the proper attitude ought to be to these passages of Wittgenstein's notebooks. On a deeper level, in any case, one can scarcely dismiss the facts of Wittgenstein's personal life as being irrelevant to a full


understanding of his thought. To think that the way his personality is reflected in his life and in his moral struggles is unrelated to his philosophical thought is to take a shallow view of the complexity of a major philosopher's thought and its roots in his personality.

There is a more direct reason, however, why some of the coded passages should be made available to philosophers. Many of the coded comments have nothing to do with Wittgenstein's private life. Instead, they are his comments on his own philosophical activity. Even though they do not tell anything directly about the content of his philosophical thoughts, they are quite revealing about the dynamics of his thinking and about his relations to other thinkers. For this reason, they offer us vital testimony concerning the development of his ideas. This is amply shown by the selection of coded passages published in Wittgenstein's Vermischte Bemerkungen in 1977. However, other philosophically relevant passages are still waiting to be made public.

NOTES

* A shorter version of this article appeared in The Times Literary Supplement N. 4565, 28 September-4 October 1990, p. 1030. The reprint of the previously published material is by permission of The Times Literary Supplement.

I am also grateful to Professors G. H. von Wright, Rudolf Haller, and David Stern as well as to Mr. Heikki Nyman for information and for other kinds of help.

Dept. of Philosophy Boston University 745 Commonwealth Ave. Boston, MA 02215 U.S.A.

DAVID STERN

THE "MIDDLE WITTGENSTEIN":

FROM LOGICAL ATOMISM TO PRACTICAL HOLISM*

1. THE "MIDDLE WITTGENSTEIN"

Wittgenstein arranged the Tractatus in its final form during the summer of 1918; Part I of the Philosophical Investigations was put into the form in which we now have it during the mid 1940s. The Tractatus was published in 1922; the Philosophical Investigations in 1953, two years after Wittgenstein's death. Because the two books were widely studied and interpreted at a time when the rest of his writing was unavailable, it became common practice to speak of the author of the first book as "Early Wittgenstein", and the author of the second as the "Late Wittgenstein". As it gradually became clear that his writing during the intervening years was not only voluminous, but also could not simply be understood as a rejection of one view and the adoption of another, it was natural to speak of the author of this further body of writing, or at least those parts of it which could not be regarded as "Early", or "Late", as "Middle Wittgenstein".

While it is certainly convenient to use this talk of an early, middle and late Wittgenstein as conversational shorthand for lengthier and more cautious ways of discussing the development of his philosophy, it also has its dangers. One of the main assumptions which commonly accompanies this periodisation is the belief that we can neatly divide the development of Wittgenstein's thought into several sharply demarcated phases. While there is some truth to this, it is only a half-truth', and for this reason it is particularly dangerous. First, it can lead to an interpretive strategy which cuts Wittgenstein up into a number of independent time-slices and so loses sight of the unity of his philosophy. Such an outlook lends itself to schematic summaries of what Wittgenstein really meant, summaries which turn his writing into just the kind of philosophical theories which he so vigorously opposed. I think it should be clear by now that we ought to take Wittgenstein's rejection of philosophical theorising, his lifelong conviction that philosophy is "not a theory but an activity" seriously, even if we don't ultimately take him at his word. 1


204 DAVID STERN

But perhaps the greatest danger in this talk of early, middle and late Wittgenstein is that we read Wittgenstein in the light of currently fashionable interpretations, rather than evaluating those interpretations against a careful reading of what Wittgenstein actually wrote. Much of the recent work on "Middle Wittgenstein" has been particularly valuable precisely because it is based on close examination of the full range of Wittgenstein's writing. While I don't think we should give up trying to provide interpretive schemata when studying Wittgenstein, such schemata cannot be based on an analysis of isolated fragments selected from his writing. Rather, we have to start by asking what Wittgenstein's problems were, and need to understand the "problem background" against which he worked. 2 To do this, we need to read his writing as a whole, rather than concentrating on isolated fragments. For this reason, I begin by looking at a passage from the Blue Book which highlights these issues. The first forty or so pages of the Blue Book are about the nature of meaning, the last thirty about solipsism and the nature of experience. In between, there is a short passage in which he compares different ways of making progress in philosophy with different ways of arranging books scattered across a library floor. Wittgenstein contrasts the straightforward case in which one can pick up each book and put it in its final place with a situation where one might have to start by putting several books in the right order, simply to show that they belong together in that order. This leads him to the following reflections:

In this case, in fact, it is pretty obvious that having put together books which belong together was a definite achievement, even though the whole row of them had to be shifted. But some of the greatest achievements in philosophy could only be compared with taking up some books which seemed to belong together, and putting them on different shelves; nothing more being final about their positions than that they no longer lie side by side. The onlooker who doesn't know the difficulty of the task might well think in such a case that nothing at all has been achieved?

In its place in the Blue Book, in between the discussion of meaning in the first part of the book and the discussion of experience in the second, the point of the simile is to explain the overall relationship between these two parts. The first part of the book argues that meaning does not consist in the occurrence of mental processes, separating two problems which he had previously thought of as belonging together. But the results achieved in the first part of the book are only provisional, and their final location is not yet determined, for "every new problem

LOGICAL ATOMISM TO PRACTICAL HOLISM 205

which arises may put in question the position which our previous partial results are to occupy in the final picture".4

Perhaps this image of organising a library, of working out what goes where, is also an apposite description of our present relationship to Wittgenstein's writings as a whole: we need to sort out which parts belong together, and why. In this paper, I offer a selective outline of my interpretation of the development of Wittgenstein's work, one which concentrates on the so-called "Middle period". 5 I do this by discussing a number of crucial passages in his writing, passages in which he decisively changes his conception of the nature of mind and language, moving away from the Tractatus and toward the Philosophical Investigations. I identify a train of thought in Wittgenstein's writings which leads from Tractarian logical atomism, through the logical holism of the late 1920s and early 1930s, and from there to his later practical holism. In outline, my reading can be summarised as follows.

Wittgenstein's initial break with the Tractatus, which probably occurred in the late 1920s, consisted in the realisation that he had been wrong to think that all logic could be reduced to the truth-functional logic of the Tractatus. Consequently, he gave up logical atomism, the doctrine that all meaningful discourse can be analysed into logically independent elementary propositions, for logical holism, the thesis that analysis leads to systems of logically related propositions. At first, he retained the Tractarian conviction that language is grounded on reference to objects, which he now identified with the contents of experience. This project of analysing the structure of the experientially given is briefly articulated in the paper, 'Some Remarks on Logical Form'. 6 At this point, in the early months of 1929, he conceived of the project as a matter of articulating a "phenomenological language" , a language for the description of immediate experience. Later that year, he gave up the idea that philosophy ought to start from a description of the immediately given, motivated by the conviction that philosophy must begin with the language we ordinarily speak. This led him to reject the idea that language is animated by intrinsically representational mental processes, in favour of a conception of a language on which the meaning of a sentence is determined by the rules for its use. Finally, he replaced the view that each case in which one applies a rule requires an act of insight with the view that the application of a rule is a matter of deciding to apply the rule in a certain way.

These changes are followed by a transitional period during the first

206 DAVID STERN

half of the 1930s in which Wittgenstein explored their implications. The transitional period comes to end in the mid 1930s, with the first exposition of what has since become known as "the private language argument", and the construction of the 'first part of what von Wright has called the "Early Investigations", which roughly corresponds to the first 188 sections of the published Philosophical Investigations. During this period, he moves away from a conception of; language as constituting a formal system of rules, embracing the view that mastery of rules is dependent on a background of shared practices. As he stresses in the Investigations, his use of "the term 'language-game' is meant to bring into prominence the fact that the speaking of language is part of an activity, or of a form of life". 7 Though these forms of life, the takenfor-granted ways of acting which make language possible, are social and practical, not individual and incorrigible, they occupy an analogous role in Wittgenstein's later philosophy to the role he gave to the experientially given in 1929 or objects in the Tractatus, for they are the point at which the later Wittgenstein acknowledges the limits of language. Thus the Philosophical Investigations also states that "what has to be accepted, the given, is - so one could say - forms of life". 8

Consequently, he no longer thinks of the rules of our language as a matter for decision or convention, though he does not return to his earlier essentialism, either; rather, he tries to achieve a clear view of the relation between logic and practice by exploring the attractions and shortcomings of both the conventionalist and essentialist positions. This practical holism is sharply opposed to the logical holism which it replaces. I take this term from Dreyfus's analysis of Heidegger and late Wittgenstein in 'Holism and Hermeneutics', where he draws a parallel distinction between theoretical holism, the view that all interpretation is a matter of trap slating between theories, and practical holism, the view that while everyday coping with things and people "involves explicit beliefs and hypotheses, these can only be meaningful in specific contexts and against a background of shared practices".9 Because this inherited background involves skills, habits and customs, it cannot be spelled out in a theory. In the remainder of this paper, I shall flesh out the line of development I have just indicated, from logical atomism to logical holism, and from logical holism to practical holism. 10 I shall also argue that a certain conception of the primacy of immediate experience lies behind the earlier view, and that the rejection of this conception of


experience is crucial for the subsequent development of Wittgenstein's philosophy.

2. LOGICAL ATOMISM

At the heart of the Tractarian system is an argument for the necessary existence of simple objects. That argument begins from, the observation that I speak and understand language, and leads to the conclusion that language must be analysable into elementary propositions, "logical atoms". This argument is extremely abstract, for it turns on establishing that it is only possible for language to be composite if there are simples out of which it is composed. As a result, Wittgenstein concluded that every significant statement must be composed of logical atoms, yet was unable to give any examples. Indeed, it was the rationalistic and abstract character of this train of thought which Wittgenstein most vehemently criticised after he rejected logical atomism in the late 1920s. Shortly afterwards, he branded his earlier work as "dogmatic" - a term with strongly Kantian overtones - precisely because he had placed so much weight on the claim that it was possible to carry out an analysis of our language yet had failed to do SO.l1 The Tractatus is an abstract metaphysical framework, a product of trying to think through a number of key issues in the philosophy of mathematics and language which Wittgenstein took from Frege and Russell. Because of this, it is misleading to read a well worked out position on the nature of experience and knowledge back into it, although that is just what Wittgenstein did in the early 1930s, when he identified the simple objects with sense-data. Instead, I want to stress the way Wittgenstein's "dogmatism" gives the Tractatus its schematic character, which lends itself to any number of interpretations of "what Wittgenstein really meant".

But the main lines of Wittgenstein's conclusions about logical atoms in the Tractatus can be summed up in a few sentences. These atoms, the so-called elementary propositions, cannot be decomposed into smaller units, but they are nevertheless made up of names, which play the role of sub-atomic particles: they refer to the simple objects which make up the world. 12 The meaning of what we ordinarily say is the logical product of the combination of these sub-atomic particles into the molecules of ordinary speech. A proposition is a picture, or a model, of reality: the fact that the names of which it is composed are related to

208 DAVID STERN

one another in a determinate way represents that things are related to one another in the same way.13 A proposition is true if things are arranged as it says they are, false if they are not. Even though Wittgenstein had found no examples of the elementary propositions, the basic components of his theory of meaning, he thought he had shown that they must be logically independent of each other. By this, he meant that the truth or falsity of each atomic proposition did not depend on the truth or falsity of any other atomic proposition. 14

Of course, the signs from which our propositions are constructed -the words of everyday language, and the corresponding psychical constituents which make up our thoughts - do not clearly display the underlying structure which Wittgenstein had deduced. IS However, he believed that any meaningful proposition of ordinary language must have an analysis which does clearly display its underlying structure. This would be a truth-functionally related ensemble of atomic propositions whose surface structure is identical with the structure of the facts it represents. Wittgenstein distinguished between the sign, the perceptible part of the proposition, and the symbol, the sign together with its application, its representational relation to the world. 16 Ordinary language consists of relatively simple signs, which stand in a very complex representational relationship with the world; a fully analysed language would consist of a much more complex arrangement of signs in a very simple representational relationship with the world. But no sign, considered in isolation, is intrinsically meaningful: one always has to see how the signs are to be applied, to grasp the way they represent. This leads Wittgenstein to distinguish two ways of conceiving of a picture, corresponding to his distinction between sign and symbol: as a fact, a determinate arrangement of objects, and that fact, together with the representational relation which makes it into a picture. 17

This ability to apply language, to see signs as symbols, as intrinsically related to their objects, is not itself a further fact in the world, but is a matter of our establishing a projective relationship between certain facts. The projective relation, the sign's meaning, cannot itself be a fact, for all facts are logically independent of one another, and there is a logical connection between a picture qua symbol and what it pictures. Thus this connection cannot itself be stated, for only facts can be stated. But it can be shown by the structure of our language, much as the projective connection between two depictions of the same thing in different perspectives can be shown. Any combination of signs is


only meaningful due to our applying them in a certain way; everyday language depends on the existence of extremely complex conventions connecting the words we use with the objects they stand for. Similarly, even the signs of a fully analysed language would have to be explained before we could understand them. Like the signs that make up the propositions we presently speak, utter and think, they would be conventionally meaningful: their meaning would be a prqduct of linguistic conventions, just as the meaning of the words we presently use is conventional. In both cases, we would also have to know how to use the words in question, how to apply them. But not all signs can be given a meaning in this way: some must be non-conventionally meaningful and so not susceptible to being either interpreted or misinterpreted. In the Tractatus, "thoughts" play this role: a thought is an applied propositional sign, a picture together with the method of projection which gives it its significance. 18 A Tractarian thought is not simply an inner monologue or image, for these are facts on a par with physical facts composed of words and pictures. Indeed, Wittgenstein explicitly told Russell that a thought consists of "psychical constituents that have the same sort of relation to reality as words. What those constituents are I don't know" .19 However, a thought is not just a concatenation of signs, it is the signs together with their application, the projective relation which gives them their life. This is the original private language, the inner symbolic processes which give public language its significance. Unlike any physical language, thoughts are essentially meaningful and so cannot be misunderstood. They encompass the "meaning-locus" which provides the ground for our use of language, the projective relationship we apply to the signs. 20 A thought, an applied and thought out propositional sign, is intrinsically related to its object. There is a logical connection between the thought and its object. Our language is like paper currency; it is only meaningful insofar as it is backed up by gold in the bank - both are intrinsically representational processes.

Wittgenstein's view of the irreducibly mental and intentional character of meaning was diametrically opposed to Russell's Humean view of meaning, on which it is nothing more than a feeling which accompanies certain mental processes. 21 But this view is only implicit in the Tractatus; it is protected from explicit formulation by the Tractarian doctrine that the relation between language and world cannot be stated, but can only be "shown". However, I believe it was motivated by a picture of the relationship between language, experience and world, a picture that

210 DAVID STERN

is best described as Cartesian, though it also has affinities with postKantian thought. While this picture is hinted at in the Tractatus, in the central role Wittgenstein gives to thought in his account of propositions, in his sympathy for solipsism and his identification of the world with life, it only emerges clearly in his subsequent work.22 For it was only in the late 1920s, when Wittgenstein realised that the Tractatus's dogmatism would not do, that he returned to grappliqg with the problems raised by his essentialism about meaning and the need for an account of the relationship between language and experience.

3. FROM LOGICAL ATOMISM TO LOGICAL HOLISM

By the late 1920s, Wittgenstein had come to think of the task of arriving at a characterisation of the ultimate level of analysis as a matter of formulating what he called a "phenomenological language". 23 However, in the first section of the Philosophical Remarks, drafted in October 1929, he wrote that he no longer had

phenomenological language, or "primary language" as I used to call it, in mind as my goal. I no longer hold it to be necessary. All that is possible and necessary is to separate what is essential from what is inessential in our language.24

The original manuscript volume entry reads instead: "I no longer hold it to be possible".zs Some commentators regard the replacement of this impossibility claim by the seemingly weaker claim that a phenomenological language is not necessary as a qualification which implies that Wittgenstein had recognized that he could not yet prove that phenomenological language is impossible. Hintikka and Hintikka, for instance, argue that this lacuna would only be filled much later by the private language argument. 26 However, the continuation of the passage in question suggests a much simpler explanation for the rewording: Wittgenstein sometimes uses the term "phenomenological language" in a restricted sense, to mean a canonical analysis of the experience of the present moment. In this sense, he consistently maintained after 1929 that such a language was indeed impossible. But he also spoke of "phenomenological language" in a looser sense, meaning by it any way of talking about the content of experience, and in this sense of the term, he holds that a phenomenological language is possible but not necessary. Thus, he turned away from phenomenological language in the narrow sense, the construction of an artificial philosophical language


that would be capable of fully describing present experience, in favour of a study of the structure of the language we ordinarily speak, which still included a study of phenomenological language in the looser sense of the term.

Wittgenstein's clearest explanation of what he had meant by the term "phenomenological language" occurs in the first section of the chapter entitled 'Idealism' in the Big Typescript, assemble<;i during 1932-33; the section is entitled 'The Representation of Immediate Experience'. There, he writes: "Phenomenological language: the description of immediate sense perception, without hypotheticaf addition". 27 Unlike our ordinary ways of describing sense perception, in terms of persisting objects, a phenomenological language would make no such hypothetical commitments; instead, it would restrict itself to representing whatever is immediately experienced. But his objection to this conception is already implicit in the broken underlining he put under "language", Wittgenstein's way of indicating that he was not satisfied witlijiis choice of wofds. For he had realised that the motives which led him to seek a phenomenological language ensured that no language could be adequate. What one really wants to do, he suggests, is to directly present what is experienced:

If anything, then depiction by means of a painted picture or something like it must surely be such a description of immediate experience. As when we, e.g., look in a telescope and record or paint the constellation seen. 28

But even the most direct language cannot be more than a re-presentation, and so the very idea of a phenomenological language turns out to be incoherent. The desire for a transparent intermediary, present to consciousness, which guarantees that my thoughts are about their objects, and which provides an ultimate basis for language, is the product of philosophical confusion.

Wittgenstein sets out his objection to phenomenological language by asking us to consider how we might go about actually reproducing sense perception; he suggests that we imagine constructing a mechanical scale model of what is seen. Seen from the correct point, the model produces the appropriate perception:

the model could be set in the right motions by a crank-drive and we could by turning the crank read off the description. (An approximation to this would be a representation in film.)

If that is not a representation of the immediate - what would be one? - Anything

212 DAVID STERN

which tried to be more immediate still, would have to give up being a description. Instead of a description what would then corne out would, rather, be that inarticulate sound with which some writers would like to begin philosophy. ("I am, knowing of my knowledge, conscious of something" Driesch. )29

The very generality of this criticism, the fact that it does not turn on any specific formulation of a sense-datum theory, implies that it would be a mistake to construe Wittgenstein's "phenoIl;lenological language" too narrowly, as expressing a commitment to a specific philosophical theory about how to analyse ordinary language into observation statements. Rather, phenomenological language inherits much of the generality of the Tractarian notion of the ultimate level of analysis: it is the language, whatever it is, that enables one to describe immediate experience without any hypothetical additions. But the work I have just been discussing was motivated by an overall conception of the relation between experience and the external world. During this period, Wittgenstein frequently explained his conception of the relation between experience and the world in terms of a comparison with the relation between the picture one sees on the screen at the movies and the pictures on the reel of film in the movie projector. Although this analogy is never fully elaborated in any of the published works, there are a number of references to it in Wittgenstein's manuscripts, in the Philosophical Remarks and Big Typescript, and in the notes of his lectures and conversations in the years following 1929.

Talking to Bouwsma in 1949, Wittgenstein mentioned that the "figure of the cinema lainp" had first struck him when he was talking to Frege in 1911.30 Bouwsma recalls a meeting of Malcolm's discussion group in Cornell in which Bouwsma began the conversation by briefly talking about Descartes's Cogito, ergo sum. Wittgenstein responded by saying that the real question was "How did Descartes come to do this?" Bouwsma asked whether he meant to ask what led up to the cogito in Descartes's own thought, to which Wittgenstein replied

No. One must do this for oneself ... I always think of it as like the cinema. You see before you the picture on the screen, but behind you is the operator, and he has a roll here on this side from which he is winding and another on that side into which he is winding. The present is the picture which is before the light, but the future is still on the roll to pass, and the past is on that roll. It's gone through already. Now imagine that there is only the present. There is no future roll, and no past roll. And now further imagine what language there could be in such a situation. One could just gape. This!31

The difference between the picture on the film-reel which is in front of


the projector and the picture on the screen is emphasised by contrasting the way in which the picture on the reel is part of a sequence of neighbouring pictures which either have been or will be projected, while the picture on the screen has no such neighbours. If we are serious about trying to represent the picture on the screen without any hypothetical additions, we must take it by itself, excluding the sequence of past, present and future pictures on the film reel; in fact, we must exclude the whole physical world. But any description of the picture would be a sequence of symbols which was another part of the physical world. Furthermore, our ordinary language is temporal; how could we use it to talk about an atemporal, self-contained world without misdescribing it?

If we restrict ourselves to the case of describing presently given experience, it may be hard to see the full force of the problem: Why worry about how to represent it when it is already present? But even if we were to accept, for the sake of argument, that representing the immediately given is unproblematic, we would still have to account for our ability to remember and think about phenomena which are not part of occurrent sensory experience. Wittgenstein's discussions of the representation of experience often employ examples in which the intended object is not given in current experience. While the events depicted on the roll of film seemed unproblematic when considered by themselves, our ability to think about those events, to grasp that certain signs mean those events, became highly puzzling. Thus, Wittgenstein wrote in late 1929:

The application of words, considered as extended in time, is easy to understand; in contrast, I find it infinitely difficult to understand the sense in the moment of application.

What does it mean e.g. to understand a sentence as a member of a system of sentences?32

Wittgenstein tried to express his conception of a categorical distinction between experience and the world by saying that the picture on the screen, unlike the picture on the film-reel, "has no neighbours". This is not a matter of saying that my experiential field has a certain location, and that there is nothing next to it. Rather, it is to say that it makes no sense to think of my immediate experience as adjoining anything else - that it is neighbourless: self-contained, complete. In lectures given in the early 1930s, Wittgenstein said that

214 DAVID STERN

... the pictures in the lantern are all "on the same level" but that the picture which is at any given time on the screen is not "on the same level" with any of them, and that if we were to use "conscious" to say of one of the pictures in the lantern that it was at that time being thrown on the screen, it would be meaningless to say of the picture on the screen that it was "conscious". The pictures on the film, he said, "have neighbours", whereas that on the screen has none. 33

This is closely connected with the idea that it makes no sense to speak of experience as "present": just as Wittgenstein' denies that experience has a spatial location, he also denies it has a temporal location. In both cases, he wants to resist the temptation to project our everyday grammar onto the phenomena. For he holds that there is a "grammatical" difference between the two; the picture on the film and the picture on the screen are not "'on the same level'''. The pictures are not two related objects which share a common space; instead, they represent two different spatialities.34 If we try to bring the two together, we shall run up against the limits of language.

In the early 1930s, Wittgenstein came to think that the mistake which leads to solipsism of the present moment, the view that only my present experience is real, can be explained in terms of the movie metaphor. On this account, the solipsist mistakenly compares "present" experience to the frame of the film which is currently being projected, in front of those past frames which have been projected and behind those future frames which will be projected. Wittgenstein's reply is to contend that the correct analogy is with the picture on the screen, which does not lie in this order at all, and so "present" - and for that matter, "my", "experience", and "real" - is inapplicable:

The present we are talking about here is not the picture in front of the projector's lens at precisely this moment, as opposed to the pictures before and after it, which have already been there or are yet to come; but the picture on the screen which would illegitimately be called present, since "present" would not be used here to distinguish it from past and future. And so it is a meaningless epithet.35

During the period when he still found the movie metaphor a compelling illustration of our predicament, Wittgenstein must have wished he could get around the need to use language to convey what cannot be said, to find a way of getting his readers to simply see the nature of the phenomena. One aspect of this problem is his recognition that language itself is part of the physical world and so is on a different level from the phenomena. Thus, early in 1929 he raised the following


question about the relation between physical language and phenomenological language:

Language itself belongs to the second system. If I describe a language, I am essentially describing something that belongs to physics. But how can a physical language describe the phenomenal?36

Shortly afterwards, he began to realise that it was this very conception of present experience which was responsible for his difficulties:

The way of looking which leads into a magic valley, as it were, from which there is no way into the open countryside is taking the present as the only reality. This present, constantly flowing or, rather, constantly changing, cannot be caught hold of. It disappears before we can think of grasping it. We stay stuck in this valley, bewitched, in a whirl of thoughts ....

What I may not think, language can't express. That is our comfort.

But if.ione says: the philosopher must step down into this encircled valley and grasp the pure reality itself and bring it to the light of day, then the answer runs that he would have to in so doing leave language behind and so come back without having achieved anything.

And yet there can be a phenomenological language. (Where must it stop?)37

Soon after, in the same notebook, Wittgenstein decisively rejected this conception of a phenomenological language. 38 In short, what Wittgenstein realised, late in 1929, is that there cannot be a phenomenological language of the kind he had hoped for - a complete analysis of experience - and that we must start from our everyday language' in describing experience. In the Tractatus, he had held that while truthfunctional propositional logic limits what can be said, its logical form shows the common structure of language and world: "Logic must take care of itself". 39 Once he gave up the logical atomist doctrine that all relations between propositions are ultimately truth-functional, it is language as a whole which takes its place: "Language has to speak for itself".40 The logical holist conceives of everyday language as a system of rules, such as the rules of a formal calculus, or a scientific theory.41 In the final section of this paper, I summarise why Wittgenstein replaced this with a practical holist conception of everyday language on which even formal rules must be understood in terms of their practical background: "rules leave loop-holes open, and the practice has to speak for itself".42

216 DAVID STERN

4. FROM LOGICAL HOLISM TO PRACTICAL HOLISM

In 1929, Wittgenstein rejected logical atomism for a logical holist conception of language as a system of calculi, formal systems characterised by their constitutive rules. But by the mid 1930s he came to see that the rules of our language are more like the rules of a game than a calculus, for they concern actions within a social context. This context, our practices and the 'forms of life' they embody, on the one hand, and the facts of nature on which those practices depend, on the other, are the background against which rule-following is possible. It is this emphasis on both the social and natural context of rule-following which is characteristic of Wittgenstein's later conception of language as a practice.

Both the logical holist conception of language as a calculus or a theory and the later practical holist notion of a language-game stress the paramount role of context, the notion that the context in which an utterance belongs is the whole of language. This is why both conceptions are holistic: the meaning of an utterance, an inscription or a thought is not an entity independent of the rest of our language, but rather consists in its relation to the rest of language. There is no sharp transition from the calculus model to the language-game model, from logical holism to practical holism: Wittgenstein does not give up the idea that our linguistic practices are rule-governed, but rather comes to see that rule-governed behaviour is only possible against a background of practices which cannot themselves be explicitly formulated as rules. Alternatively, one might say that his conception of language becomes increasingly broad, until it includes the whole range of human activity.

Despite these continuities, Wittgenstein's conception of language changed radically during the 1930s. During the early 1930s, Wittgenstein frequently compares language to a calculus, a formal system of rules. While he retains this analogy in subsequent writing, it is usually as an object of comparison, as a way of bringing out the disanalogies between ordinary language and a calculus. Thus, he dismisses the idea that we can think of the meaning of a word as an entity, a "meaningbody", which lies behind the use of our words, in favour of a description of the rules which we accept for the use of the word. 43 In the Philosophical Investigations, Wittgenstein implies that the analogy between a calculus and ordinary language had been responsible for his conception of language as governed by a system of rules:

F. P. Ramsey once emphasized in conversation with me that logic was a "normative


science". I do not know exactly what he had in mind, but it was doubtless closely related to what only dawned on me later: namely, that in philosophy we often compare the use of words with games and calculi which have fixed rules, but cannot say that someone who is using language must be playing such a game ....

All this can only appear in the right light when one has attained greater clarity about the concepts of understanding, meaning and thinking. For it will then also become clear what can lead us (and did lead me) to think that if anyone utters a sentence and means or understands it he is operating a calculus according to definite rule~. 44

By the mid 1930s, Wittgenstein plays down the role of explicit rules in explaining what a word means, and instead stresses that in practice, we usually explain the meaning of words by giving paradigmatic examples, not by ostensive definition or stating necessary and sufficient conditions. The examples need not be given in such a way that they are protected against all possibilities of misunderstanding; it is enough that they usually work. In discussing the Tractarian theory of the nature of the proposition, Wittgenstein replies in section 135 of the Philosophical Investigations: "Asked what a proposition is ... we shall give exampIes". Most of the next one hundred sections of the Philosophical Investigations are occupied with exploring and undermining the two main avenues of reply to this position: the view that meaning consists in mental processes and the view that meaning consists in implicit rules, views which Wittgenstein had previously been attracted to. The aim of this discussion is to discredit the idea of hidden processes which underlie meaning, whether they be subjective mental processes or objective rules.

A key argument which motivates this train of thought is that just as no mental content is intrinsically meaningful, so no strict rule by itself can determine how we go on, as all determination of meaning is dependent on interpretation. Given any mental process or any formulation of a rule, it is always, in principle, open to a further, deviant, interpretation. 45 No occurrent act of meaning or intending, or of grasping an essence or of deciding to go on in a certain way, can give a rule the power to determine our future actions, because there is always the question of how that act is to be interpreted. As a result, the idea that a rule can determine all its future applications turns out to be misguided. Only if we ignore the context can we think that some isolated act or event can have a determinate meaning regardless of its context. A change in the context of application can yield a change in meaning, and therefore meaning cannot be identified with anything independent of context.

218 DAVID STERN

We can see a parallel development in Wittgenstein's conception of following a rule. In the Philosophical Remarks, he still thinks that the application of a rule always depends on an act of insight, the insight that the rule can be applied in this case:

Is it like this: I need a new insight at each step in a proof? ... Something of the following sort: Supposing there to be a certain general rule (therefore one containing a variable), I must recognise afresh that this rule may be applied here. No act of foresight can absolve me from this act of insight. Since the form to which the rule is applied is in fact different at every step:6

But there is a marginal note in the original copy of the Philosophical Remarks which encapsulates the next phase of Wittgenstein's thought. Next to "No act of foresight can absolve me from this act of insight" he wrote in the margin: "Act of decision, not insight". That is, the application of the rule is no longer treated as a matter of my seeing that it must apply, but rather in terms of my deciding to apply it here. The issue arises again in the Brown Book in an early version of the rule-following discussion in Philosophical Investigations section 185ff. Wittgenstein discusses the possibility that someone might learn how to add one as we do with small numbers, but does what we would call adding two when asked to add one to numbers between one hundred and three hundred, adds three when asked to add one to larger numbers, and persists in regarding this procedure as a correct application of the rule he or she was taught. This leads Wittgenstein's interlocutor to ask whether he thinks an act of intuition will always be needed to protect us against the possibility of a deviant interpretation of the rule:

"I suppose what you say comes to this, that in order to follow the rule 'Add l' correctly a new insight, intuition is needed at every step. ,,47

Instead of giving a direct answer to this question, Wittgenstein replies by asking the interlocutor to explain the notion of following the rule correctly, a notion which he has simply taken for granted in his question:

- But what does it mean to follow the rule correctly? How and when is it to be decided which at a particular point is the correct step to take?48

The interlocutor responds by appealing to the rule-giver's intentions:

"The correct step at every point is that which is in accordance with the rule as it was meant, intended.,,49


In the ensuing dialogue, the interlocutor tries to specify what the rulegiver's intentions consist in, and Wittgenstein repeatedly undermines him by asking how the application of the intention, meaning, mental act or whatever other candidate, is offered can be guaranteed in advance: the same deviant possibilities can always be raised. A page later, Wittgenstein sums up:

If the mere words of the rule could not anticipate a future transition, no more could any mental act accompanying these words.

We meet again and again with this curious superstition, as one might be inclined to call it, that the mental act is capable of crossing a bridge before we've got to it. This trouble crops up whenever we try to think about the ideas of thinking, wishing, expecting, believing, knowing, trying to solve a mathematical problem, mathematical induction, and so forth.

It is no act of insight, intuition, which makes us use the rule as we do at the particular point of the series. It would be less confusing to call it an act of decision, though this too is misleading, for nothing like an act of decision must take place, but possibly just an act Of writing or speaking. so

Here, there is no suggestion that there must be an act of decision; only that if any mental process at all is involved, it is a decision, not an intuition. The search for a self-interpreting interpretation only arises if one treats the words and actions in which the rule was expressed as an interpretation, a construal of the rule which still needs to be made completely determinate. In some cases, of course, our words or actions will be ambiguous. But in others, we can just get on with it and write or say the next term in the series. Wittgenstein is proposing that we look at these cases, the cases in which we do not do any interpreting, but simply grasp the rule in practice, such as everyday conversation and arithmetic, as prototypical instances of rule-following. As he puts it in On Certainty:

As if giving grounds did not come to an end sometime. But the end is not an ungrounded presupposition: it is an ungrounded way of acting. s1

In pursuing these issues in Philosophical Investigations section 138ff., Wittgenstein focusses on the question: What is it to understand a word in a flash or, as he had previously put it, "to understand the sense in the moment of application,,?52 For, on the one hand, understanding a sentence is a matter of being able to use those words correctly, in applying them "in the course of time"; on the other hand, we may grasp the meaning of a sentence in a flash, when it "comes before our

220 DAVID STERN

mind in an instant".53 In other words, there is both a subjective and an objective aspect to understanding and we need to understand how they hang together. The problem is directly descended from Wittgenstein's earlier worries about the relationship between the words I use in describing my experiences and the experiences themselves, and the way in which the words seemed to be unable to describe "that which goes on in the reading of the description" ,54 the mental processes which animate our words. Certainly we do, on occasion, understand words in a flash, but the danger here is to think that this can give us an insight into the essence of understanding. The same image can mean different things in different contexts:

What is essential is to see that the same thing can come before our minds when we hear the words and the application still be different. Has it the same meaning both times? I think we shall say not. 55

Wittgenstein holds that it is' the circumstances in which the experiences occur, not the experience taken by itself, to which we should look if we want to get at what justifies someone in saying that he or she has understood. The therapy he proposes is that we consider relatively simple cases of mental activity, such as what goes on when we read out loud, in order to see how the temptation of thinking that ineffable mental processes are involved arises.56 In other words, he asks us to consider "the activity of rendering out loud what is written or printed; and also of writing from dictation, writing out something printed, playing from a score, and so on". 57 The first point Wittgenstein makes in this connection is that although we are all very familiar with such activities, we would find it difficult to describe the part which they play in our life "even in rough outline". The observations that follow suggest that this is due to the differences between what goes on when a skilled reader reads, where all kinds of things may go on, and often nothing at all over and above the successful completion of the task, with what goes on with a beginner, who makes a conscious effort to read. And if we concentrate on the case of the beginner we shall indeed be inclined to say that it is "a special conscious activity of the mind". 58 The idea is that there must be some special conscious act of reading, "the act of reading the sounds off from the letters". 59 Here Wittgenstein replies by thinking of cases in which the experience goes on, but the "reader" does not really understand (perhaps he or she has been drugged), and cases in which the reader does understand, but nothing or something


else goes on. Whether something is reading or not is a matter of whether the activity is successful, not a matter of whether I consciously apply a rule or feel guided or whatever. One wants to say that in reading "the words come in a special way" or that "I experience the because", but in practice, the words don't have to come in a special way and we needn't experience anything in particular. 60

In most cases of proficient reading, we just get on with it and do it. Here we have an example of what Heidegger calls "readiness-to-hand" [Zuhandenheit]: our ordinary use of everyday things does not call for reflective awareness of what we are doing. We only become aware of these things when something goes wrong or some other unusual circumstance draws our attention to them, making them "present-athand" [vorhanden].61 Thus, under normal circumstances, reading a familiar language, "can we say anything but that ... this sound comes automatically when we look at the mark?". 62 But if we try to understand the cases where we are proficient on the model of what goes on in abnormal or problematic cases, we shall inevitably look at what goes on when we make an effort to read as revealing the essence of being influenced, an essence that is concealed in normal usage. 63 We think of particular cases of being guided or being influenced, and think that the experience we have in this or that case is paradigmatic, what goes on in every case.

Ultimately, our explicit beliefs and interpretations are only meaningful in specific contexts and against a background of shared practices -these practices are the skills and customs which we have learnt, ways of acting which were not acquired as beliefs, even though we may express them in beliefs. It is this "way of grasping a rule which is not an interpretation, but which is exhibited in what we call 'obeying the rule' and 'going against it'" which ultimately ends the regress of interpretations.64 In other words, "It is our acting, which lies at the bottom of the language game". 65

NOTES

* Earlier versions of this paper were presented at the University of Iowa, at a symposium on the "Middle Wittgenstein" at an APA meeting in Oakland, California, and at the Wittgenstein centennial conference at the Florida State University, Tallahassee, Florida. I am indebted to members of those audiences for their constructive comments - especially to Jaakko Hintikka, David Pears and Hans Sluga. 1 L. Wittgenstein: 1933, Tractatus Logico-Philosophicus, translated by C. K. Ogden

222 DAVID STERN

(London: Routledge and Kegan Paul), 4.112. Cf. Philosophical Investigations: 1967, translated by G. E. M. Anscombe (Oxford: Blackwell) # 109ff. , #124ff. The German text and English translation are on adjacent pages. While the quotations from Wittgenstein's published writing in this paper are based on toe available translations, they are sometimes rather more literal. 2 J. Hintikka: 1988, '''Die Wende der Philosophie': Wittgenstein's New Logic of 1928", Proceedings of the Twelfth International Wittgenstein Symposium (Vienna: HolderPichler-Tempsky), p. 380. 3 L. Wittgenstein: 1975, The Blue and Brown Books [hereafter either Blue Book or Brown Book] (Oxford: Blackwell), pp. 44-45. He introduces the analogy as an illustration of the way in which philosophical problems are interdependent. 4 Blue Book, p. 44. 5 While it is clearly impossible to do justice to the development of Wittgenstein's philosophy during this period in a paper of this length, I believe it is possible to indicate some of its main characteristics. I explore these themes in greater depth in Wittgenstein on Mind and Language (Oxford: Oxford University Press, forthcoming). 6 L. Wittgenstein: 1929, 'Some Remarks on Logical Form', Proceedings of the Aristotelian Society, supplementary volume, pp. 162-71. 7 L. Wittgenstein, Philosophical Investigations, #23. 8 Philosophical Investigations, p. 226. 9 H. Dreyfus: 1980, 'Holism and Hermeneutics', The Review of Metaphysics 34, p. 9. Cf. the discussion of the background in chapter 5 of J. Searle: 1983, Intentionality (Cambridge: Cambridge University Press). 10 While this way of dividing up the development of Wittgenstein's thought amounts to qualified support for the notion of a "Middle Wittgenstein", these are certainly not the only important turning points in Wittgenstein's work. For instance, his criticism of his earlier work culminates in the completion of Part I of the Philosophical Investigations in the mid 1940s, after which he made a fresh start. This work resists classification but can loosely be described as being on philosophical psychology, the inner and the outer, knowledge, certainty and relativism. 11 See F. Waismann: 1979, 'On Dogmatism', in Ludwig Wittgenstein and the Vienna Circle: Conversations Recorded by Friedrich Waismann, edited by B. F. McGuinness, translated by J. Schulte and B. F. McGuinness (Oxford: Blackwell), 9 December 1931, p. 182 ff. German edition, with the same pagination: 1967, Ludwig Wittgenstein und der Wiener Kreis: Gesprdche aufgezeichnet von Friedrich Waismann, edited by B. F. McGuinness (Oxford: Blackwell). 12 Tractatus, 3.2 ff. 13 Tractatus, 2.15. 14 Tractatus, 1.21,2.062,4.211,5.134-5.135. 15 Tractatus, 4.002. 16 Tractatus, 3.262, 3.31, 3.32. 17 Tractatus, 2.14, 2.1513. 18 Tractatus, 3.5; see also 3 ff., and 4. 19 L. Wittgenstein: 1974, Letters to Russell, Keynes, and Moore, edited by G. H. von Wright (Ithaca, NY: Cornell University Press), 19 August 1919, p. 72. 20 B. Goldberg: 1968, 'The Correspondence Hypothesis', Philosophical Review 77,438-54. 21 See: R. M. McDonough: 1986, The Argument of the Tractatus (Buffalo, NY: SUNY


Press), Ch. VI.1; and S. S. Hilmy: 1987, The Later Wittgenstein (Oxford: Blackwell), pp. 109 ff. 22 See Tractatus, 3-3.12, 5.6-5.641, and 6.431-6.4311. 23 See MSS 105-107 and 'Some Remarks on Logical Form'. I discuss this material in greater detail in Wittgenstein on Mind and Language.

References to Wittgenstein's typescripts and manuscripts use the numbering system in G. H. von Wright's catalogue of the Wittgenstein papers, originally published in the Philosophical Review 78 (1969). The latest revisions can be found in the version published in S. Shankar: 1986, Ludwig Wittgenstein: Critical Assessments (Wolfeboro, NH: Croom Helm), volume 5, pp. 1-21. 24 L. Wittgenstein: 1975, Philosophical Remarks, 2nd edition, edited by Rush Rhees, translated by R. Hargreaves and R. White (Oxford: Blackwell), #1. German edition, with the same pagination: 1964, Philosophische Bemerkungen, edited by R. Rhees (Oxford: Blackwell) . 25 MS 107, p. 205. 26 M. Hintikka and 1. Hintikka: 1986, Investigating Wittgenstein (Oxford: Blackwell), pp. 137 ff., 172, 241 ff. 27 Big Typescript, #101, p. 491. The German reads:

Phan6menologische Sprache: Die Beschreibung der unmittelbaren Sinneswahrnehmung, ohne hypothetische-Zutat.

The Big Typescript, TS 213 in von Wright's catalogue, is a book-length draft which Wittgenstein assembled in 1932-33, based on material which he had written since his return to Cambridge in 1929. For a discussion of the place of the Big Typescript in the Wittgenstein oeuvre, see A. Kenny: 1976, 'From the Big Typescript to the Philosophical Grammar', edited by 1. Hintikka, Essays on Wittgenstein in Honour of G. H. von Wright, Acta Philosophica Fennica 28; reprinted in Kenny: 1984, The Legacy of Wittgenstein (Oxford: Blackwell). 28 Big Typescript, #101, pp. 491-92. The German reads:

Wenn etwas, dann muss doch wohl die Abbildung durch ein gemaltes Bild oder dergleichen eine solche Beschreibung der unmittelbaren Erfahrung sein. Wenn wir also z.B. in ein Fernrohr sehen und die gesehene Konstellation aufzeichnen oder malen.

29 Big Typescript #101, p. 492. The German reads:

Denken wir uns sogar unsere Sinneswahrnehmung dadurch reproduziert, dass zu ihrer Beschreibung ein Modell erzeugt wird, welches, von einem bestimmten Punkt gesehen, diese Wahrnehmungen erzeugt; das Modell konnte mit einem Kurbelantrieb in die richtige Bewegung gesetzt werden und wir konnten durch Drehen der Kurbel die Beschreibung herunterlesen. (Eine Annaherung hierzu ware eine Darstellung im Film.)

Ist d a s keine Darstellung des Unmittelbaren - was sollte eine sein? - Was noch unmittelbarer sein wollte, mtisste es aufgeben, eine Beschreibung zu sein. Es kommt dann vielmehr statt einer Beschreibung jener unartikulierte Laut heraus, mit dem manche Autoren die Philosophie gerne anfangen mochten. CIch habe, un mein Wissen wissend, bewusst etwas" Driesch.)

224 DAVID STERN

Cf. Philosophical Remarks, #67-68; Philosophical Investigations, #261. The quotation from Driesch is taken from page 19 of his Ordnungslehre, where he

calls it "our first philosophical proposition, the primal philosophical proposition. It still points to the birthplace of all philosophy, 'experience', [Erleben] but it nevertheless lifts itself out of the everyday toward language" (Jena: Eugen Diederichs, 2nd edition, 1923). Cf. his Wirklichkeitslehre (Leipzig: Emmanuel Reinicke, 1922), p. 8. 30 O. K. Bouwsma: 1986, Wittgenstein: Conversations 1949-1951, edited by J. L. Craft and R. Hustwit (Hackett, Indianapolis), 5 August 1949, p. 10. 31 Bouwsma, op. cit., 7 August 1949, p. 13. See also Ludwig Wittgenstein and the Vienna Circle, p. 50; and Big Typescript, #102. 32 MS 107, p. 233. The German reads:

In der Zeit ausgedehnt betrachtet ist die Anwendung der Worter leicht zu verstehen; dagegen finde ich es unendlich schwierig den Sinn in Moment der Anwendung zu verstehen.

Was heiBt es z.B. einen Satz als ein Glied eines Satzsystems zu verstehen?

33 G. E. Moore: 1959, 'Wittgenstein's Lectures in 1930-33', Philosophical Papers (London: Allen & Unwin), p. 310. Originally published in three parts in Mind (1954-55). Cf. Wittgenstein's use of the term "neighbour" in the "Notes for Lectures on 'Sense Data' and 'Private Experience"', Philosophical Review 77 (1968), p. 297, and in the Blue Book, p.72. 34 Cf. Zettel, #648: "One language-game analogous to a fragment of another. One space projected into a limited extent of another. A 'gappy' space. (For 'inner and outer' .)" L. Wittgenstein: 1967, Zettel, edited by G. E. M. Anscombe and G. H. von Wright, translated by G. E. M. Anscombe (Berkeley and Los Angeles: University of California Press). The first two sentences are from material published as the Remarks on the Philosophy of Psychology I, edited by G. E. M. Anscombe and G. H. von Wright, translated by G. E. M. Anscombe (Oxford: Blackwell, 1980), #936. 35 MS 108, p. 3; Philosophical Remarks, #54. 36 MS 107, p. 114; Philosophical Remarks, #69. 37 MS 107, pp. 1,2-3 (1929).

Die Betrachtungsweise die gleichsam in einen Talkessel des Magischen fiihrt aus dem kein Weg in die freie Landschaft fiihrt ist die Betrachtung der Gegenwart als des einzig Realen. Diese Gegenwart in standigem FluB oder vielmehr in standiger Veranderung begriffen laBt sich nicht fassen. Sie verschwindet ehe wir daran den ken konnen sie zu erfassen. In dies em Kessel bleiben wir in einem Wirbel von Gedanken verzaubert stecken ....

Was ich nicht den ken darf, kann die Sprache nicht ausdriicken. Das ist un sere Beruhigung.

Wenn man aber sagt: Der Philosoph muB aber in diesen Kessel hinuntersteigen und die reine Realitat selbst erfassen und ans Tageslicht ziehen, so lautet die Antwort daB er dabei die Sprache hinten lassen miiBte und daher unverrichteter Dinge wieder heraufkommt.


Und doch kann es eine phanomenologische Sprache geben. (Wo muB diese Halt machen?)

The translation of the first paragraph is based on the one in Hallett: 1977, Companion to Wittgenstein's Philosophical Investigations (Ithaca, NY: Cornell University Press), p. 471. 38 See the discussion of this passage, MS 107, p. 205, at the beginning of this section. 39 Tractatus, 5.473. 40 Philosophical Grammar, p. 40. 41 There is thus a close affinity between Wittgenstein's logical holism, once he had given up the goal of a phenomenological language, and what Dreyfus calls "theoretical holism", the view that all understanding is a matter of formulating a theory. 42 On Certainty, #139. There is a valuable discussion of the tryptich formed by this quotation and the preceding two in K. S. Johannessen: 1988, 'The Concept of Practice in Wittgenstein's Later Philosophy', Inquiry 31, 357-69. 43 See Philosophical Grammar, #16, where Wittgenstein discusses how one might explain the difference between the "is" of identity and the "is" of predication in these terms [Edited by R. Rhees, translated by A. J. P. Kenny (Oxford, Blackwell, 1974)]. Cf. Philosophical Investigations, #558-60. 44 Philosophical Investigations, #81. In both the early and intermediate versions of the Investigations, the parenthetical phrase "(and did lead me)" read "(and did lead me (Tractatus»" . 45 See, e.g., the discussion of a schematic leaf (#73-74), following arrows (#86), the drawing of a cube (# 139 ff.). 46 Philosophical Remarks, #149 (1930). Cf. #104, #107, #164. See also A. Ambrose: 1979, Wittgenstein's Lectures, Cambridge, 1932-1935 (Chicago: University of Chicago Press), pp. 131-34. 47 Brown Book, p. 141 (1934-35). Cf. Philosophical Investigations, #185ff., and L. Wittgenstein: 1970, Eine Philosophische Betrachtung, edited by Rush Rhees (Frankfurt am Main: Suhrkamp), pp. 214-16. 48 Brown Book, p. 142. 49 Brown Book, p. 142. 50 Brown Book, p. 143. 51 L. Wittgenstein: 1969, On Certainty, edited by G. E. M. Anscombe and G. H. von Wright, translated by G. E. M. Anscombe and D. Paul (Oxford: Blackwell), #110. 52 MS 107, p. 233 (cited at greater length above, p. 213.) 53 Philosophical Investigations, #141, #139. 54 Big Typescript, #102, p. 496. The German reads:

Von welcher Wichtigkeit ist denn diese Beschreibung des g e g e n - war t i g e n Phanomens, die fUr uns gleichsam zur fixen Idee werden kann. Dass wir darunter leiden, dass die Beschreibung nicht das beschreiben kann, was beim Lesen der Beschreibung von sich geht.

55 Philosophical Investigations, # 140. 56 Cf. Philosophical Investigations, #431-2, on the idea that understanding animates signs, and #435-6, on the idea that understanding is a hidden rapid process. 57 Philosophical Investigations, #156.

226 DAVID STERN

58 Philosophical Investigations, #156. 59 Philosophical Investigations, # 159. , 60 Philosophical Investigations, #165, #177. 61 See M. Heidegger: 1962, Being and Time, translated by J. Macquarrie and E. Robinson (New York and Evanston: Harper and Row), #15-16. 62 Philosophical Investigations, #166. 63 This is very clearly stated in Philosophical Investigations , # 170; also the last paragraph of #175. 64 Philosophical Investigations, #201. 65 On Certainty, #204.

Dept. of Philosophy University of Iowa 269 English-Philosophy Bldg. Iowa City, IA 52242 U.S.A.

M. R. M. TER HARK

THE DEVELOPMENT OF WITTGENSTEIN'S VIEWS

ABOUT THE OTHER MINDS PROBLEM*

The aim of this article is to examine the development Wittgenstein undergoes between 1929 (the year of his return to Cambridge) and 1951 (the year of his death) in his approach to the other minds problem. Wittgenstein's way of dealing with this problem is in terms of an analysis of the use of psychological concepts in the third person. However, in contrast to his extensive treatment of psychological concepts in the first person in Philosophical Investigations (PI) and other posthumously published works, he remains rather reticent about the correct analysis of third-person attributions of sensations, emotions and thoughts. Therefore it comes as no surprise that the little that has been written about this aspect of Wittgenstein's philosophy of mind is controversial. For instance, some commentators deny that Wittgenstein was ever a behaviourist and even try to explain away the apparent behaviourism in Philosophical Remarks (PR). Others, instead, read Wittgenstein as a behaviourist even in his later works. According to R. Fogelin, for instance, Wittgenstein takes it for granted in Zettel par. 488 that the third person employment of psychological concepts simply give information that can be verified by observation and the position he ascribes to Wittgenstein is "straightforwardly behaviouristic". 1 And to S. Kripke Wittgenstein's 'famous slogan' in Philosophical Investigations about our 'attitude towards a soul' sounds "much too behaviouristic". 2

In support of their claims commentators often act more on a hunch than by offering extensive exegetical evidence. Consequently, whether or not these claims are correct can rarely be seen from the little evidence accompanying their interpretations. My main reason, therefore, for making a detailed study of Wittgenstein's views about the other minds problem, i.e., his analysis of third-person attributions of mental states, is the fact that there is an extensive array of still unpublished remarks in the Nachlass that throw considerable light upon the precise meaning of published remarks. On the basis of the original context of published remarks in the Nachlass and many still unpublished remarks about other minds I shall argue the thesis that the development of this topic from Philosophical Remarks to Philosophical Investigations has to be


22S M. R. M. TER HARK

viewed as a (rather slow) transformation of a behaviouristic into a nonbehaviouristic way of thinking. In particular, I shall try to show that the apparent behaviourism of Philosophical Remarks is real and cannot be dismissed so easily. Such is the intent of Section 1. Next I shall argue that forcing Wittgenstein's remarks about the third person, in Philosophical Investigations and later works, into the position of behaviourism is an interpretation for which there is np licence. The burden of Section 2 is that the meaning of Wittgenstein's emphasis on our "attitude towards a soul" can be grasped only in the context of his repudiation of logical behaviourism in manuscripts from 1941 and 1949/50. I shall end, in Section 3, with a discussion of Wittgenstein's last, unpublished writings about the concept of pretending, the upshot of which will be that his way of dealing with that problem is quite at odds with a behaviouristic ignorance of the problem.

Before I attempt these tasks, there are some preliminary points about the chronology of Wittgenstein's writings about the other minds problem that need to be made. The first time Wittgenstein deals, in his published writings, with the other minds problem is in Philosophical Remarks chapter VI. The typescript published as Philosophical Remarks was compiled in 1930 out of manuscripts 105, 106, 107 and the first half of lOS. Unlike many other 'definitive' typescripts, most of the fragments in Philosophical Remarks have come unaltered from manuscripts 105, 106, 107 and lOS. For instance, of the thirty-four fragments composing chapter VI, twenty-eight fragments have found their way unaltered into Philosophical Remarks. Changes concern only the order and sequence of fragments. In that respect the status of Philosophical Remarks is unique for in all his later writings Wittgenstein continually changes his formulations or thoughts. Maybe this is the reason that G. E. Moore spoke of the 'confused,3 character of Philosophical Remarks. That Wittgenstein was not very satisfied especially with chapter VI is proved by the fact that in less than two years later, in 1931, Wittgenstein takes up only half of the fragments (nineteen) in a comparable chapter in Big Typescript, called "Schmerz haben". The remaining bulk of fragments in this chapter of TS 213 were culled from manuscripts of the years 1931 and 1932 and, as we shall see, testify of rapid and fundamental changes in Wittgenstein's thinking about other minds. The story of this first phase of Wittgenstein's development will be told in Section 1.

The second phase of Wittgenstein's development in relation to the other minds problem occurs as late as 1941, in manuscript 123. This

WITTGENSTEIN ON THE OTHER MINDS PROBLEM 229

late dating may seem surprising and consequently is in need of some explanation. Apart from a few rather implicit references to the other minds problem in Notes for Lectures on "Private Experience" and "Sense Data" and in the Blue Books, the first time Wittgenstein occupies himself with this problem again and especially with his own earlier behaviouristic approach occurs in 1941. This is not to say that he wrote nothing about the philosophy of mind before 1941. On the contrary, many of the fragments about private language in Philosophical Investigations, par. 243-421 were drafted already as early as 1937/38. But in these paragraphs of Philosophical Investigations and the relevant manuscripts, the emphasis is on the first person use of psychological concepts. In MS 123 (1941), however, he devotes himself exclusively to the third person and those remarks shed considerable light upon the history and precise meaning of Wittgenstein's most condensed aphorism about other minds in Philosophical Investigations part II: "My attitude towards him is an attitude towards a soul. I am not of the opinion that he has a soul". The most recent source of this remark is MS 169, written in 1949. The story of this second phase of Wittgenstein's development will be told in Section 2.

The third phase of Wittgenstein's development is, as the second, a critique of his first phase and is especially concerned with the problem of pretending. These remarks were written between 1949 and 1951, in manuscripts 169, 171, 173, 174 and 176. The latter three are the same manuscripts in which Wittgenstein writes On Certainty and Remarks on Colour and it is striking to note how he finally applies his philosophy of certainty and doubt to the other minds problem in general and the problem of pretending in particular. The story of this last phase of Wittgenstein's development will be told in Section 3.

These preliminary deliberations about the chronology of Wittgenstein's writings are of course no substitute for a concrete examination of their content. Addressing this task will offer more genuine insight into the development of Wittgenstein's treatment of the other minds problem.

1. THE BEHAVIOURISM OF THE PHILOSOPHICAL REMARKS

In this section I shall give a strongly behaviouristic interpretation of Wittgenstein's remarks about other minds in Philosophical Remarks and the corresponding manuscripts. Commentators4 have often tried to

230 M. R. M. TER HARK

explain away the apparent behaviourism in Philosophical Remarks as a rhetorical way of endorsing some form of non-behaviourism. However, remarks in unpublished manuscripts unambiguously show that Wittgenstein's endorsement of behaviourism was not just apparent, but real. Furthermore, these remarks explain how a rather bold version of behaviourism was forced on Wittgenstein by assumptions concerning the Ego and the nature of self-knowledge he shared with, James and Russell.

Wittgenstein's path to behaviourism has roughly the following form: in the early period of his later philosophy Wittgenstein subscribes to the rather traditional view that mental experiences are known directly from the inside. Given this conception of thought, Wittgenstein feels a difficulty in attributing mental states to others. But whereas he accepts, like Russell, that knowledge of other minds is knowledge by description, unlike Russell, he rejects the argument by analogy and consequently is forced into behaviourism.

In fact the first two remarks written by Wittgenstein about other minds, in 1929, hint at the distinction between knowledge by acquaintance and knowledge by description:

Why do I call toothache "my toothache"? When I say of someone else, he has toothache I mean with "toothache" as it were an abstract [AbstraktJ form what I normally call "my toothache". (MS 107, p. 199)

In what follows I shall interpret the term 'abstract' in the sense that it has to be contrasted with the concrete and direct acquaintance we have with our own pain. Then it will be argued that the transition from concrete to abstract, i.e., the attribution of mental states to others, forces Wittgenstein into behaviourism.

In an important sense the appeal to knowledge by acquaintance was meant by James and Rusell to dismiss talk of a metaphysical Ego as pointless. Nonetheless, RussellS continues to speak of a cognitive relation between a subject and an object since acquaintance by introspection clearly implies the occurrence of a mental act distinct from the mental event with which the act is acquainted. James is even more explicit in his acceptance of acquaintance and his rejection of the Ego. One passage in Principles of Psychology vol. 2 is of special importance in this context, for there James describes how the Ego and its objects may be in large part an artifact of the methods typically used for studying them:


Take the pain called toothache for example. Again and again we feel it and greet it as the same real item in the universe. We must therefore, it is supposed, have a distinct pocket for it in our mind into which it and nothing else will fit .... Thereupon of course comes up the paradox and mystery. If the knowledge of toothache be pent up in this separate mental pocket, how can it be known cum alio or brought about into one view with anything else? This pocket knows nothing else; no part of the mind knows toothache. The knowing of toothache cum alia must be a miracle. And the miracle must have an Agent. And the Agent must be a Subject or Ego 'out of time'. (Ja~es, p. 5)

Toothache is also Wittgenstein's favourite example in Philosophical Remarks. Apart from Wittgenstein's choice of this example, the use of some of his metaphors reveals the philosophical heritage of James. In Philosophical Remarks he warns of the misleading comparison between a toothache and a purse (PR, par. 62) or a matchbox (PR, par. 65) -things one typically possesses in one's pocket. The point made by Wittgenstein is that the comparison between pain and an object easily misleads one into thinking that the object is in possession of an Ego, which in its turn leads to the solipsistic inability to make sense of real feelings other than one's own. A purse can have an owner, because it can also be possessed by none. But to speak of pain as something one possesses is pointless precisely because it is pointless to speak of unowned pains:

What is essentially private, or seems, has no owner. (MS 110, p. 7; TS 213, p. 508)6

The word'!, does not refer to an owner in sentences about having immediate experiences nor does it show that the word 'I', in this metaphysical sense, is superfluous here. Wittgenstein therefore says that we could have a language from which'!, is omitted from sentences describing immediate experiences. When we leave out the word'!, and instead say 'There is toothache' we can still describe the phenomenon formerly described by 'I am in pain'.

Now while this shows clearly that it is wrong, from Wittgenstein's point of view, to speak of an Ego that possesses something, the proposed elimination of the word 'I' is not exactly pellucid, for what is expressed by 'There is toothache'? In Philosophical Remarks par. 58, Wittgenstein says that 'There is pain' "could have anyone at all at its centre ... but the one with me at its centre has a privileged status". How are we to understand this privileged status? My answer is that this privileged status is the same as the knowledge by acquaintance we have of our immediate experiences. The proposition 'I have toothache' is


verified by direct acquaintance with the experience of pain, although an identification of an owner is not required by this verification. In the context of a discussion concerning the differences between propositions which are conclusively verifiable and propositions which are not thus verifiable (i.e., hypotheses), Wittgenstein gives as examples of the former:

"Do you see this indicator move; if it will have reached 10' you will feel headache". Is such a proposition not verifiable? Or: "The red circle you see now will gradually change into a rectangle". That also seems indeed to be directly verifiable. (MS 107, p. 250)

'I have toothache' is a proposition conclusively verifiable by reference to phenomenal experience. That this verification by reference to phenomenal experience is a form of acquaintance by introspection is clear from this remark:

The proposition 'A is in pain' relates undoubtedly to [bezieht sich zweifellos auf] my experience of pain. (MS 107, p. 271)

Like Russell, Wittgenstein holds that the meaning of 'I am in pain' consists of a relation and thus a relation between a subject and an object. Equally like Russell, he holds that the relation between subject and object is incorrigible ("zweifellos"). Together these two features constitute the nature of acquaintance by introspection. Moreover, this adherence to knowledge by acquaintance is also well conveyed by Wittgenstein's own retrospective account of it in 1932:

One might (falsely) conceive of the matter thus: The question "How do you know that you have toothache" is therefore not being posed, because one experiences this from the toothache (itself) at first hand, whereas that a person is in the other room, is experienced from second hand, for instance through a voice. The former I know via immediate observation [unmittelbare Beobachtung], the latter 1 experience indirectly. Thus: "How do you know that you have toothache" - "I know it, because I have it" - You learn it from the fact, that you have it; but for that must you not already know that you have it. (MS 113, p. 104)

In this manuscript Wittgenstein for the first time 7 points out that phenomenological propositions are not verifiable at all, and consequently he abandons his earlier position. Meanwhile, however, he was still treating the self-ascription of bodily sensations as it were based on acquaintance by introspection.

These considerations determine our next step. We must examine how


Wittgenstein's introspective and verificationistic approach to the first person comes to be juxtaposed with a behaviouristic approach to the third person. In this he distances himself from Russell but conforms to the behaviouristic doctrine to which Carnap adheres.

The main thesis defended by Carnap, in 1928,8 is that the epistemological core ("Kern") of our knowledge of other minds consists of observations of behaviour; the content of experience is only a "Nebentei! vom Physischen". Only the observation of physical behaviour is necessary for the justification of sentences about other minds. Alleged claims to knowledge of the content of experience of other persons can all be reduced to what Carnap considers the epistemological core. In a second article dating from 19329 Carnap explicates his behaviourism in more detail by stressing that the meaning of sentences about one's own mind and other minds can be interpreted physically as asserting "the existence of a physical structure characterized by the disposition to react in a specific manner to specific stimuli". The principle behind this translation of psychological concepts into physical language is verificationistic: "A sentence says no more than what is testable about it". Consequently, the meaning of sentences about other minds is entirely exhausted by the observation of physical behaviour.

An important assumption made by Carnap is that ascriptions of mental predicates in the first person and in the third person would be symmetrical in respect of verification. First-person as well as thirdperson statements obtain their "rational support" from observation of behaviour. Although Wittgenstein never followed Carnap in his behaviouristic translation of the first person, the same symmetrical assumption is apparent in his early writings, the difference being only a difference in method of verification: first-person statements are verified by reference to phenomenal experience, i.e., via acquaintance by introspection, whereas in the third-person case, statements are verified by observation of physical behaviour. When I ascribe to someone else toothache, Wittgenstein says, I mean by 'toothache' an 'abstract' of what I normally call my toothache. The contrast between 'concrete' and 'abstract' alludes to the problem how communication between me and you about our sufferings is possible. The problem is that, as the meaning of pain in the first person is based on a "zweiJellose Beziehung" to the experience of pain eo ipso, one is deprived of this privileged access in the third person. The relation between the first person and the third person is of course symmetrical: I am acquainted


with my pain and not with his as he is acquainted with his pain and not with mine. At best it is only possible to make an inference by analogy, i.e., on the basis of self-observation 'concluding that the behaviour of other people is in many ways analogous to our own and then inferring that it must have analogous causes. Wittgenstein, however, cuts off this route to any such argument by analogy, and therefore I shall argue, is forced into behaviourism. I

In Philosophical Remarks par. 62, Wittgenstein opposes the following approach to the other minds problem:

Very simply, I know what it means, that I have toothache, and when I say, that he has toothache, then I mean, that he has now, what I had then.

In this fragment Wittgenstein does not attack the argument by analogy as such but its more broader assumption that 'He has toothache' can be explained by reference to what one knows from one's own case. As Russell, a defender of the argument by analogy, puts it: "What people would say is what we should say if we had certain thoughts, and so we infer that they probably have these thoughts".10 Wittgenstein offers two reasons for denying that this appeal to the same makes sense. The first reason is rather obvious from what has been said before about the elimination of the 'Ego'. Traditionally the difference between 'I am in pain' and 'He is in pain' has been explained by reference to the one who possesses pain. 'Pain' in 'I am in pain' and 'He is in pain', according to this view, both refers to the same sensation but this same sensation is attributed to different Egos. By precluding identification of an owner, Wittgenstein, of course, cuts off this route. Another possibility to interpret 'He is in pain' as referring to the same sensation as 'I am in pain' is that, although these sentences are not about an Ego, they are about a body. The meaning of 'He is in pain' is then conceived of as locating a pain in his body. Starting from one's own case one could then simply extend the idea of what is immediately felt into other people's bodies. This possibility is also excluded by Wittgenstein. Believing that one can simply extend the idea of what is immediately felt into other people's bodies is not only based on a false analogy but also will give you only an idea of having feelings in their bodies, not of their having feelings. In a manuscript from 1932 this is expressed very clearly:

Instead of saying the other is in pain we say "His tooth does ouch" [macht au]. "But you don't want to deny that the other can have what you have". Surely not. I want to know only how I have to imagine this. I know, for instance, in the case of the grey hair


that you and I could have. Also in the case of bad teeth. But when I apply this concept in the case of pain I will never come from my pain to his but from my pain in my tooth to my pain in his tooth. (MS 156, p. 59)

In short, 'toothache' in 'I have toothache' and 'He has toothache' is not univocal. 'Toothache' cannot refer to the same sensation in both sentences. It is also obvious that 'toothache' cannot refer to different sensations in both sentences, otherwise, one has to be; in a position to distinguish between them, and clearly, no one is. But as we have seen in the first person, the meaning of the term is given by acquaintance with some sensation. The consequence seems to be that the meaning of 'He is in pain' is not at all about a sensation, but exhausted by the observation of physical behaviour.

A possible way out of the almost inevitable behaviouristic position would be to maintain, as is done by proponents of the argument by analogy, that in order to verify the sentence 'He has toothache' it is necessary to use a representation of phenomenal experience or an inner ostensive definition of pain. Wittgenstein's insistence on acquaintance by introspection and his rejection of the argument by analogy cuts off this route. In Philosophical Remarks he says:

If I pity someone else, because he is in pain, I do imagine the pain, but I imagine that I am in pain. (PR, par. 65)

This is a slightly different formulation of the thought quoted above (see p. 230) that knowledge of other person's pain is an abstract from knowledge of our own pain. 'Pain' is essentially private ("wesentlich privat") and can only be known from within, via acquaintance by introspection. The implication seems to be that pain with which I am not acquainted is something I cannot represent. In a remark preceding the one just quoted Wittgenstein stresses exactly that point:

A matchbox that the other has I can imagine but not someone else's pain, that is pain I do not notice [spure]. (MS 107, p. 287)

Consequently, while communicating about our sufferings, we are forced into the same symmetrical position: I notice my pain, but he doesn't and I do not notice his pain, but he does. But if I can only imagine pain with which I can be acquainted and if in that sense I cannot imagine the pain of someone else, isn't the only conclusion to draw that the content of experience of other persons is logically redundant and epistemologically a "Nebenteil". Although not expressed in

236 M. R. M. TERHARK

these technical terms this very same thought is contained in the following remark:

When I say 'A is in pain', then I use the representation of pain in the same way as 1 use the concept of flowing, when 1 speak of an electric current flowing. (PR, par. 64)

In MS 107 this is followed by: ,

When suddenly hearing from the room next to us in an unknown voice the utterance 'I am in pain' we do not understand [verstehen] it. (MS 107, p. 285)

The point of the latter remark is that it would be tempting to use a representation of the pain as it is felt in order to understand the sound coming from the room next to us, but that as a matter of fact it doesn't help at all. On the contrary, in verifying the sentence no representation of phenomenal experience is used and the only way to understand the utterance is to observe physical behaviour and probably the circumstances in which it occurs. The utterance does not inform us of anything unless we understand it, that is, unless we can test it. And we can test it iff we know what physical behaviour would verify it. Deprived of that sort of observation we do not understand the utterance at all.

This constraint upon communication about our sufferings forces Wittgenstein into behaviourism. And this is what we do in fact find:

If 1 make myself understood by him in language, then it has to be understanding rver· stehen] in the sense of behaviourism. That he has understood me is a hypothesis, as is, that 1 have understood him. (MS 110, p. 8)

In order to specify in more detail what Wittgenstein means by the term 'behaviourism' more must be said about his use of the term 'hypothesis'. What Wittgenstein means here with hypothesis has to be opposed with what he calls 'genuine propositions'. The latter are directly and conclusively verifiable by reference to phenomenal experience. Hypotheses, instead, are not conclusively verifiable and they are not true or false in the same sense in which genuine propositions are. They are probable and have to await future confirmation. Thus conceived, the hypothetical nature of our knowledge of other minds is indeed indistinguishable from Carnap's logical behaviourism, according to which the meaning of sentences about other minds has to be explained in terms of dispositions to behave in specific ways in specific circumstances.

However, the meaning of 'hypothesis' in relation to behaviourism is not exhausted by 'a disposition to behave'. Wittgenstein uses the term


in this context with the extra implication that error or illusion is always possible. One of his many characterisations of 'hypothesis' is:

Propositions for which it counts that one can always be mistaken I call hypotheses. (MS 109, p. 16)

Applied to other minds it is obvious what 'possibility of error' means: the other can always be pretending to be in pain or, simply lying. In the language of behaviourism, which restricts itself to the observation of outer behaviour, one cannot account for the distinction between real pain and simulated pain and the case of a perfect imitator cannot even be formulated consistently.ll Wittgenstein's reference to the problem of pretending has escaped the notice of many commentators. But in the following two fragments his use of 'hypothesis' refers to the possibility of error identified as the possibility of pretending:

(A) The two hypotheses, that other people have toothache, and that they behave just as I do but don't have toothache, possibly have identical senses. That is, if I had, for example learned the second form of expression, I would talk in a pitying voice about people who don't have toothache, but as behaving as I do, when I have it. (PR, par. 64) (B) The two hypotheses, that others have pain, and that they don't, and merely behave as I do when I have it, must have identical senses if every possible experience confirming the one confirms the other as well. In other words, if a decision between them on the basis of experience is inconceivable. (PR, par. 65)

These two fragments have been the topic of much debate in the critical literature. 12 The upshot of it is very unsatisfying. Several authors have tried to read into (A) and (B) not only a non-behaviouristic approach but also a rejection of behaviourism. No other evidence is cited in support of these interpretations than (A) and (B) themselves. However, (A) and (B) can be interpreted equally well along behaviouristic lines. Consequently, a decision to choose between these conflicting interpretations has to be based upon some other evidence. This is the reason for examining the original context of (A) and (B).

Both fragments occur for the first time in MS 107, (A) at page 270 and (b) at page 287. The context of (A) is different from the context in Philosophical Remarks, the context of (B) is identical, but its initial formulation is slightly different. These facts will make clear that Wittgenstein's use of two almost identical fragments in a 'definitive' typescript, as Philosophical Remarks is, ought to have caused more surprise than it in fact did.

The fragment after (A) in MS 107 is the following:


(C) A proposition so conceived, that it can be true or false without any possibility of controlling this is completely detached from reality, and doesn't function I Iworkl I any longer as a proposition. (MS 107, p. 270; PR, XXII, par. 225)

On the basis of (A) and (C) the following behaviouristic position could be ascribed to Wittgenstein. Detached from reality is a proposition like this: 'One can never know what goes on in his mind for behind the fa~ade of his outward behaviour he can think qr feel totally different or just nothing'. In this case our knowledge corresponds only to the observable behaviour, not to the supposed content of experience. Even if we made a mistake here the mistake could never be discovered which means that one cannot speak of a mistake. The inevitable conclusion for Wittgenstein to draw is that the sentence 'He is in pain' and the sentence 'He merely acts as if in pain' are identical in meaning, i.e., in both cases the epistemological core of our knoweldge consists of the observation of behaviour.

But maybe this conclusion is too quick. For from the fact that Wittgenstein explicitly realises this consequence of his verificationistic behaviourism one could be tempted to conclude that, unlike Carnap, he is not willing to identify the two sentences. More can be learnt from the formulation of (B) in MS 107. It is split into two parts:

(D) Is there yet no difference between the hypotheses that the others are in pain and that they are not and just behave as I do, when I am in pain? (E) According to my principle both assumptions must be identical in meaning if all possible experience confirming the one confirms the other. If that is to say no distinction is conceivable on the basis of experience. (MS 107, p. 287)

The question-form in (D) obviously refers to (A) at page 270 of the same manuscript. Moreover the question suggests even a correction of (A), that is the two sentences can be distinguished after all. Fragment (E) equally suggests a correction, for it says: if every possible experience confirming the one confirms the other, then according to the principle of verification the two sentences must be identical. The conditional seems to imply that it is possible to find experiences that do differentiate between the two.

David Pears remarks in this context that the phrasing of (B) indicates Wittgenstein's reluctance to commit himself to the identity of the two hypotheses, but "there is no hint of any good way of avoiding the identification". 13 However, Pears, as so many others, forgets to involve the fragment following (B) in the discussion about pretending:


To say that the others are not in pain, presupposes that it makes sense to say, that they are in pain. (PR, par. 65; MS 107, p. 287)

Here is a hint of avoiding the identification: to be able to speak about pretending presupposes logically to be able to speak about genuine cases of pain. The statement 'He seems to be in pain, but is not' has a sense iff the statement 'He is in pain' has a sense. This logical prior status of attributions of genuine pain implies that it inust be possible to distinguish between cases of pretending behaviour and cases of genuine pain-behaviour. The conclusion of this reconstruction can be that Wittgenstein, in Philosophical Remarks, alternates between a behaviouristic ignorance of the problem of pretending and a confrontation with the problem without committing himself either to behaviourism or introspectionism. In any case, the fact that Wittgenstein did publish both (A) and (B) indicates that his views still had to be cut out, not to say they;were in a 'confused state'.

Conclusive evidence for my interpretation of (B) comes from TS 213 in which Wittgenstein takes up (B) and omits (A) and writes another remark in which he explicitly says that we do distinguish between cases of real pain and cases of feigned pain:

Behaviourism. "It seems to me, I am sad, my head droops so much". Why does one not pity, when a door is unoiled and weeps in opening and closing? Do we pity the other, that behaves as we do, when we are in pain, - on philosophical grounds, that have led to the result that he suffers, as we? Physicists might just as well make us scared, by assuring us, that the earth is not compact after all, as it seems, but consists of loose particles, that wander around erratically. "But we would not pity the other, if we knew, that it is just a doll, or that he merely feigns his pain?" Naturally - but we do have quite specific criteria for something being a doll, or for someone feigning to be in pain and these criteria oppose those we call criteria for something not being a doll (but for instance a human) and for someone not feigning his pain (but really being in pain). (TS 213, p. 509)

In this important fragment14 many new lines of thinking about other minds announce themselves but must await further elaboration until 1941 and even 1949/50. The first line of thought is stated in the last two sentences. The sceptical thesis that others can always feign their pain and that the only way to find out what the real meaning of their behaviour is, is rebutted by Wittgenstein: we do not need to infer hypothetically from the outer to the inner because there are in fact behavioural criteria that do distinguish between cases of feigned pain and cases of real pain. From the fact that Wittgenstein takes up at page


507 of this chapter fragment (B) from Philosophical Remarks it can safely be concluded that he already meant to distinguish between these two cases in MS 107 in 1930. So concerning pretending, Wittgenstein does not commit himself to a behaviouristic ignorance of the problem like Carnap. As Wittgenstein lets the problem rest until 1949, I, too, shall let it rest and return to it in Section 3.

A second line of thought prepares us for SeGtion 2. It is expr~ssed in the first part of the quote above. There Wittgenstein suggests that our knowledge of other minds is at a fundamental level not a question of hypotheses and in that sense he distances himself from an intellectualistic tradition in which both behaviourism and introspectionism share. Wittgenstein's question, if we pity someone else when he is in pain on account of philosophical considerations, expresses doubt with regards to his own earlier solution that our knowledge of other minds is a hypothesis. This can be seen from the analogy he draws with the physicist's notion of nature. The point of the analogy is that our ordinary non-hypothetical conception of space as something we experience which is full of matter cannot come into conflict with the hypothetical conception of space as empty, or is a mere aggregate of electrons. They cannot come into conflict because they are incommensurable, i.e., the fullness of space with matter does not correspond to the fullness of space with electrons (and thus to emptiness) in the physical conception, but to the frequency of electrons. IS Consequently, the ordinary conception of space is as adequate as the physcial one and is certainly not improved upon by the use of physical hypotheses. By analogy, our ordinary conception of other minds is non-hypothetical and is not improved upon by the use of hypotheses concerning inner mental states, or as in Carnap's proposal, the neurophysiological structure underlying dispositions to behave. This insight is as yet not further elaborated by Wittgenstein and is still not incompatible with a form of behaviourism. However as regards the philosophy of mind, the problem of psychological sentences in the first person will want the centre of his attention, especially between 1932 and 1938. Not until 1941 does Wittgenstein resume the thread of his analysis of the third-person case.

2. "EINSTELLUNG ZUR SEELE"

Having laid the groundwork for some of his later views about the correct analysis of the third-person case in TS 213, Wittgenstein moved


on, roughly between 1932 and 1939, to work out the correct analysis of the first-person case. The upshot of his extensive treatment of the first person is that self-ascriptions of pain are primarily expressions rather than statements and that in expressing one's pain no claim to privileged access or knowledge is made. That the analogy with natural expressions affords Wittgenstein a means of overcoming the deadlock in the discussion between dualists and behaviourists l simply take for granted here. 16 But this cannot be emphasised enough: the importance Wittgenstein attaches to natural expressions of pain is a clear manifestation of his relativisation of the mainly intellectualistic approach of logical behaviourists and dualists. Realising this pre-linguistic foundation of the concept of pain implies for Wittgenstein that in an important sense it is pointless to speak of knowledge here. My first thesis in this section will be that in 1941 he follows the same strategy with regard to our knowledge of other minds. More precisely: at a certain fundamental level neither the concepts of knowledge nor of certainty and doubt have any bearing on the sentence 'He is in pain', and consequently, the meaning of that sentence cannot be exhaustively equated with a claim to knowledge supported or refuted by the observation of behaviour. My second thesis will be that this relativisation of the intellectualistic starting-point for posing the other minds problem has as its result that the behaviouristic translatibility of psychological concepts into physical concepts is untenable.

An important part of Wittgenstein's strategy to show that the other minds problem is mainly the product of a detached intellectualistic view is to abandon the symmetrical construction of the first and the third person and to present an alternate, asymmetrical construction of their relation. Instead of saying that both the first and the third person are about observation and knowledge, Wittgenstein will say that only the attribution of mental states to others is based on observation and implies a claim to knowledge. However, his analysis does not stop here and if it did one indeed could accuse Wittgenstein of naive behaviourism. The following two fragments show that Wittgenstein's asymmetrical proposal amounts to more than simply observation of behaviour in the third-person case:

The inner is hidden from us means, it is hidden from us in the sense that it is not hidden from him. And it is not hidden from the owner [Besitzer) in the sense, that he expresses it and that we give credit to the expressions under certain conditions and that no mistake


exists there [und es da den [rrtum nicht gibt]. And this asymmetry of the game is expressed by the sentence, the inner is hidden from us /the other/. (MS 169, p. 56)17 Can one know what goes on in someone else, in the way he knows it? - But how he knows it? He can for instance express his feeling /express his experience/. Doubt about the fact whether he really has this experience - analogous to the doubt if he has such or such illness - does not enter into the game, and therefore it is false to say he knows what he experiences. The other, however, can very well doubt it whether he has that experience. Doubt does enter into the game, but precisely because of that it is also possible that certainty [Sicherheit] exists. (MS 176, p. 47)18 ;

The most salient feature of this asymmetrical construction is that even in the third-person case, at a certain level, mistakes are excluded. Normally the term observation does imply the possibility of error. Consequently, the meaning of the sentence 'He is in pain' is not exhausted by observation of behaviour. I shall argue below that a significant part of the meaning of 'He is in pain' is constituted by what Wittgenstein calls' Einstellung zur Seele'.

If at a certain level it is pointless to speak of mistakes in our attribution of mental states to others, it seems impossible for Wittgenstein to accept the traditional epistemological view according to which we have 'only indirect outer evidence' of other minds. In MS 17319 he rejects precisely this roundabout approach to other minds which readily leads to the sceptical conclusion that we are always in the dark about other minds:

The distinctive feature of the inner [vom Seelischen] seems to be, that it has to be guessed at from the outer of the person and is known only from within. But when through accurate consideration this conception vanishes into thin air, the inner indeed has not become the outer, but for us there is no longer direct inner evidence and indirect outer evidence for the inner. (MS 173, p. 33) It is not as if I had direct evidence for my inner, he only indirect evidence. But he has evidence for it, (but) I do not. (MS 173, p. 42)

The question to be answered here is what Wittgenstein means by 'evidence'. The use of the term is not epistemological, for he has eliminated the traditional epistemological properties of 'evidence', respectively, 'direct inner' and 'indirect outer'. To the traditional epistemological approach Wittgenstein opposes a logical one:

What I want to say is rather, that the inner distinguishes itself for its logic from the outer. And that it is certainly the logic which explains the picture of the inner and the outer /the expression 'the inner'/, makes it understandable. (MS 173, p. 34) The inner is not only connected with the outer by experience, but also logically. (MS 173, p. 36)


From a logical perspective, it seems, the fact that evidence makes someone else's feeling merely probable is irrelevant, for Wittgenstein says:

And the evidence, to the extent that it is uncertain, it is not, because it is only outer evidence. (MS 173, p. 42)

That is, Wittgenstein does not use the concept of the. inner to explain the uncertainty and unpredictability of the outer, as is usually done in epistemology. The reverse is true: the indeterminacy of human life provides an explanation for the use of the concepts of soul and inner. What matters from a logical point of view is the fact "that we construct a statement on this involved sort of evidence, and hence that such evidence has a special importance in our lives and is made prominent by a concept" (Remarks on the Philosophy of Psychology, II, par. 709 [RPP]). The role of the notion of evidence in the case of uncertainty I shall postpone until Section 3, here I shall confine myself to the role of the notion of evidence in the case of certainty. My point will be that Wittgenstein's famous remark that our attitude towards him, as an attitude towards a soul, has to be understood in terms of his application of the logical distinctions between knowledge and certainty to the other minds problem. In the following fragment he makes clear that in a sense we cannot speak of knowing a mental state of another person because of the role of the notion of evidence:

If 'I know .. .' means: I can convince the other if he gives credit to my evidence, then one can say: I may be as certain [sicher] about his mood, as about the truth of a mathematical proposition, but it is still false to say: I know his mood. (MS 174, p. 13)20 If I thus know, that he is glad, I feel myself certain, not uncertain in my satisfaction, and that, one could say, is not knowledge. (MS 169, p. 1).

Wittgenstein wishes to say that the evidence for knowledge is of a different kind from the 'evidence' in the case of certainty. In the latter case he sometimes speaks of 'sure evidence' [sichere Evidenz], meaning that it is evidence we accept as sure and that we go by in acting surely (cf. On Certainty, par. 196). It is precisely this emphasis on acceptance, on certainty of reacting and absence of doubt or error that Wittgenstein wishes to convey with his metaphor 'Einstellung zur Seele'. A very first draft of that metaphor makes this clear:

Instead of saying 'Attitude towards a soul' one could also say: 'Attitude towards a human [zum MenschenJ'. I could always say of a human, that it is an automaton (that I could


learn at school during lessons in physiology) and yet it would not influence my attitude towards the other. I could even say it of myself. But what is the difference between an attitude and an opinion? I might say: the attitude comes before opinion. An opinion can be mistaken. But how should a mistake look like here? (MS 169, pp. 60-61)

Wittgenstein's point is that an attitude is logically antecedent to an opinion and thus to a supposition or an hypothesis. A hypothesis about other minds has point only where there is room for doubt and error. An attitude is precisely the absence of such room.

However, even this emphasis on attitude can seem to be a veiled form of behaviourism, as Kripke thinks. Therefore, I shall trace the very first starting point of Wittgenstein's famous dictum in his manuscripts for there is explicit evidence that Wittgenstein's repudiation of logical behaviourism was a major theme in the emergence of his later emphasis on attitudes.

According to logical behaviourism, sentences about other minds are hypotheses to be checked by (future) experience. Supposing someone else to be in pain means forming an hypothesis concerning a disposition to behave in a specific manner in specific circumstances. In the following fragment Wittgenstein wishes to stress that the behaviouristic doctrine is a detached and purely intellectual construction which itself is only possible on the basis of something more primitive:

How when I said: supposing someone in pain, means to suppose something that would only be confirmed by that sort of behaviour. Such an attempt at a translation into a behaviouristic way of expressing seems somehow foolish [kindisch]. Why? (The experience that the attempt is foolish must be taken seriously) It is an undertaking to secure [sichern 1 something, that is secured after all. (MS 123, 23-5-41 )21

What is secured after all comes out very clearly in a passage written two weeks later:

If someone asks: What is the difference between the representing of a pain and painbehaviour, I would explain: in the former case you imagine something painful, a stabbing pain, a feeling, let's say in the mouth !tooth/ - in the latter case a position or movement of the body. Now it is peculiar, that when I really represent pain I do not, it is true, represent the other in a painful position, but I pull myself a painful face. (MS 123, 3-6-41)

The point that needs to be made about this passage is that Wittgenstein carefully avoids both the argument by analogy as well as the behaviour-


istic translation of sentences about minds, without professing himself to offer a third theory. What he has to offer is a careful description of the way in which we set up and maintain pain-language in real life. In real life we do not regard sentences about other minds as 'assumptions' or 'hypotheses' to be checked against experience, neither as hypotheses in the sense of inferences by analogy nor as hypotheses concerning future behaviour. The way we act, or better, react" shows what is secured after all when ascribing pain to others. Consequently, the meaning of psychological concepts in the third person is not entirely exhausted by their reference to observable behaviour. The following remark is rather illuminating in this respect:

The objection against a behaviouristic way of expressing of propositions about the immediate experience is not that his way of expressing would not be about experiences but about something else. But that actually we playa different /somewhat different/ game with the expressions of experiences in comparison with the descriptions of behaviour. -Not that is an objection, that this way of expressing is about outward behaviour, for what it is about shows itself not unconditionally in the propositions and their ostensive definitions, but in the system of the use of the propositions. If someone says anxiously: 'He complains awfully', one can say, that he does not speak of behaviour. (MS 123, 3-6-41)

What is needed to let the problem of other minds dissolve is a careful description of the way our propositions about other minds are interwoven with our daily practices. Such a description will allow us to see beyond the distinction between the inner and the outer. Wittgenstein's objection is that behaviourism as a matter of fact makes the same appeal to ostensive definitions as its opponent and his criticism focuses on the supposed use of such ostensive ceremonies. What he wishes to stress is that we do not describe behaviour when we pity someone else in pain. The reason we don't intend to describe behaviour is the fact that the one in pain is expressing his pain. An expression is not a physical property of a thing, the body, of which a physical description can be given. For example, if someone is wounded in his hand it is not the hand who says that he is in pain. He says it, the person, with his mouth and his eyes. Observing him, we do not react to the body conceived physically as a thing, but to his expressions, to him as a person. For instance, we do not say 'That poor hand is in pain' and we do not console the hand, but rather look the other in the eye (ct. PI, par. 286). So the game we are playing while watching someone in


pain is not one of describing but one of reacting to expressions of pain, that is, our attitude towards a soul is part and parcel of the game.

The emphasis on attitude is far from having behaviouristic implications. Our immediate reactions to other people's pain shows that inner and outer are internally related. Insofar as one treats someone else as a human being eo ipso one treats him as somebody with an inner. So Wittgenstein is not a metaphysical behaviourist, for far from denying the inner he connects it morejirmly, i.e., logically to the outer. Neither is he a logical behaviourist for the meaning of psychological sentences in the third person in an important sense is not given by descriptions of behaviour.

3. PRETENDING

The precise meaning of 'Einstellung zur Seele' can be grasped only if we finally involve the problem of pretending in our discussion, for one could still be tempted to argue as follows: even if Wittgenstein's emphasis on attitudes were acceptable, there would still be scope for the other mind's scepticism. There might, in principle, still be pain-behaviour but no pain, that is, we might, in principle, observe people's pain-behaviour and yet not take up the appropriate attitude towards them. 22 Consequently, the reference to attitudes cannot bring out the difference between 'He is in pain' and 'He merely acts as if in pain'.

We have seen above that Wittgenstein, already in 1932, criticises a behaviouristic perspective within which the problem of pretending cannot even be formulated consistently. He suggested that there are quite special criteria that distinguish between real pain and simulated pain. In 1941, in the same manuscript in which he criticises behaviourism, he refers to the problem of pretending in his way:

"But even if all the particularities of behaviour occurred, I could always imagine that he is not in pain". That is what one says, and there must be a ground for it. In that a main feature of the grammar of the expression 'being in pain' has to reside. (MS 123, 23-5-41)

What is striking about this passage is Wittgenstein's unwillingness to formulate the problem of pretending in traditional epistemological terms. He seems to suggest that the problem pertains to the nature of different language-games and is in that sense grammatical and logical. Epistemologically the problem is formulated in terms of the evidential


relation between pain and pain-behaviour, that is the relation between inner and outer. The consequence of this emphasis on the evidential relation is that in the case of pretending one is readily inclined to say that the relation between the inner and the outer is disturbed. When people pretend, an absolute gap seems to be created between observation of behaviour and the true inner facts of behaviour. Pretending seems to devalue, to annul, all evidence.

Wittgenstein's way out of the problem will be to say that pretending is a different kind of language-game from the game in which someone expresses his pain sincerely and somebody else reacts to it sympathetically. The problem now becomes, in the first place, a problem concerning the logical relations between different kinds of language-games. 23

Wittgenstein's opposition to the sceptical consequences attached to pretending can be reconstructed in three stages: (i) hidden psychic medium is irrelevant; (ii) there is evidence for pretending; and (iii) pretending is a language-game which logically presupposes more primitive games. I shall discuss these stages in that order.

Of course, uncertainty tends to be thought of in terms of situations where one feels that one is being deceived or duped as in (i). In these situations somebody deliberately conceals something and disguises his behaviour in such a way as to make his inner unrecognisable. But Wittgenstein gives a number of instances where uncertainty is created by exactly the opposite:

Think, that we not only don't understand the other when he hides his feelings, but also often not, not when he is hiding them, indeed when he is doing his utmost to make himself understood. (MS 169, p. 43)

Uncertainty here has nothing to do with a 'hidden' inner which lies beyond one's reach, but rather with an outer which remains closed, like a handwriting that cannot be deciphered. It is also possible to hide one's thoughts from somebody by expressing them in a language unfamiliar to him (RPP II, par. 564) or by withholding one's diary (Last Writings, par. 974). These cases do not involve anything metaphysically hidden, so that it can never be found. On the contrary, there is relevance in what is being hidden here. In all these cases uncertainty cannot be attributed to the fact that one only possesses indirect outer evidence and that what the evidence should prove is elusive. The examples show clearly enough that it is not elusive, so that Wittgenstein remarks:


One might even say: The uncertainty about the inner is an uncertainty about something outer. (MS 174, p. 13)

There is evidence, or signs, for pretending (ii):

Above all has pretending its characteristic outer signs. How else could one speak of pretending at all. (MS 169, p. 68)

Wittgenstein wishes to say that both signs for d,eception and signs for sincerity 'inside' can be recognised on the outside. So the issue is not an epistemological contrast between inner and outer. There must be signs for pretending, since it would otherwise be impossible to expose somebody as an impostor: one can only expose somebody if one knows, no matter how, that he wears a mask. Thus Wittgenstein has no reason to abandon his idea that inner processes too have meaning only within the rule-guided activities of language-games. He is explicit about this with regard to pretending:

Also what goes on in him is a game, and pretending is not present [gegenwiirtig] in him like a feeling, but like a game. (MS 169, p. 49)

In other words, to ask whether somebody is posing or not is to ask about the kind of language-game that is being played, not about our knowledge of the relation between his behaviour and something inside him.

Pretending is a different kind of language-game from the languagegame of spontaneous expression of feelings of (iii). As the Hintikkas put it: "Wittgenstein never admits that we can, for instance, drive a wedge between pain and pain-behaviour in primary language-games. What happens is that another (secondary) language-game is superimposed on the primary one". 24 The following two remarks seem to support this interpretation:

The expressions of my feelings can be unreal [unecht]. In particular they can be feigned. That is a different language-game from the primitive language-game of genuine expressions. (MS 169, p. 63). Thus I wish to say, that there is an original, genuine expression of pain; thus that the expression of pain is not to the same extent [gleichermassen] connected with pain and pretending. (MS In, p. 1)

That the language-game of pretending is a different game from that of genuine expressions can be seen from the fact that a child has to learn a great deal before it can dissemble, so that we only talk about pretending in a fairly complicated pattern of life. If the pattern were not that


complicated we should be able to imagine a newborn child dissembling. That this cannot be imagined is also clear from the fact that language is constitutive for pretending. For like children, animals do not have the ability to pretend: a dog does not dissemble, nor is it sincere (PI II, xi, p. 229).

The internal relation between pain and expression remains intact, regardless of the possibility of pretence. This language-game does not disturb the original pattern, but makes the concept pain more complex. In 'I feel pain', the sincere expression, the relation between expression and sensation, is internal; the expression is the sensation and cannot be conceived of without the sensation, otherwise, the expression is embedded in the language-game of pretending. The relation between expression and feeling is not internal here; expression and sensation can be separated. That the relation is not internal also appears from the fact that there is no primary expression in this language-game. At any rate 'I am merely pretending that I feel pain' is not regarded as an expression of pretending, in the way that 'I feel pain' is regarded as an expression of pain. There is a spontaneous expression of pain functioning on a more fundamental level than the language-game of pretending, in the sense that the certainty in the sincere language-game is not prejudiced by the possible uncertainty in the insincere language-game. On the contrary, precisely the fact that there is room for doubt and uncertainty in the insincere language-game implies that there is certainty, too, witness Wittgenstein's logic of 'knowing' and 'certainty'. Just as it is meaningless to talk about doubt and therefore about knowing in the language-game of the first person, so it is meaningless not to talk about certainty, if on a different level, where it is possible to talk meaningfully about doubt and knowing: the language-game of the third person.

However, it would be misleading to conclude from this, as the Hintikkas seem to do, that the observation of hiding behaviour does not necessarily change the evidential situation, in the sense that it is "not harder to discover whether someone really is in pain". 25 This is misleading to say because it ignores the very special nature of the evidence for judging whether someone really is in pain. Wittgenstein calls this sort of evidence 'imponderable evidence' (PI II, pp. xi, 228) - such as subtleties of glance, of tone, of gesture - and his question is: What does imponderable evidence accomplish? To answer this question Wittgenstein compares the evidential situation in the case of pretending


with the role of evidence in mathematical judgements and judgements about colours. In the case of the latter two there is in general complete agreement in judgements, whereas "There is in general no such agreement over the question whether an expression of feeling is genuine or not" (PI II, xi, p. 227). This lack of agreement does not imply that one is never certain that someone else is pretending; what it does imply is that some third person is not sure and that I cannot convince him (PI II, xi, p. 227).

The remarks in Philosophical Investigations devoted to the role of 'imponderable evidence' are few in number, but in his manuscripts he says more about it:

Why did I wish to say, '2 x 2 = 4' is objectively sure. 'This man is in pain' is subjectively sure. (MS 169, pp. 35-36)

The meaning of 'objectively sure' is obvious. In mathematics or judgements about colours disagreement may exist, however, total agreement can be reached and is reached more often than not by giving proofs or by checking. Why does this sort of objective certainty not exist in the case of judgements about the genuineness of expressions of feelings? It should be obvious by now what a wrong answer is: it would be pointless to say that objective certainty does not exist here because we cannot look into someone else's mind. That would be appealing to the epistemological contrast between direct inner evidence and indirect outer evidence, whereas Wittgenstein wants to do away with these. The lack of objective certainty is a constitutive feature of the language-game in question. Consequently, the presence of subjective certainty and of uncertainty is equally constitutive. More precisely, it is a constitutive rule for our language-games in which we judge about the genuineness of expressions of feelings that they are based on 'fine shadings of behaviour', like subtleties of glance. There is no uniformity or regularity of behavior here and consequently our concepts do not have fixed limits. Therefore, the uncertainty whether someone is dissembling his feelings or not has not so much to do with an inner that conceals itself behind an outer but with the connection between elastic concepts and all but unspecifiable external circumstances. As Wittgenstein puts it:

We play with elastic, yes also flexible concepts. That means however not, that they can be reformed as one pleases /without offering resistance/, that is that they are useless. For if trust and mistrust were not to have a foundation in objective reality, then they would be only of pathological interest. (MS 169, p. 37)


For instance, variability and irregularity are an essential part of the human physiognomy, so that the concepts of emotion, which are mainly based on facial expressions, lack focus and have a kind of elasticity. Here evidence includes often 'imponderable evidence', that is, there is no sharp borderline between sufficient evidence and insufficient evidence. Thus there is an elastic margin in which the evidence for real laughter is insufficient, but not so insufficient as to be evidence for the opposite.

So what does imponderable evidence not accomplish? It does not lead to knowledge in the sense that there are no (universally) valid principles from which a proof can be derived:

"I am sure, he is in pain". What does that mean? How does one use it? What is the expression of certainty in behaviour; what makes us sure? Not a proof. That is, what makes me sure, does not make another sure. But there are limits to the discrepancy. (MS 169, pp. 31-32)

This fragment also indicates what imponderable evidence does accomplish: it can make me sure. And the subjective certainty in this case is a form of reacting, in short an attitude towards a soul:

Do not conceive of being certain as a state of mind, a kind of feeling, or something like that. The important thing of certainty is the way of acting, not the expression of the voice with which one speaks. (MS 169, p. 32)

CONCLUSION

My interpretation of Wittgenstein's remarks about other minds has suggested the following view of his development from Philosophical Remarks to Philosophical Investigations. In the former Wittgenstein endorses a form of logical behaviourism that reminds strongly of Carnap's behaviourism. Together his analysis of the first-person case and his rejection of the argument by analogy provide the main reason for Wittgenstein's behaviouristic approach to other minds. Between 1933 and 1938 Wittgenstein devotes himself to a non-introspectionistic as well as a non-behaviouristic analysis of the first-person case in terms of 'expressions' and consequently he attacks his own earlier analysis of the first person in terms of acquaintance by introspection. In this period he says almost nothing about the third person, in any case, nothing that hints at a criticism of logical behaviourism. Probably he thought that his criticism of acquaintance by introspection and his own construc-


tive account in terms of 'expressions' implied automatically a rejection of behaviourism about other minds. However, not until 1941 does he come to realise that he still has to offer arguments that demonstrate the untenability of logical behaviourism. In the last two years of his life he finally succeeds in giving a coherent account of our knowledge of other minds that is compatible with his non-epistemological but logical descriptions of language-games, forms qf life and the primacy of human action. If these descriptions of language-games still make a behaviouristic impression to some it is because of the character of language-games: language-games are 'outer' phenomena. But they are 'outer' phenomena that constitute the meaning of concepts of 'inner phenomena' .

NOTES

* I wish to thank the copyright owners of Wittgenstein's Nachlass, Prof. G. E. M. Anscombe and Prof. G. H. von Wright for graciously permitting me to quote from unpublished work by Wittgenstein.

For the designation of the unpublished manuscripts and typescripts I have made grateful use of the system of reference devised and published by von Wright in his 'The Wittgenstein Papers' in von Wright, G. H.: 1982, Wittgenstein, Oxford, Basil Blackwell. 1 See Fogelin, R.: 1976, Wittgenstein, London, Routledge and Kegan Paul, p. 176. 2 See Kripke, S.: 1981, 'Wittgenstein on Rules and Private Language', in Block, 1. (ed.), Perspectives on the Philosophy of Wittgenstein, Oxford, Basil Blackwell, pp. 238-313; esp. p. 303. 3 According to Moore, Wittgenstein himself used this term to refer to the remarks published as Philosophical Remarks. See Moore's letter to Russell 13 March 1930 in Russell, B.: 1968, The Autobiography of Bertrand Russell, 1914-1949, London, Allen & Unwin, p. 436. 4 See, for instance, Hacker, P. M. S.: 1987, Insight and Illusion, Oxford, p. 224; Pears, D.: 1988, The False Prison, vol. 2, Oxford, pp. 308, 309; and Bouveresse, J.: 1976, Le My the de !'[nteriorite, Paris, p. 350. 5 See, Russell, B.: 1970, 'Knowledge by Acquaintance and Knowledge by Description', in Mysticism and Logic, London, pp. 152-68. 6 This is a more accurate formulation than the quotation of Wittgenstein by Schlick ("immediate data have no owner"), quoted in its turn by Hacker, P. M. S.: 1975, Insight and Illusion, 2d ed. Oxford, p. 195. 7 Usually one refers to Moore: 1955, 'Wittgenstein's Lectures in 1930-1933', in Mind 64, p. 12, for Wittgenstein's first abandonment of verificationism. However, the remarks of Moore give no datings and their content is only suggestive. 8 See Carnap, R.: 1928, Scheinprobleme in der Philosophie. Das Fremdpsychische und der Realismusstreit, Berlin.


9 See Carnap, R.: 1959, 'Psychology in Physical Language', in Ayer, A. J. (ed.), Logical Positivism, New York, pp. 165-98. Appeared originally in Erkenntnis, III (1932-33). 10 See Russell, B.: 1948, Human Knowledge. Its Scope and its Limits, New York, p. 483. 11 In his Scheinprobleme Carnap acknowledges that in the case of other minds the possibility of error always exists. But to him this is only a problem if one makes an appeal to the content of experience. If a case of pretending occurs, Carnap says, the core of our knowledge corresponds to a state of affairs in reality, but not to our putative knowledge about the content of experience. According to Carnap this proves that the content of experience is only an eliminable "Nebenteil". 12 See Kenny, A.: 1973, Wittgenstein, London, chapter 7; and Pears, D., op. cit. p. 312. 13 See Pears, D., op. cit., p. 313. 14 Strangely enough, this fragment was not selected by R. Rhees for his compilation of Philosophical Grammar, while it occurs in three sources: MS 114 (p. 26), TS 211 (pp. 752-53) and TS 213. 15 See Philosophical Remarks, par. 36: "The visual table is not composed out of electrons". 16 For an interpretation of the first case largely based on unpublished material see ter Hark, M. R. M.: 1990, Beyond the Inner and the Outer, Wittgenstein's Philosophy of Psychology, Dordrecht, Kluwer Academic Publishers. 17 Von Wright underestimates the contribution of this manuscript to PI II, see von Wright: 1982, Wittgenstein, Oxford, Basil Blackwell, p. 134. For instance, PI II, par. viii, ix and x are here drafted for the first time. The main part of MS 169, however, is devoted to an analysis of the concepts 'inner' and 'outer'. 18 In the manuscript of On Certainty, par. 426-637 are written. However, an important discursive stretch of remarks concerning other minds is written between what has since been published as On Certainty, par. 523 and 524. 19 Besides remarks on the inner and the outer this manuscript contains part III of Remarks on Colour. 20 Besides On Certainty par. 66-193, this manuscript contains thirty pages devoted to the inner and the outer. 21 This manuscript was written between 25 September 1940 and 6 June 1941. Between 16 May 1941 and 16 June 1941 Wittgenstein writes about 'seeing-as' and behaviourism. 22 See Locke, D.: 1968, Myself and Others, Oxford, pp. 81-84. 23 With this interpretation I follow in the main the Hintikkas' view in Hintikka, M. B. and Hintikka, J.: 1986, Investigating Wittgenstein, Oxford, Basil Blackwell, pp. 279-84. 24 Ibid., p. 281. 25 Ibid., p. 283.

Faculty of Philosophy University of Groningen A-Weg 30 9718 CW Groningen Holland

C. GRANT LUCKHARDT

PHILOSOPHY IN THE BIG TYPESCRIPT*

PHILOSOPHY AS TRIVIAL

One of the most distinctive features of Wittgenstein's 'later philosophy is philosophy's concern with itself. What philosophy is, and what it should be, are two questions that occupied much of Wittgenstein's thought. It is very easy to read passages from his later works as suggesting a profound cynicism about the answers that should be given to both questions. Philosophy as traditionally conceived and practiced seems to come in for much criticism, not to say abuse. And philosophy as it ought to be can very easily be seen as both self-deprecating and selfdestructive. What is left for philosophy to do, once its limitations are understood, is repair work - that of a handyman, not of an architect or even a builder. And once those repairs are done, if they are done well, the repairman can be dismissed. Philosophy, in short, can be viewed as putting an end to itself.

Certainly part of traditional philosophy's appeal is its claim to universality and primordiality. Conceived as exploring and constructing foundations on which most of the rest of human thought rests, it is easy to see why philosophy's twin metaphors of itself as underlying and overarching render it so deep, so exalted, and so important. Investigating 'being qua being' grabs the imagination, if not the soul. By contrast, "assembling reminders for a particular purpose" must seem paltry fare, hardly enough to make a single meal of, much less the diet of a life.

One response to such invidious comparisons between what Wittgenstein's philosophy has to offer, and what most of the rest of philosophy claims to provide is to turn one's attention away from attractiveness, toward the uncosmetic question of truth. If Wittgenstein's views as to the nature of philosophy are true, then no matter whether anyone is attracted to them. And no matter whether the philosopher operates at the intellectual level of a plumber, whom one calls in to fix one's problem, and then sees no more of. At least, following this metaphor, philosophy would be an honest job, which someone has to do.

This is one response to the charge that Wittgenstein's view of philosophy is self-deprecating and self-destructive. But it is, I believe, inap-


256 C. GRANT LUCKHARDT

propriate. For I believe that another reading of his views is possible -one that emphasizes the depth and importance of philosophy as it ought to be practiced, in contrast to the false profundity promised by so many other philosophers. According to this reading, those passages in his writings that might be read as suggesting that philosophy is either, in the words of recent commentators, 'superficial' or 'trivial,l or 'impotent',2 and as suggesting that Wittgenstein is dismissive and cavalier about its practice, need to be balanced against others that suggest exactly the opposite.

Several passages in the early 100s of the Investigations can be, and have been, read to imply the former sort of view. In the following section of this paper, I turn to those passages in an attempt to make the strongest case for this view. Many of these passages have the same manuscript source, however, and so I propose in the second part of this paper to look closely at that source, as well as some of the surrounding passages in the Investigations, to get a fuller and different picture of his views about philosophy. Indeed, the manuscript to which I shall refer is entitled 'Philosophy'. It is one of some nineteen 'chapters' of the 'Big Typescript', which Wittgenstein compiled in 1932-33 from manuscripts he wrote between 1930 and 1932. That is to say, virtually immediately upon his return to philosophy in 1929, Wittgenstein began to write about the nature of philosophy itself - both as it is traditionally conceived, and as he thought it ought to be practiced. Within four years, this material was molded into a complete chapter of the massive typescript that he produced. Although he was never satisfied enough with this typescript to have it published, Wittgenstein continued to return to it and to draw remarks from in his later writings. Indeed, selected remarks from two large sections of it appear virtually verbatim in the final post-war version of the Investigations. One of these sections is the chapter entitled 'Philosophy', several remarks from which appear in the early lOOs. It is the remainder of these remarks - those that appear in the typescript but not in the Investigations - that I shall be concerned with here, for many of them provide a significant context for the remarks that made it into the Investigations. It is not that these published remarks argue clearly for the view of philosophy as trivial and impotent; surely many members of two generations of interpreters have not read Wittgenstein this way. Rather, what I shall argue is that placed back in their original context, and supplemented by other remarks there, it is simply impossible to construe Wittgenstein as dispar-

PHILOSOPHY IN THE BIG TYPESCRIPT 257

aging the importance either of traditional philosophy or of the new 'method' of philosophy he claimed to have found.

I should say that I am aware of a double risk in arguing this way. First, Wittgenstein was patently dissatisfied with the 'Big Typescript', to the extent that he did not want it published. Surely there is a risk in using an early piece of a philosopher's work, which he worked on to change into the later published work, to cast light on the later work, for one is always faced with the question: If he had been satisfied with a sentence or a remark the way it was, why did he change or eliminate it? Second, it is arguable that as a general rule, Wittgenstein's changes were almost always changes for the better. Anyone who has worked with the manuscript and typescript sources cannot fail to notice that when he went back to them, his changes almost always read better, and usually one can appreciate exactly why he made them. (In the case of typescripts, with which we are dealing here, the principle is even more universal. As the typist was typing the original material, Wittgenstein would enclose possible corrections next to it in sets of double slashes. The words and phrases between slashes are usually so evidently better that one wonders why he even bothered to have the original versions typed.) So one who probes into the early versions of material which was culled through, changed, and added to to produce the Investigations faces the twin difficulties that Wittgenstein preferred the later versions, and the changes in them are arguably better.

Nevertheless, I believe there is much of value in the 'Big Typescript', and other material from the early 1930s. Some commentators have made much of the differences between this material and the 'later' philosophy, and so the term 'middle period' has been coined to designate not just a chronological, but a distinct philosophical period of Wittgenstein's life. With a few exceptions, however, what strikes me as noteworthy about the 'Big Typescript' is not its differences from the later period, but its striking similarities and overlap. And in particular, it is noteworthy that the conception of philosophy he had developed by 1933 was not essentially changed, or added to, in the post-war Investigations. Rather, the by now famous remarks about philosophy in the early 100s are for the most part verbatim excerpts from the 1933 'Big Typescript'. It remains to be shown that the truncated version is the one that allows for the interpretation that Wittgenstein is dismissive toward past and future philosophy, and that the earlier more complete treatment suggests something quite different.


PHILOSOPHY IN THE INVESTIGA TIONS

In considering Wittgenstein's views on philosophy, three questions need to be distinguished: (1) What did he think of the status and importance of the claims of traditional philosophy?; (2) What did he think of the status and importance of Wittgensteinian critical philosophy (i.e., philosophy that is critical of (1))?; and (3) What, if anything, did he think there was left for philosophy to do once itl has shown the claims of traditional philosophy to be either false or confused or meaningless? Certain passages in the Investigations can be read as (1) denigrating the importance of the claims of traditional philosophy, (2) denigrating the importance of the Wittgensteinian enterprise itself, and (3) implying that effective criticism puts an end to the philosophical enterprise.

If one were to make the case that Wittgenstein is contemptuous of the status and importance of traditional philosophy, there would be perhaps no better place to begin than with Investigations 118. There he asks whence his investigation (lit.: 'the observation') derives its importance, since "it seems only to destroy everything interesting, that is, all that is great and important? (As it were all the buildings, leaving behind only bits of stone and rubble.)" The answer he gives does not deny that his philosophy destroys; rather, it denies the importance of the object of his destruction, claiming that it is much less significant than one might have thought. "What we are destroying", he says, "is nothing but buildings in the air" (Luftgebaude). The clear implication is that whereas the results of traditional philosophy are taken by those who formulate them to be far-reaching and important, they are in fact insignificant - mere human constructions that are not well-grounded. In destroying them we are not destroying anything, much less all, that is great and important. The claims of traditional philosophy are not important at all, according to this interpretation.

The very next remark in the Investigations seems to bear this out, for it characterizes the objects of philosophical criticism as pieces of 'plain nonsense', and as 'bumps' on the head of understanding. The metaphor hardly suggests something to be taken seriously - no serious malady, which could threaten someone's life or well-being, but merely a bump on the head, which might in time go away on its own, without the help of a diagnostician or surgeon or therapist. Concern over these bumps seems out of place. Further, what critical philosophy reveals is not just nonsense, but plain (schlichten) nonsense - nonsense that again one would be foolish to take seriously, and that one might well be


embarrassed for ever having been duped by. The philosopher who uncovers it, like the lover of Forms who descends to the cave, must find it tedious and boring, not to say unpleasant, having to spend his or her time dealing with such foolishness. After all, it is with people whose stupidity rivals that of flies that one is dealing (Philosophical Investigations 309; hereafter, PI), and showing them the way out of their difficulties can hardly be more intellectually stimu~ating than pointing out to the pitiful souls in the cave that they are only watching a puppet-show. Thus it is that both the objects of philosophical criticism, viz., the claims of traditional philosophy, as well as the advocates of the claims, seem to be regarded by Wittgenstein not simply with scorn, but with an attitude approaching contempt. And given this attitude, it is easy to appreciate why the conceits of philosophy and philosophers must be dashed utterly to the ground.

There would appear to be a problem with this view of philosophy. For if traditional philosophy is totally valueless, then Wittgenstein's original question remains - What does make our investigation important, if all we are doing is destroying buildings in the air? There seems here to be a double edge to Wittgenstein's sword: If what he is destroying were important, then the question would be, why do you want to destroy it? Isn't change, or reform, called for, rather than destruction? On the other hand, if the object of destruction is not important, then why bother with it? Housewreckers who go after pasteboard shacks can hardly be said to have earned a day's wages. At least those who tear down real buildings earn their pay. That is to say, the activity of Wittgenstein's own critical philosophy seems to be called into question. 'What makes our investigation important?' appears not so much as a rhetorical question, but an unanswered one, or one whose answer is - 'Nothing'. This self-denigration can be read as extending beyond the point made above, because, on the one hand, Wittgensteinian critical philosophy (hereafter, 'critical philosophy') appears to be a simple matter requiring little effort, and on the other, one that is best done quickly, and then abandoned. That is to say, critical philosophy appears not only to criticize nothing worth criticizing, but also to require little effort, and to have nothing left to do once it has completed its simple but worthless task.

Professor Anscombe's translation of Luftgebaude seems to amplify the impression that critical philosophy is easily done. Houses of cards are virtually self-destructive, requiring only one more card, or a breeze, or a flick of one's finger to bring them down. And even a more literal


translation suggests that critical philosophy is easy. It isn't clear how one dismantles buildings in the air, but surely, it appears, doing so can't require much effort. Russell's view that Wittgensteinian critical philosophy has 'lazy consequences' and that it renders philosophy as "at best, a slight help to lexicographers, and at worst, an idle tea-table amusement,,3 might seem borne out as well by the last phrase of 118. Not only do we destroy buildings in the air, but, we then "clear up the ground of language on which they stand". At least in this passage, Wittgenstein gives no reason for clearing the ground. Is the idea that one is preparing it for future buildings, or does the need to do so arise merely out of aesthetic fussiness? And although the next remark does state that the bumps on the head of understanding "make us see the value of the discovery", the fact that they are merely bumps surely vitiates the value of the discovery. In 119, in fact, it is apparently not even necessary to treat or remove the bumps. The philosopher merely uncovers them. Presumably they'll go away on their own. PI 309, which I have already mentioned, also seems to bear out the point about the ease with which critical philosophy is done, but perhaps even to add an additional flavor of intellectual superiority. The fly, stupid as it is, or victim of the perspective it has, cannot realize the simplicity of the solution to its difficulty. We, on the other hand, see clearly and easily how simple it is to resolve its predicament. Just retrace your steps, and you're free! The solution is obvious to one who sees it, and easy to follow for one to whom it is shown.

Parts of PI 124 and 126 may very well seem to sustain this interpretation. Remark 124 says that philosophy cannot interfere with the use of language, that it cannot ground it, and that it leaves everything as it is. Remark 126 says: "Philosophy simply puts everything before us, and neither explains nor deduces anything. -Since everything lies open to view there is nothing to explain". It is easy to conclude from this that there is little work for the critical philosopher to do. Nothing is to be changed, or justified, or explained; the status quo is apparently to be maintained, and one needs simply to reiterate it: "The work of the philosopher consists in assembling reminders for a particular purpose" (127). The proper work of the critical philosopher is to remind, not to create, which is to say, nothing new will come out of his work. Indeed, if something new came out of it, it wouldn't be philosophical, since 'philosophy' names "what is possible before all new discoveries" (126).

Parts of the Investigations seem to suggest that criticism is all there


is to Wittgensteinian philosophy. Since it is wholly a meta-discipline, there would be nothing for it to criticize were it not for the errors and confusions of traditional metaphysicians. And once it has done that, it will vanish. Among other passages, Wittgenstein's famous remark that the real discovery is "the one that makes me capable of stopping doing philosophy when I want to" (PI 133) strongly suggests that the goal of philosophy is to quit doing it. Similarly, once the philosopher has shown the fly the way out of the bottle, it can fly on. But the philosopher's work is done. Having achieved his goal (Ziel), he has nowhere else to go, and nothing else to do. Indeed, Wittgenstein's use of words such as 'goal', 'aim' and 'result' in the Investigations may also suggest that the goal of philosophy is simply to put an end to it. The clarity we are aiming at (anstreben), he says in 133, means that "philosophical problems should completely disappear", and it is the uncovering of plain nonsense and the bumps on the head of understanding that are the 'results' (Ergebnisse) of philosophy.

In summary, according to the interpretation I have been outlining it is difficult to imagine how any thinker who set out to reform his discipline could set his sights any lower, or render his discipline any more insignificant. As a potential job description, this prescription for philosophy surely would be the last to be funded by any organization or agency, for the limited scope of what it can do, the unimportance of what it does, the wholly negative results it reaches, and the ease with which it can be done seem to render it trivial. Following this interpretation, David Pole's question - why not just have philosophers take a drug that would cause them to lose interest in philosophy - is well-taken.

PHILOSOPHY AS IMPORTANT

Parts of the Investigations can be read, as we have seen, as lending some support to the idea that the problems of traditional philosophy are trivial. On the other hand, there are passages, such as remark 111, that speak against this reading: "The problems arising through a misinterpretation of our forms of language have the character of depth. They are deep disquietudes; their roots are as deep in us as the importance of language." It is this latter kind of point - that the problems of philosophy are anything but trivial - that is emphasized in the 'Big Typescript' (hereafter 'BT'4) , and so it is to this typescript we must


turn if we are to find a way of reconciling remarks such as those about Luftgebaude with those that describe philosophical problems as having depth. The 'BT' contains, I believe, all important distinction that allows us to see how, in one sense of the word, traditional philosophical problems are not deep, but how, in another sense, they are. The first half of the Luftgebaude remark - the part that asks where our investigation gets its importance from, since it s,eems to destroy everything that is great and important - occurs in the 'BT', but the second half, which says that all we are destroying are buildings in the air, does not. The remark that immediately precedes it, however, helps to explain the sense in which what we are destroying is taken to be great. It reads:

(Questions of different kinds occupy us, for instance 'What is the specific weight of this body', 'Will the weather stay nice today', 'Who will come through the door next', etc. But among our questions there are those of a special kind. Here we have a different experience. The questions seem to be more fundamental than the others. And now I say: if we have this experience, then we have arrived at the limits of language.)5

I understand this to say ~hat the sense ('experience') that there are ordinary questions, on the one hand, and fundamental ones, on the other, is itself an illusion. To attempt to make the distinction is to begin to transcend the bounds of the sensible. Earlier in the 'BT' Wittgenstein also rejects this distinction between the fundamental and the accidental. This time it is with regard to philosophical problems. 'Roughly speaking', he says,

according to the old conception - for instance that of the (great) western philosophers - there have been two kinds of problems in fields of knowledge: essential, great, universal, and inessential, quasi-accidental problems. And against this stands our conception, that there is no such thing as a g rea t, essential problem in the sense of 'problem' in the field of knowledge. 6

In denying the distinction between great and fundamental and important problems versus the inessential and accidental ones, Wittgenstein is denying the very distinction that would allow one to say that he regards philosophical problems as trivial. 'Trivial' must stand in contrast to 'non-trivial', or 'important', but Wittgenstein's point is that there are simply problems and questions, about which no distinction in terms of depth can be made. Hence to say that the philosophical problems he is destroying are not important, etc., is not the same as saying that they are unimportant or trivial. It is simply to say that they are on a par with all others.


To deny the distinction between essential and inessential problems is not to say that traditional philosophical problems may not be deep in another sense, and indeed the 'BT' contains many references to profundity and depth. What is being referred to, however, is not their own depth, but the depth of the unease and discomfort they create. "The effect of a false analogy taken up into language", he says, is "a constant battle and uneasiness (as it were, a constant stimulus)".7 Elsewhere he refers to the 'irritating' character of grammatical unclarity,8 of problems as "intangibly weigh(ing) down our consciousness" ,9

of the 'uneasiness and confusion' they create,lO of solutions to the problems "calm(ing) us after we have been so profoundly uneasy", 11

of that "particular peace of mind that occurs"12 when they are solved, of the philosopher as "exaggerat(ing), shout(ing), as it were in his helplessness",13 of a false picture lying "at the bottom of our feeling of helplessness", 14 of the "conflict in which we constantly find ourselves",15 and of the 'turbulence' of philosophical conjectures and explanations. 16 All of these expressions give a very different picture, I suggest, than that given by talk of bumps on the head. The problems of philosophy, one might say, are deep ones of the soul, not superficial ones of the body.

In presenting my devil's advocate interpretation of the Investigations, I presented the problems of philosophy as occurring in others, but as recognized and solved by the Wittgensteinian critical philosopher. But according to much in the 'BT', this view is incorrect, in two different ways. First, as we have just seen, the problems of philosophy are pictured by Wittgenstein as being problematical for the very person who falls into the traps that language sets. It is not that the Wittgensteinian philosopher has to produce the unease, discomfort, and feeling of helplessness for the traditional philosopher; rather he is portrayed as already experiencing it, and crying out for help. The unease of traditional philosophy is the unease of the traditional philosopher, and the Wittgensteinian philosopher is not there to make trouble, but to confront it.

But even this way of putting things tends to distort, according to much of the 'BT', for it tends to suggest that there is a difference of person between the traditional philosopher and the critical philosopher. But it is important to recognize that in the 'BT', the philosopher who is bewitched and befuddled by grammatical errors is often, if not usually, the same person as the philosopher who must discover his own


solution to his problem. It is, after all, our consciousness that is weighed down, our feeling of helplessness, our conflict that we find ourselves in, and we who are so profoundly uneasy. In a manuscript from the early 1930s Wittgenstein had written: "Philosophy is an instrument whose only use is against philosophers and against the philosophers in US".17 And in the 'BT' he says: "Work on philosophy is - as work in architecture frequently is - actually more of a kipd of work on oneself. On one's own conception. On the way one sees things. (And what one demands of them.),,18 The metaphor of the fly and fly-bottle in the Investigations can make it appear otherwise - as if it were a matter of us and them. We see the way out for those confused souls who have been so stupid as to fall into the traps of language. But at least in the early thirties, Wittgenstein saw himself and his readers as all falling into those same traps. "Language contains the same traps for everyone" ,19 he says in the 'BT', and it is clear that he thinks the author of the Tractatus continues to be as vulnerable to them now as ever.

Since those who discover the way out of philosophical difficulties are the same as those who got themselves in in the first place, it follows that those who fall into them can be no more stupid than those who discover the way out. In the 'BT' Wittgenstein emphasizes that philosophical problems arise not from stupidity, or by mistake. His idea, rather, is that the traps that language sets for us are among the easiest of all for humans to fall into. In PI 109 Wittgenstein speaks of the 'urge to misunderstand' the workings of our language, and in the 'BT' he speaks of the 'inclination' (Neigung)2o people have to think exactly the way they do, and thus to become "deeply imbedded in philosophical, i.e., grammatical confusions". 21 Furthermore, he remarks how easily all of us are 'seduced' by language. It is this very feature of language, he says, that explains Kant's scandal:

One keeps hearing the remark that philosophy really makes no progress, that the same philosophical problems that had occupied the Greeks are still occupying us. But those who say that don't understand the reason it must be so. The reason is that our language has remained the same and it seduces us into asking the same questions over and over. As long as there is a verb 'to be' which seems to function like 'to eat' and 'to drink', as long as there are adjectives like 'identical', 'true', 'false', 'possible', as long as one talks about a flow of time and an expanse of space, etc., etc., humans will continue to bump up against the same mysterious difficulties, and stare at something that no explanation seems able to remove. 22

Elsewhere he asks why grammatical problems are so tough and seem-


ingly ineradicable. His answer is that this is because "they are connected with the oldest thought habits, i.e., with the oldest images that are engraved into our language itself (Lichtenberg)". 23 These old images are retained and preserved in our current linguistic practices, such that language contains an "immense network of well-kept false paths" .24 Not to tread where so many others have gone before is the difficult thing, which is to say, what is to be expected is that we "following all of (our) instincts (will) live within the herd that has created this language as its proper expression". 25 As with Plato, there is in Wittgenstein a strong linkage between the masses, custom, and error. And because of this linkage, there can be no question of triviality. What runs deep in us all, what is instinctive, what is contained in our history and above all in our language, may bring us into error, but cannot be taken lightly.

Again, as with Plato, what one faces when one reckons with philosophical error is not simply an intellectual problem. According to Wittgenstein, these errors are involved with the will. The difficulty of philosophy, he says, is "not the intellectual difficulty of the sciences, but the difficulty of a change of attitude. Resistances of the will must be overcome".26 It is that they are so deeply felt that makes them so difficult to solve, and so the task of the philosopher who wishes to solve them, either in himself or in others, is by no means easy. The depth of the commitment to errors is tracked by the deep difficulty in solving them. Wittgenstein sees the philosopher who wants to stand against the desires of the herd - as standing against all temptation and inclination - as standing against what is most natural, both in himself as well as others. In two passages at the beginning of the section of the 'BT' labelled 'Philosophy', Wittgenstein compares the difficulty of correcting philosophical error with that of correcting error in science:

As I have often said, philosophy does not lead me to any renunciation, since I do not abstain from saying something, but rather abandon a certain combination of words as senseless. In another sense, however, philosophy requires a resignation, but one of feeling and not of intellect. And maybe that is what makes it so difficult for many. It can be difficult not to use an expression, just as it is difficult to hold back tears, or an outburst of anger.

(Tolstoy: the meaning (meaningfulness) of a subject lies in its being generally understandable. - That is true and false. What makes a subject difficult to understand - if it is significant, important - is not that some special instruction about abstruse things is necessary to understand it. Rather it is the contrast between the understanding of the subject and what most people wan t to sec. Because of this the very things that are most


obvious can become the most difficult to understand. What has to be overcome is not a difficulty of the intellect, but of the will. )27

This latter passage brings out another difference between the solutions to philosophical and scientific problems. Not only does the critical philosopher confront strong desires to see things certain ways, but he faces the paradox that those things that need tp be seen are in some sense the most obvious. "One of the greatest impediments for philosophy", Wittgenstein says, "is the expectation of new, deep / / unheard of / / elucidations". 28 The novel and deep are what is expected of any good philosophical answer to a problem, and so when the familiar and the simple are presented, it must seem that they can't be solutions. And yet it is the familiar and the simple that Wittgenstein calls "the philosophically most important aspects of things".z9 In a remark strongly suggestive of Plato, Wittgenstein says, "Learning philosophy is rea 11 y recollecting. We remember that we really used words in this way".30 Unlike Plato, of course, what we are to recollect is grammar, which we learned when we learned (in this life) to speak.

Wittgenstein gives an example of a familiar rule of grammar to illustrate his claim that "what we do is to bring words back from their metaphysical to the normal use in language": "The person who said that one cannot step into the same river twice said something wrong; one can step into the same river twice". 31 The point can of course be extended beyond Heraclitus to all sorts of theories of identity, and Wittgenstein himself extends it to all of philosophy: "this is what the solution of all philosophical difficulties looks like. Their answers, if they are correct, must be homemade and ordinary". To those who require novel answers, answers such as these will clearly never satisfy, and so it is difficult to convince anyone of them.

Another factor that Wittgenstein speaks of as making the task of philosophical correction anything but easy stems from his belief that philosophical problems involve feeling as much as intellect. Because of this, the philosopher is required not just to point out their errors to those (including himself) who are philosophically confused, but to resolve their uneasiness and deep disquietudes as well. It is not enough, so to speak, to point out that the person has fallen into a trap, for the trap must be removed and the discomfort alleviated. And this means that the person in the trap must acknowledge the solution to his problem as being the correct one. Without acknowledgment the philosopher


may have solved a problem of the intellect, but will not have solved the one involving the will. "One of the most important tasks", Wittgenstein says,

is to express all false thought processes so characteristically that the reader says, "Yes, that's exactly the way I meant it." To make a tracing of the physiognomy of every error.

Indeed we can only convict someone else of a mistake if he acknowledges that this really is the expression of his feeling.

For only if he acknowledges it as such, is it the correct expression. (Psychoanalysis.) What the other person acknowledges is the analogy I am proposing to him as the

source of his thought. 32

The reference here to psychoanalysis brings to mind the talk in the Investigations of philosophy as therapy, but the point made here is one that is not made there - viz., that a doctor's cure is not a cure at all if the patient doesn't respond. A cure that doesn't work, however satisfying it may be to the person who administers it, is simply not a cure, and so the philosopher must be sensitive whether the unease the philosophical difficulty has brought about has been removed - to whether, in Wittgenstein's words, "complete satisfaction comes". 33 This only happens, he says, when "no question remains".

Throughout the 'BT' Wittgenstein suggests several strategies for 'curing' philosophical problems. He offers no discrete list, but the text is studded with suggestions. Often for example, pointing to an analogy that has been followed, but that was either followed too far, or was incorrect to begin with, or that was not recognized as an analogy will bring about a cure:

If I correct a philosophical mistake and say that this is the way it has always been conceived, but this is not the way it is, I always point to an analogy that was followed, and show that this analogy is incorrect. 34

A philosophical cure can also consist, he says, in 'rejecting false arguments,.35 At other times it will suffice to point out that a word has more than one meaning:

The particular peace of mind that occurs when we can place other similar cases next to a case that we thought was unique, occurs again and again in our investigations when we show that a word doesn't have just 0 n e meaning (or just two), but is used in five or six different ways (meanings).36

Other times philosophical therapy requires that we 'establish a rule'. 37

An example of this might occur


if a society came together without clearly written rules, but with a need for them; indeed also with an instinct following which they observed certain rules at their meetings; but this is made difficult by the fact that nothing is clearly expressed about this and no arrangement is made which clarifies the rules. Thus they in fact view one of them as president, but he doesn't sit at the head of the table and has no distinguishing marks, and that makes doing business difficult. Therefore we come along and create a clear order; we seat the president in a clearly identifiable spot, seat his secretary next to him at a little table of his own, and seat the other full members in two rows on both sides of the table, etc. etc. 38 '

The philosophical difficulty with this, Wittgenstein says,

lies only in understanding how establishing a rule helps us. Why it calms us after we have been so profoundly uneasy. Obviously what calms us is that we see a system which (systematically) excludes those structures that have always made us uneasy, those we were unable to do anything with, and which we still thought we had to respect. 39

At other times what is necessary is for the philosopher to discover a single word, what Wittgenstein calls 'the liberating word' (das erlosende Wort).40 This is the kind of word that "finally permits us to grasp what up until then has intangibly weighed down our consciousness". Once found, the philosopher "delivers the word to us with which one / / I / / can express the thing and render it harmless". 41 Once the liberating word is found, Wittgenstein suggests that using it to dispel problems is quite easy. It is finding it that is the hard part. Apropos such words, he compares philosophical problems to locks on safes,

which can be opened·by dialing a certain word or number, so that no force can open the door until just this word has been hit upon, and once it is hit upon any child can open it. 42

Other times what will work to effect a philosophical cure is the familiar "assembling (of) reminders for a particular purpose". An example of this is:

The conflict in which we constantly find ourselves when we undertake logical investigations is like the conflict of two people who have concluded a contract with each other, the last formulations of which are expressed in easily misunderstand able words, whereas the explanations of these formulations explain everything unmistakably. Now one of the two people has a short memory, constantly forgets the explanations, misinterprets the conditions of the contract, and therefore continually runs into difficulties. The other one constantly has to remind him of the explanations in the contract and remove the difficulty.43

Last, but surely not least, Wittgenstein speaks of developing a perspicuous representation. A perspicuous representation "produces just


that comprehension / / understanding / / which consists in 'seeing connections'. Hence the importance of finding intermediate cases. ,,44 Our grammar, which is said to be "lacking in perspicuity", 45 is to be "laid out completely clearly". 46 Such a synoptic view Wittgenstein describes as being "of fundamental significance for us". 47 It 'solves' the philosophical problem which is "an awareness of disorder in our concepts" by "ordering them". 48

All of these techniques and devices of the philosopher are described by Wittgenstein as being of service in the dissolution of philosophical problems - dissolution, he says, "in the actual sense of the word -like a lump of sugar in water" .49 As I have so far presented the case, the problems need to be dissolved because of the unease and discomfort they bring to the person involved in them, whether that is the philosopher himself or another person. But it is important to note that in the 'BT', the value of philosophy is not merely therapeutic. Its importance derives from at least two other factors.

First, philosophy can serve as much a preventive as a critical and corrective role:

Language contains the same traps for everyone; the immense network of well-kept false paths. And thus we see one person after another walking the same paths and we know already where he will make a turn, where he will keep on going straight ahead without noticing the turn, etc. etc. Therefore wherever that false paths branch off I should put up signs which help one get by the dangerous places. 5o

A perspicuous representation in particular would seem to contain such signs. Taking steps to avoid, and allow others to avoid, the misery of philosophical discomfiture in the first place might even be seen as preferable to philosophical therapy. An ounce of prevention, after all

On the other hand, in the 'Philosophy' chapter of the 'BT' Wittgenstein makes some statements that suggest a totally non-utilitarian justification of the value of philosophy. One of the section titles for this chapter reads: "The method of philosophy: the perspicuous representation of grammatical / / linguistic / / facts. The goal: the transparency of arguments. Justice". 51 'Justice' is not a word that Wittgenstein uses often (never in the Investigations), and its striking use in this context suggests that he saw this goal (Ziel - the same word, incidentally, he uses in connection with the fly-bottle) of philosophy as an important one. Indeed, in the text he says "Our only task is to be just. That is,


we must only point out and resolve the injustices of philosophy, and not posit new parties -and creeds".52 I take it that what Wittgenstein regards philosophy as being unjust to,ward is language, and that doing away with those injustices is an end that is desirable in itself. In a manuscript written in late 1930, Wittgenstein says that in our civilization, "even clarity is sought only as a means to (an) end, not as an end in itself. For me on the contrary, clarity! perspicuity are ends in themselves". 53 With the achievement of these ends will come the disappearance of the old parties and creeds - determinism, idealism, solipsism, behaviorism, the picture theory, etc., together with the exaggerations and distortions they contain. ("It is difficult", he says, "not to exaggerate in philosophy". 54) And that this is desirable in itself hardly requires arguing, at least for one who is committed to truth.

NOTES

* I wish to thank Professor Robert Arrington for his comments on an early version of this article. 1 J. F. Findlay, in his recent Wittgenstein: A Critique (London: Routledge and Kegan Paul, 1984), states that Wittgenstein recommends superficiality in philosophy (p. 210), and 'prefers' 'trivialization' (p. 211). 2 O. P. Baker and P. M. S. Hacker, in An Analytical Commentary on Wittgenstein's 'Philosophical Investigations' (Oxford: Basil Blackwell, 1980), express the concern that Section 124 of the Investigations 'might be taken to intimate the impotence of philosophy' (p. 236). 3 Bertrand Russell, My Philosophical Development (New York: Simon and Schuster, 1959), p. 217. 4 All quotations from the 'Philosophy' chapter of the 'Big Typescript' are taken from my translation in Synthese 87, 3-22. 5 'Big Typescript', p. 7. 6 Ibid., p. 5. 7 Ibid., p. 6. 8 Ibid. 9 Ibid. 10 Ibid., p. 9. 11 Ibid., p. 10. 12 Ibid. 13 Ibid., p. 13. 14 Ibid., p. 17. 15 Ibid., p. 15. 16 Ibid., p. 19. 17 L. Wittgenstein, TS. 219, p. 11, quoted with the permission of the executors of Wittgenstein's literary estate.

PHILOSOPHY IN THE BIG TYPESCRIPT

18 'Big Typescript', p. 5. 19 Ibid., p. 15. 20 Ibid. 21 Ibid., p. 14. 22 Ibid., p. 15. 23 Ibid., p. 14. 24 Ibid., p. 15. 25 Ibid. 26 Ibid., p. 5. 27 Ibid. 28 Ibid., p. 12. 29 Ibid. 30 Ibid. 31 Ibid., p. 8. 32 Ibid., p. 7. 33 Ibid., p. 14. 34 Ibid., p. 6. 35 Ibid. 36 Ibid., pp. 1O-1I. 37 Ibid., p. 10. 38 Ibid. 39 Ibid. 40 Ibid., p. 6. 41 Ibid. 42 Ibid., p. 11. 43 Ibid., pp. 15-16. 44 Ibid., p. II. 45 Ibid. 46 Ibid. 47 Ibid. 48 Ibid., p. 13. 49 Ibid., p. 14. 50 Ibid., p. 15. 51 Ibid., p. 9. 52 Ibid., p. 13.

271

53 L. Wittgenstein, Culture and Value, ed. G. H. von Wright, tr. Peter Winch (Chicago: University of Chicago Press, 1980), pp. 6-7. 54 'Big Typescript', p. 13.

REFERENCES

Baker, G. P. and Hacker, P. M. S.: 1980, An Analytical Commentary on Wittgenstein's 'Philosophical Investigations', Basil Blackwell, Oxford.

Findlay, J. F.: 1984, Wittgenstein: A Critique, Routledge and Kegan Paul, London. Russell, Bertrand: 1959, My Philosophical Development, Simon and Schuster, New York. Wittgenstein, Ludwig: (1932-33), TS. 219 of the von Wright catalogue.


Wittgenstein, Ludwig: 1980, Culture and Value, ed. G. H. von Wright, trans. Peter Winch, University of Chicago Press, Chicago.

Wittgenstein, Ludwig: 1991, 'Philosophy: Sections 86-93 of the so-called "Big Typescript"', ed. Heikki Nyman, trans. C. G. Luckhardt and M. A. E. Aue, Synthese 87, 3-22.

Dept. of Philosophy Georgia State University Atlanta, GA 30303-3083 U.S.A.

DAVID PEARS

WITTGENSTEIN'S ACCOUNT OF RULE-FOLLOWING

Wittgenstein's treatment of rule-following in Philosophical Investigations is compelling but enigmatic. It gives people a strong sense of the direction in which it is moving and yet there is no general agreement either about its starting-point or about its destination. The theory on which he turns his back is agreed by all to be Cartesianism, but there are many versions of that picture of the mind, and anyway, much depends on the question which it is taken to be answering. Is the problem the threat of scepticism about constancy of meaning? Or, is it the difficulty of understanding what gives meaning a stability which is not in doubt? Or perhaps, what needs to be explained is the credence generally put in a person's own account of what he means. The divergence between the different views of Wittgenstein's destination is equally striking. Some take his conclusion to be that meaning is fixed solely by agreement in judgements. Others think that he neither sought nor claimed to have found any single criterion of the correct use of language, but treated it as a system with many different ways of maintaining its stability, none of which would serve in sufficiently adverse circumstances.

In this paper no attempt will be made to deal with all these issues. It will contain notes on several aspects of Wittgenstein's treatment of rule-following, but no comprehensive interpretation. It will, however, suggest a general thesis about some of the interpretations of his later philosophy of language which have been put forward by others. Although he offers no theories and confines himself to judicious description, there are two ideas which dominate this part of his work. One is the idea that what at first sight looks like a report is often itself part of the very thing that would have been reported if it had been a case of thing and report. This idea is one of the things that lead people to attribute a particular theory to Wittgenstein. They feel that because he is moving in a single direction, he must end with a single theory.

One aspect of this idea is familiar. If I have told someone to add 2, and later say, "I already knew at the time when I gave the order that he ought to write 1,002 after 1,000," I am not reporting what went


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through my mind at the time; what I mean is something like, "If I had been asked what number should be written after 1,000, I should have replied '1,002,.1 But two more points need to be added to this. First, this conditional is not my hypothesis about what my reply would have been, but a manifestation of the very intention with which, if I am right, I gave the original instruction. Second, some distance out on the same line there are cases where what a person; says later might be a further development rather than a manifestation of something that already existed at the time. There is an intermediate example, halfway to that point, near the end of Part I of Philosophical Investigations:

"You said, 'It'll stop soon.' - Were you thinking of the noise or of your pain?" If he answers "I was thinking of the piano-tuning" - is he observing that the connexion existed, or is he making it by means of these words? - Can't I say both? If what he said was true, didn't the connexion exist - and is he not for all that making one that did not exist?2

The idea - that what looks at first sight like a report is often itself part of the very thing that would have been reported if it had been a case of thing and report - is obviously a strong antidote to Cartesianism. What is not so obvious is that it is closely connected with a second leading idea in Wittgenstein's later writings. That is the idea that what looks like a description of a sensation is often (but not always) a form of words substituted early in the speaker's life for the natural expression of the sensation which would have been described if it had been a case of thing and description. This is, of course, a different idea and it produces a different result when it is applied to intentions: the natural manifestation of an intention is appropriate action, and so, if at first sight it is surprising that we have non-inferential knowledge through our intentions of our own futures, it becomes less surprising when we realise that the tendency to use the right words in advance is an offshoot of the tendency to do the right thing later. But though this is a different idea, it is connected with the first idea and reinforces it by showing how, in certain cases, language is grafted onto pre-existing patterns of behaviour. The two ideas operating together make a powerful combination, and they give Wittgenstein's later philosophy of language a unity which is easily mistaken for the unity imposed by a single theory.

It is often instructive to go back to an earlier stage in the development of his philosophy and to look for the first emergence of a problem, or even earlier, for the ideas in which it was lying latent. In the Tractatus the theory of names leaves many questions unanswered but it is explicit

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on two points: the naming of objects is a rule-governed activity, but the rules can never be stated but only shown by the actual application of the names. This is not presented as an unfortunate consequence of the picture theory, an unsolved problem to be cleared up later, but as the central point of the early semantics:

There is a general rule by means of which the musician can obtain the symphony from the score, and which makes it possible to derive the symphony from the groove on the gramophone record, and, using the first rule, to derive the score again. That is what constitutes the inner similarity between these things which seem to be constructed in such entirely different ways. And that rule is the law of projection which projects the symphony into the language of musical notation. It is the rule for translating this language into the language of gramophone records.

The possibility of all imagery, of all our pictorial modes of expression is contained in the logic of depiction. 3

However, the inner similarity or shared form is not something which can be represented in the same way:

Propositions can represent the whole of reality, but they cannot represent what they must have in common with reality in order to be able to represent it.

In order to be able to represent logical form, we should have to be able to station ourselves with propositions somewhere outside logic, that is to say outside the world. 4

This is not mystery-mongering. The point is that the best that anyone could do if he were asked to state the rule linking a name to its object would be to say" 'a' must be used as the name of a". But though this gestures in the direction of a rule, it does not specify it. That would be impossible. The only way to convey the rule to someone else would be to show him what it is by applying the name to the object:

What signs fail to express, their application shows. What signs slur over, their application says clearly.

The meanings of primitive signs can be explained by means of elucidations. Elucidations are propositions that contain the primitive signs. So they can only be understood if the meanings of those signs are already known. s

This should be compared with §201 of Philosophical Investigations:

What this shows is that there is a way of grasping a rule which is not an interpretation, but which is exhibited in what we call "obeying the rule" and "going against it" in actual cases.6

The point is put very clearly in the lectures that Wittgenstein gave in

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Cambridge in 1930-32. He is explaining the leading ideas of the Tractatus and the example that he uses is a sentence expressing an expectation:

"Whatever necessary conditions I lay down for the fulfilment of an expectation must be added into the expression of the expectation ....

What expression and fulfilment have in common is shown by the use of the same expression to describe both what we expect and its fulfilment .... This common element in expectation and fulfilment cannot be described or expressed in any proposition ....

What is "in common" between thought and reality must already be expressed in the expression of the thought. You cannot express it in a further proposition and it would be misleading to try". 7

Here as in the Tractatus what is "in common" is the form which is shared by thought and state of affairs given the rules for the use of the words used in the expression of the thought.

In philosophy it often happens - perhaps more often than in other disciplines - that a change in the point of view from which a phenomenon is described makes a problem out of something which had previously seemed unproblematical. In his early theory of language, Wittgenstein took the standpoint of logical analysis and asked how words derive their meanings from things. If complex words derived, or at least, could derive their meanings through simple words, the essential links with the world would be revealed most clearly in the case of simple words which had no intermediaries. It did not seem to be a problem that the rules for the use of simple words could not be stated, or that the rules for the use of complex words relied on those unstatable rules. On the contrary, there would have been a problem if analysis had not terminated in this way.

Later, when Wittgenstein took the standpoint of the philosophy of mind and asked what we are really doing when we apply words to things, the very thing that had seemed unproblematical became the central problem. If the content of a rule can only be shown by someone following it, is there any real difference between a speaker following a rule and a rule following a speaker? Why not say that the so-called "rule" is receiving progressive, but always incomplete, specification from what the speaker does? There is a description of an interesting case halfway between these two points in the long discussion of rulefollowing in Philosophical Investigations:

Imagine someone using a line as a rule in the following way: he holds a pair of compasses,


and carries one of its points along the line that is the 'rule', while the other one draws the line that follows the rule. And while he moves along the ruling line he alters the opening of the compasses apparently with great precision, looking at the rule the whole time as if it determined what he did. And watching him we see no kind of regularity in this opening and shutting of the compasses. We cannot learn his way of following the line from it. Here perhaps one really would say: "The original seems to intimate to him which way he is to go. But it is not a rule".8

The next case out on this line would be the case of pu~e improvisation. But before the search for the positive content of Wittgenstein's dis

cussion of rule-following can be started, something needs to be said about its negative aspect. What exactly is the theory that he is rejecting?

The Blue Book gives a typical example of the rejected theory. A philosopher claims that, when we hear the word "yellow", we understand it because we get images of the colour. This primitive explanation of understanding the meaning of a general word would work only if each of us could always derive from his image all the correct applications of the word. But the ability to do that is an instance of the very thing that needed to be explained and, therefore, cannot provide its explanation.9 Here it is worth noting that what has to be explained is our correct understanding of the word and not our knowledge of the way in which we take it, correctly or incorrectly, although, of course, the second of these two achievements is contained in the first one. Similarly, the longer and more detailed treatment of rule-following in Philosophical Investigations is an investigation of following a rule correctly, both when the rule is one that governs the use of a descriptive word and when it is one that governs the development of a mathematical series. This is enough to show that these discussions are not powered solely, or even mainly, by interest in the question, "Why do we allow so much authority to the rule-follower's own account of what he is doing?" They are focussed onto the correctness of his performance and the criteria for its correctness.

If someone understands the meaning of the word "yellow", he will be able to pick yellow objects from a variously coloured set. If he understands an algebraic formula, he will be able to write down the series that it generates. Both these performances involve a direction of fit which is the opposite of that involved in the description of an object. So they seem to offer no foothold for Wittgenstein's idea that what at first sight looks like the description of an inner thing may itself be part of the very thing that would have been described if it had been a case

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of thing and description. However, the idea can be stretched to cover this kind of example: an outward performance, which looks at first sight as if it must be derived from an inner model, is really a direct manifestation of the very same ability that would have been required for the production of the right inner model.

The emphasis on mental pictures both in the Blue Book and in Philosophical Investigations lO may seem to take the discussion away from the philosophy of language down a disused side-track. True, Russell had tried to revamp the old idea that images are the real bearers of meanings,l1 but what made images a prime target for Wittgenstein's attack was that they seemed to approximate most closely to what his opponents wanted - "a picture the intention of which cannot be questioned, that is, a picture which we don't interpret in order to understand it, but which we understand without interpreting it". 12 Or, to put their ideal in another way, "the meaning mustn't be capable of interpretation. It is the last interpretation". 13

It is often assumed that this ideal had inspired Wittgenstein's own earlier treatment of sentences as pictures, but that is less than a halftruth. He never took images to be the real bearers of meanings. What he did was to generalise the concept of a picture so that it included sentences. However, it is true that he treated the sense of a sentence as a perfect shadow of the state of affairs that would verify it, a shadow which could actually be seen in the sentence. 14 Or putting it the other way round, even if a sentence could not be given a further interpretation, it could always show its sense immediately to anyone who had grasped the rules for its useY However, it was only later that he realised that this put all the weight on the distinction between random and rule-governed vocalisation.

His criticism of the attempt to base meaning on images is only part of an argument with a much wider scope: neither images nor analytical formulae, nor anything else that might occur in the mind of a person who understood the meaning of a word could possibly determine, by itself, the correct use of the word. The net is cast even more widely to include other kinds of mental event. Someone who is trying to grasp the meaning of an unfamiliar word may suddenly feel that he has got it. Russell regarded this as the achievement of acquaintance with a universal. 16 Wittgenstein, naturally, acknowledges the phenomenon but points out that these flashes of understanding cannot anticipate all the correct uses of the word. Nothing can completely prefigure practice. 17


The positive content of his account of rule-following is more difficult to identify. If we do not, and could not, derive the correct uses of words from images or from any other key that might occur in our minds, what does ensure that we use them correctly? Presumably, each person has to use the vocabulary in the same way throughout his speaking life, and if language is to be a means of communication, in the same way as everyone else. But what is this using; of words in the same way? His early theory of language had tied identity of meaning to the identity of the unstatable rules which were supposed to link words to things. So in his later philosophy of language he faced the daunting task of explaining the criteria of identity of linguistic rules. The question "What ensures that we use our vocabulary correctly?" means "What tells us for sure that we are in that happy position?"

It is worth observing that there is another interpretation of the question, which is recessive in his later writings. It could mean, "What brings; it about that we use our vocabulary correctly?" The question, taken in this way, is recessive, because he habitually avoids inquiries which would take him across the border from philosophy into science. However, it is not entirely absent, because at several points in his later work there are brief expressions of the idea that language is grafted onto pre-existing patterns of behaviour. In Lectures on the Foundations of Mathematics he points out that human beings find it natural to continue certain segments of open-ended series in the same way, and that this is a fact of the greatest importance for the philosophy of language. 1s These natural tendencies are pre-linguistic and they can be observed in the most primitive sorting of objects.

Near the beginning of this paper it was suggested that commentators often show a tendency to look for a single theory in Wittgenstein's later philosophy of language when no such theory is there to be found. Several explanations of this tendency were offered, and another one can now be added. When people read his elaborate answer to the first version of the question, "What is the criterion of sameness of rule?", their understanding of it may be influenced by what he might have allowed himself to say in a full answer to the second version of it. The shadow of a possible unifying scientific theory is cast on the actual investigation of the criterion of identity and perhaps makes them see in it a unity which is not really there.

But is it true that the investigation does not lead to the discovery of any single criterion of identity of rule? Perhaps two people who agree

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in their applications of a word must be following the same rule. True, agreement in judgements for any period of time might be followed by divergence later. But that would still allow us to attribute to Wittgenstein the view that this is our only criterion, and that, even if it never gives us a decisive positive answer, it progressively approximates to that result by testing for divergence in more and more cases. However, he only says that if language is to be a me;ans of communication, there must be agreement in judgements,19 and he avoids committing himself to the theory that this is the only resource available to someone using a descriptive vocabulary. It is, therefore, reasonable to infer that he deliberately allowed for the possibility of a solitary language-user who would treat the truth of his predictions about his environment as a criterion of the regularity of his usage. 20 In fact, it would be plausible to maintain that the fulfilment of this criterion is taken for granted when the other one, agreement in judgements, is used.

If this pluralistic treatment of criteria of sameness of rule seems no great advance on the earlier theory, that rules can only be shown in practice, it is worth asking what kind of advance might reasonably have been expected. Wittgenstein describes rule-following very fully, deals with teaching, both successful and unsuccessful, contrasts the practice with other related but different practices, like waiting for inspiration, and examines the phenomenology in order to discover what it feels like to follow a rule. If he fails to give a single decisive criterion of sameness of rule, that maybe because the concept is more like an idea of reason, to which the use of language approximates by eliminating divergences without any finality. It would not be surprising if his move from semantics to the philosophy of mind led to a holistic application of his originally atomistic concept of showing.

I shall end this paper with a note on immunity from mistake. As already explained, grasping the meaning of a descriptive word does not, in general, involve immunity from mistakes in the use of it. It is only certain inward-looking performances which exhibit this immunity, and the most important one for rule-following is expressing an intention. A learner may try, but fail to follow a rule correctly, but he cannot try, but fail to express the intention which he mistakenly believed that the rule required him to form.21 To put the point in another way, we bow to the authority of his sincere expression of his intention in a case like this, and take sincerity to entail truth. One aspect of this important doctrine has already been mentioned. If we ask what makes it possible


for a person to express his intention without any possibility of error, the answer is not that he turns his attention inwards, considers it and finds the correct description of it obvious?2 It is, rather, that his expression of it is a manifestation of the same tendency that will later produce the intended compliance with the rule. That, of course, is an answer to a question on the borderline between philosophy and science, like the observation that the use of the word "pain" is grafted onto the natural expression of pain. The special feature of the use of the word "intention" is that it is grafted onto a tendency to do something later and it refers to that later performance. But though it is a more complicated case than "pain", it has the same general structure: language is based on an established pattern of pre-linguistic events.

However, Wittgenstein, as already remarked, does not pursue this line of inquiry. His concern is with the other question, "What are the criteria for ascribing intentions?" This is connected with the question of immunity from mistake in the following way: if it really were possible for a rule-follower's sincere expression of his intention to be mistaken, that could only be because what he said might turn out to be false by some independent criterion. If no such independent criterion can be found, sincerity will entail truth.

This is the principle that powers the Private Language Argument. If a philosopher suggests that his pain may be unlike other people's pain in spite of the fact that he and they have been taught the use of the word "pain" in the usual way, so that their reports of their own pains are equally authoritative, then he must be supposing that there is another criterion for this type of sensation, independent of all the ordinary criteria. So we can challenge him to produce it. The application of the principle is very clear in this case: if a mistake of the kind suggested really were possible, then there must be some new criterion, independent of all the ordinary criteria, which would show when such a mistake had been made. But no such criterion can be found, and without it, the suggestion collapses.

But the application of the principle is much less clear when the independent criterion required for the possibility of a mistake is not a new criterion, independent of all the ordinary criteria, but an ordinary criterion which is independent of the resources used by the person himself. It is, for example, arguable that people can make mistakes about their own intentions when they are more complex and more emotionally charged than the intention to follow a rule in a certain

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way, but in a problematical case it is not easy to judge the independence of the criterion that would be used to establish that such a mistake had actually been made. If someone does not carry out a project about which he might well have had inhibitions, when would this behavioural criterion be sufficiently independent of resources available to him in advance, so that his original expression of his intention could be regarded as mistaken rather than insincere?

There is no easy answer to this question, but the difficulty is underestimated in many discussions of immunity from error. There seem to be two reasons for the underestimate. One is that in the limiting case of immunity from error the problem does not arise. If I feel a pain, it is mine, and even someone who believed that I might conceivably be mistaken about the type of the sensation could hardly claim that I might have mistaken the sufferer for myself.23 I do not turn my attention inwards in order to find out whether the affected subject is my ego or someone else's. I do not even choose the mouth which uses the word "I". In fact, nothing would be lost if this word were omitted from my report and I merely said "There is pain here". For this is a case where the grafting of language onto the pre-established sequence of events adds nothing significant to it. If I could choose the mouth that spoke, I would have a new way of faking, but I still could not make a mistake about my ownership, unless there were some more radical change in the way in which my sensations came to me. Wittgenstein, as usual, avoids the scientific question, "How do we come to speak a language with this particular immunity from error?", and merely asks what I would say in circumstances strange enough to put a strain on the language, but not so far out that they would make it unusable. His treatment of the self-ascription of sensations is an extreme application of the idea that what looks at first sight like a report of a thing - in this case, the relation of ownership - is really an exemplification of it.

However, this is the limiting case of immunity from error, and when we take up the question of a sensation's type, we find a very different situation. If I cannot be mistaken about certain types of sensation, when I have them, it is certainly not for this reason. But the existence of the limiting case may well have led people to underestimate the complexity and difficulty of the problem in the central cases.

The other factor which has contributed to this underestimation is the failure to appreciate the difference between claiming that a person may make a mistake about his own intention and claiming that one person's


pain might be quite different from another's in spite of the fulfilment of all the ordinary criteria of identity in both cases. The first of these two claims, unlike the second, does not require a new criterion of identity, independent of all the ordinary criteria. But this crucial difference is easily overlooked, especially if the disputants use the customary Wittgensteinian shorthand and discuss the question whether sensations can, or cannot, be treated like objects, and steer the disqussion towards cases where they are expressed rather than described.

1 Philosophical Investigations, I, §187. 2 Ibid., I, §682.

NOTES

3 Tractatus Logico-Philosophicus, 4.0141-4.015. 4 Ibid., 4.12. Cf. letter to Russell 19 August 1919, para. 5, (Notebooks 1914-1916, p. 130). , 5 Ibid., 3.262-63. 6 Philosophical Investigations, I, §201. 7 Wittgenstein's Lectures, Cambridge, 1930-32, pp. 35-36. 8 Philosophical Investigations, I, §237. 9 The Blue and Brown Books, pp. 11-12. 10 Philosophical Investigations, I, §§139-41. 11 Russell: 1956, 'On Propositions', in Essays in Logic & Knowledge, ed. R. C. Marsh, London: the article was written in 1919. 12 The Blue and Brown Books, p. 36. 13 Ibid., p. 34. 14 Ibid., pp. 35-36. 15 Tractatus Logico-Philosophicus, 4.023. 16 Russell: 1912, The Problems of Philosophy, WiIIiams and Worgate, London, Ch. V. 17 Philosophical Investigations, I, §§195-97. 18 Wittgenstein: Lectures on the Foundations of Mathematics, pp. 182-84. 19 Philosophical Investigations, I, §242. 20 See D. F. Pears, The False Prison, Vol. II, Ch. 14. 21 This is not to say that a person can never make a mistake, which is not purely verbal about his own intention. 22 This is not to say that introspection is never needed by a person whose intention is questioned. 23 See the discussion of ownership of sensations in Philosophical Remarks, §§57-66.

Christ Church Oxford University Oxford, OX1 1DP England

MICHAEL LEE KELLY

WITTGENSTEIN AND MAD PAIN

1. LEWIS ON MAD PAIN

Despite Wittgenstein's most valiant efforts in Investigations, Zettet,I and other scattered writings, philosophers continue to be philosophers and speak utter nonsense, or to be charitable, to speak what Wittgenstein would call utter nonsense. I have in mind here what has been written on pain, though of course the list can be multiplied greatly. My target will be David Lewis's "Mad Pain and Martian Pain", 2 but I shall take him on in a rather narrow way. What I mean by this is that I shall not attack the theoretical claims he makes in his article for his particular "materialist theory of mind". Rather, I shall try to apply some Wittgensteinian therapy on a claim for which he gives no argument, for which he admits he has no argument, but also for which he thinks it is unimportant whether an argument is supplied. Let me stop being so mysterious and allow Lewis to speak for himself.

He writes:

There might be a strange man who sometimes feels pain, just as we do, but whose pain differs greatly from ours in its causes and effects. Our pain is typically caused by cuts and burns, pressure and the like; his is caused by moderate exercise on an empty stomach. Our pain is generally distracting; his turns his mind to mathematics, facilitating concentration on that but distracting him from anything else. Intense pain has no tendency whatever to cause him to groan or writhe, but does cause him to cross his legs and snap his fingers. He is not in the least motivated to prevent pain or get rid of it. In short, he feels pain but his pain does not at all occupy the typical causal role of pain. 3

Lewis goes on to say that we would doubtless think of this man as a madman, and so he dubs this madman's pain "mad pain". This whole scenario strikes me at first blush as the problem of other minds in reverse; I shall explain what I mean in a moment (again, I apologize for being so mysterious). As I said, Lewis does not argue for his claim that there might be such a thing as mad pain. Again I quote:

I said there might be such a madman. I don't know how to prove that something is possible, but my opinion that this is a possible case seems pretty firm. If I want a credible theory of mind, I need a theory that does not deny the possibility of mad pain. I needn't


286 MICHAEL LEE KELLY

mind conceding that perhaps the madman is not in pain in quite the same sense that the rest of us are, but there had better be some straightforward sense in which he and we are both in pain. 4

Now, if a student of mine wrote in a paper, "I don't know how to prove this, but my opinion that it's possible is pretty firm", I would comment snidely on his paper and mark off severely. But Lewis is an important philosopher and not a student of mind so I shall simply comment here on his claim that, because he is of the firm opinion that mad pain is possible, a credible theory of mind must not deny the possibility of it. I take this as analogous to the claim that, because an important philosopher was of the firm opinion that it is possible that space is absolute, a credible theory of physics must not deny the possibility of it. This analogy speaks for itself. 5

Now, what does all of this have to do with Wittgenstein? Well, clearly it can be made to have a lot to do with Wittgenstein, for certainly he had a lot to say about pain, and unless I, and many others, read him incorrectly, he would want to say, if not what Lewis says about mad pain is outright nonsense, at least there is something terribly wrong with it. What, if anything, is terribly wrong with it is what I shall be examining in this paper.

2. THREE INTERPRETATIONS OF MAD PAIN

First let me explain what I mean when I say that Lewis's story of mad pain strikes me as the problem of other minds in reverse. Whereas the problem of other minds deals with the possibility that others who act like we do when we feel pain really do not feel pain, Lewis's story deals with the possibility that others who act nothing like we do when we feel pain nevertheless really do feel pain. So far, this fits in with some of the traditional accounts of the problems of other minds. Here is how it differs: the problem of other minds is usually at least partially an epistemological problem, How do we know that he really feels pain? Or, how do we know that when she acts as though she feels pleasure she isn't really feeling what we feel when we're in pain? But Lewis, at least at the beginning of his article, drops the epistemological problem. Presumably we all know that his sufferer of mad pain is in pain, otherwise I see no reason why we would think that he is mad, as Lewis says we would. It might be a bit odd if someone turned his mind intently

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to mathematics, crossed his legs and snapped his fingers after a bit of physical exercise on an empty stomach, but we would not call him "mad" unless we thought he did this while feeling pain. We would just call him a loony mathematician. But how would we know that he is in pain whenever he goes through this series of behavior? Setting aside this question for a moment, let me posit three interpretations of Lewis's scenario of mad pain, going in order from the strongest to the weakest claim (I believe that Lewis accepts the first interpretation; the other two are possible interpretations, thus they are worth looking at):

(1) Our madman (call him "Dave") tells us that he is in pain and does feel pain, and even though he does not act in the least like he is in pain (indeed, when he needs to solve a math problem he works hard to bring on more pain) we believe him; however, we do think he is insane, because only a madman would want to induce all this pain. (2) The situation is the same as in (1) except here we do not believe Dave; instead we think he is crazy, because only a madman would claim so sincerely that he is in pain when he so clearly (or at least we think he so clearly) is not in pain. (3) Dave does not tell us he is in pain when he feels pain, because he does not know that he has a pain, because he has learned to use the word 'pain' in roughly the way we have (with one major difference that 1 shall mention in a moment), and so attributes pain to those who exhibit pain behavior; furthermore, he wrongly believes that he has never felt pain, because (and here is where his learning of the word 'pain' differs from ours) pain never served the normal causal role for him,6 so as a child no one ever said "Oh you hurt yourself", or asked "Where does it hurt?" etc., when he felt pain, and so he never came to associate the word 'pain' (or the concept 'pain') with his feeling of pain. These are three interpretations of scenarios of mad pain; 1 am suppos

ing for the moment that they do not contain numerous absurdities, though they do. 1 am not supposing that they exhaust all possible interpretations; clearly there are others, and 1 shall add to the list later, but these three will give me something to start with.

You may be tempted to object that 1 am confusing the issue greatly. After all, 1 pointed out that for Lewis there is no epistemological problem (or at least, that epistemology is not his concern when it comes to mad pain); we could say perhaps that it is more of an ontological


question. But what distinguishes my three scenarios is the difference in epistemological relationships and what consequences arise from them. What differs between (1) and (2) is that in (1) we believe Dave when he says he is in pain, and in (2) we do not. What differs between (2) and (3) is that in (3) Dave does not know or even believe that he feels pain. If epistemological relationships do not matter, then anyone of the above scenarios will do.

To forestall an objection, Lewis writes:

I can hear it said that I have been strangely silent about the very center of my topic. What is it like to be the madman ... ? What is the phenomenological character of his state? If it feels to him like pain, then it is pain, whatever its causal role or physical nature. If not, it isn't. It's that simple!7

As if that were simple. It is not clear whether the points that this last quotation raises should be called epistemological, but in any case, this seems to rule out scenario (3). It seems to, but does it? Even this is not that simple, for Lewis is not necessarily saying that madman Dave will know that this "thing" that feels like pain, this feeling of pain, is pain, even though it is pain. But is any of this coherent? To whom must it feel like pain? Well, to him. Yet if he does not think that it is pain that he is feeling, then does it make sense to say that it feels like pain to him? And what does pain feel like? Well, surely we all know what pain feels like; at least I do. How? Do I know it from my own case? Pardon my lack of subtlety in doing so, but I have now set the stage for Wittgenstein's entrance.

3. WITTGENSTEINIAN THERAPY FOR MAD PAIN

Look at Section 149 in Remarks on the Philosophy of Psychology II. Here Wittgenstein gets anachronistically close to a direct comment on Lewis's article.

Perhaps someone will say: How can you characterize the concept 'pain' by referring to the occasions on which pain occurs? Pain, after all, is what it is, whatever causes it! -But ask: How does one identify pain?

The occasion determines the usefulness of the signs of pain.

In Zettel Sec. 532-34, he writes:

The concept of pain is characterized by its particular function in our life.

WITTGENSTEIN AND-MAD PAIN 289

Pain has this position in our life; has these connexions; (That is to say: we only call "pain" what has this position, these connexions).

Only surrounded by certain normal manifestations of life, is there such a thing as the expression of pain.

Clearly these conflict strongly with Lewis's story of mad pain. But of course I do not want simply to pit the words of Wittgenstein

against the words of Lewis. I want to use them to suggest that Lewis's sentences simply do not make sense, though on the surface they may seem to. (Let me clarify this. I am not saying that what Lewis says is false, except in some rather broad sense of the term, and I am not claiming that mad pain is impossible, rather I am simply saying that it is nonsensical to say that there is any such thing; that is, I do not think that there is any way to know what it would be like for there to be such a thing, as Lewis describes it.)

So, how am I to use Wittgenstein here? Well, let us reexamine Zettel Sec. 532: "The concept of pain is characterized by its particular function in our life". Well, what particular function does mad pain have in our lives or would it have if there were such a thing? Lewis answers this in his original description: it turns our attention to mathematics and away from everything else; it is not particularly unpleasant, for we do not want to get rid of it; it makes us cross our legs and snap our fingers, but not - I want to say, not in a pained way, but this would bias the case in my favor - what should I say? It makes us cross our legs but not as if we were writhing, and we do not groan as we do so.

But if all of this is so, then why do we call it 'pain', mad or otherwise Lewis's only answer seems to be, because it feels like pain! Now, I do not know exactly what sense to make of the peculiar phrase "feels like pain";8 the closest phrase to this that I'm familiar with is "feels pain", for which we have a rather clear-cut function and the function of "mad pain" does not come close to this. It does not even have a slight familyresemblance to it, unless the family is a white Anglo-Saxon Protestant one that has just adopted a Zulu baby.

Here, I think, is the sort of picture Lewis has that makes him think his account of mad pain makes sense. All of us have a clear picture, he thinks, of what pain feels like. Take a pin and jab it into your arm: there, that is a pain. Now take this "thing" and in your imagination dissociate it from its causes and effects. (One of the things that Lewis would say is an effect of pain is our writhing and groaning; I would not, and I think Wittgenstein would not, accept this terminology. Rather I


would say that it is an expression of our pain. But remember, I am simply describing Lewis's picture here.) His picture is much like that given in Hume's discussion of causation. We know what a billiard ball looks like, and we can imagine its rolling apart from its usual causes and effects. We can imagine the ball's rolling being caused by nothing at all, or a vocal command, and its effect upon hitting a second ball not being that of sending the second ball off in a straight-line direction, but rather of the first ball rolling backward over its original path. 9 Now, if all of this makes sense with billiard balls, I think Lewis would say, why not with pain? They are equally imaginable. We can call those mad billiard balls, this mad pain. Remember, however, Zettel Sec. 250: "That one can 'imagine' something does not mean that it makes sense to say it".

One response to Lewis is to say that the grammar of objects, the grammar of looking at and seeing objects, even the grammar of feeling objects, is very different from the grammar of feeling pain. As Lewis said, if it feels like pain, it is pain. 10 This cannot be said about seeing objects or feeling objects. If I reach into my pocket and pull out a coin that feels like a dime, it may, nevertheless, be a penny that I extract. 11

Also part of the grammar of pain is the expression of pain behavior. The tendency, and this is what I think Lewis has done, is to make a picture of pain: there is an outer picture, or a picture of the outer aspects of pain, and an inner one (as if it makes sense to say we have an inner picture of pain).12 Lewis tosses away the outer picture and replaces it with another. It is as if he gets rid of the outer picture of pain behavior by the rule of logical simplification, leaving just the inner picture, and then as the rule of logical addition allows, he hooks it up with any picture he so chooses. That is how he comes up with 'mad pain'.

Yet I do not see how this can get us past scenario (3), since we clearly learn how to use the word 'pain' in roughly the way Wittgenstein describes it:

A child has hurt himself and he cries; and then adults talk to him and teach him exclamations and, later, sentences. They teach the child new pain-behavior. (Investigations I, Sec. 244)

Our sufferer of mad pain, Dave, however, has never cried when he felt his mad pain, so he has never learned to associate the word 'pain' with this sensation that accompanies his desire to do math. Yet if even Dave


does not think that he feels a pain, I do not see what right we have to say that pain enters here at all.

Let me suggest a fourth scenario that does on first glance look more plausible than the three I have already given; it seems, at least, to have some of the grammar of pain present. Imagine that Dave at one time was perfectly ordinary. He once felt pain as the result of cuts and burns and pressure. He once tried to avoid pain, and would; writhe and groan when he did feel pain. And so, he learned to use the word 'pain' in the same sort of way that the rest of us did. But then something happened. As the result of a neurological disease, all of this changed. Now when he feels pain - but wait, this time I am biasing the case in Lewis's favor; let me say instead of "now when he feels pain" (after all that is the issue we are trying to decide - does it make sense to say that he feels pain in the case?) let me say, now when he says things like, "Oh, I have a pain", instead of writhing he casually crosses his legs ..and snaps his fingers and concentrates on math, and does nothing to avoid all of this.13 Now, shall we say that he is in pain? Rather, I think we would say not that the neurological damage made his pain have different causes and effects, but that the neurological damage affected his seman tical ability: he no longer knows what pain means (at least, not in the first person case).

Perhaps Lewis would say, "Yes, but this is really like your second scenario: Suppose he really does feel pain, and despite his testimony we incorrectly deny that he does". Here finally we seem to have an honest disagreement: two interpretations of a situation. An unfortunate ordinary fellow suffers a neurological disease. As a result, he claims he feels pain when none of the occasions, connections, or surroundings are present. 14 My interpretation is that, because none of these are present, we should simply say that he has lost some of his seman tical competence. Lewis, on the other hand, I am supposing, would say, "No, he really does feel pain - mad pain".

So, now, do we really have an honest disagreement? If so, I shall have to concede Lewis's point. (I am assuming that to have an honest disagreement both positions must make sense.) I submit that I do not have to do so.

I have good reason for saying that Dave has simply lost some of his semantical competence: he once used the word 'pain' in the right way, when the right surroundings were present. Now he does not. His use of the word 'pain' is now quite esoteric (which is not to say "mad,,).15


It may have some use - we now know that when he says he is in pain that he is doing math, etc. But I suggest that this use of the word 'pain' has no more in common with the ordinary use of the word 'pain' than the use of the word 'bank', meaning a financial institution, has to the use of the word 'bank', meaning the land next to a river. 16

On the other hand, Lewis has no good reason to say that Dave is really feeling the same sensation as he was before. ,Recall Wittgenstein's suggestion from Investigations II, p. 207:

Always get rid of the idea of the private object in this way: assume that it constantly changes, but that you do not notice the change because your memory constantly deceives you.

What difference would it make if this were so, that Dave's "private object" (his pain) constantly changed, but he did not notice this because his memory constantly deceived him. Well, if this had some "external" consequences, then of course that would be the difference that it makes; but then what does the private object matter? We would know that it was the case by some external criteria, but if there is no external effect, then there is no practical or detectable difference (for, ex hypothesi, there is no practical or detectable "internal" criterion, since Dave's memory changes along with his sensation). And so, what can Lewis mean when he says that Dave feels pain? Wittgenstein says in Investigations I, Sec. 353.

Asking whether and how a proposition can be verified is only a particular way of asking "How d'you mean?" The answer is a contribution to the grammar of the proposition.

If Lewis can give us no practical or detectable difference that would be made if all of this were to happpen, then there can be no way of saying whether it is true that the "private object" that is felt after the neurological damage (Dave's supposed pain) is the same as that felt before the damage. And if we do not know what it would be like for it to be true or false, then there is no answer to the question, "How d'you mean?" In other words, despite appearances, the claim means nothing, and all of Lewis's talk of "mad pain" is, as I have held all along, utter nonsense.


4. CONCLUSION

I have explicitly criticized Lewis in this paper, but with only minor redirection these arguments can be brought to bear on many other recent discussions, for instance, Thomas Nagel's "What Is It Like to Be a Bat?" comes immediately to mind. That Lewis's and Nagel's theoretical notions are so disparate suggests how widespread and deeply held are certain intuitions that, if ever held up to I the appropriate therapeutic scrutiny, would be seen to be incoherent nonsense. This only serves to show once again the importance of Wittgenstein's thought, and the need to meet him on his own ground.

Now, if I may be allowed a closing flight of fancy, let me announce: "The Fight of the Century. In this corner: Ludwig Wittgenstein. In that corner: David Lewis. The outcome: Wittgenstein wins by a knockout; Lewis, meanwhile, sits in his corner, crosses his legs, snaps his fingers, does math, and suffers mad pain".

NOTES

1 The works of Wittgenstein to which I refer are: 1958, Philosophical Investigations, 3d. edition, translated by O. E. M. Anscombe, Macmillan Publishing Co., New York; 1967, Zettel, edited by O. E. M. Anscombe and O. H. von Wright, translated by O. E. M. Anscombe, University of California Press, Berkeley; and 1980, Remarks on the Philosophy of Psychology, Vol. II, edited by O. H. von Wright and Heikki Nyman, translated by C. O. Luckhardt and M. A. E. Aue, Blackwell, London. I refer to each by section number, with the exception of Part II of Investigation, to which I refer by page number. 2 David Lewis: 1980, 'Mad Pair:! and Martian Pain', in Readings in Philosophy of Psychology, Vol. I, edited by Ned Block, Harvard University Press, Cambridge, pp. 216-22. 3 Ibid., p. 216. Lewis never tells us anything about what happens to this "strange man" when he suffers cuts, burns, pressure and the like. Lewis's wording seems to suggest (though it is far from clear) that this man does not feel pain in such cases. I would simply like to point out here that if he does not react as we do when in these cases we feel pain, he will not live long to do his math, cross his legs, and snap his fingers. 4 Ibid. 5 One may object that the type of possibility that Lewis talks about is logical possibility, and indeed our theory of physics does not rule out the logical possibility of absolute space. But physical theories have little to say about logical possibility, and they may just as well rule out the logical possibility of absolute space, given the general irrelevance of logical possibility in such a theory (other than the need for the theory itself to be consistent). What is important here is simply this: what, at some time before theorizing, seems to be possible need not be so afterwards. 6 I am not comfortable with talk of the "causal role" of pain; it strikes me as an awkward


and probably misleading way of speaking. It is, however, Lewis's way of speaking, so in presenting this scenario I have followed him. 7 Lewis, op. cit., p. 221. 8 For the best sense that I can make of it, see note 10. 9 See Hume's Enquiry Concerning Human Understanding, 1st ed., 1748, Section IV, Part I. 10 If this means anything, it must mean what Wittgenstein says in Investigations Sec. 246:

It can't be said of me at all (except perhaps as a joke) that I know I am in pain [for this read "that my sensation feels like pain"]. What is it supposed to mean - except perhaps that I am in pain? ... The truth is: it makes sense to say about other people that they doubt whether I am in pain; but not to say it about myself.

11 The question of our supposed incorrigibility about pain has been much discussed, and our perplexity over it is likely caused by our confusion about the grammar of feeling objects with the grammar of feeling pain, and by the attendant belief that something like what Lewis says about mad pain makes sense. 12 Lewis seems to forget that, if it does make any sense to talk of an "inner picture", part of the inner picture is the unpleasantness of pain and our desire to avoid it. 13 I have doubts that even this scenario is neurologically or physiologically plausible, but I posit it as Lewis's best last hope. Note, however, that as Lewis's case demands, all the causes and "effects" of pain for this man have changed - all, except for the "effect" of his verbal utterances and conscious awareness concerning his supposed sensations of pain. Lewis never notes the oddity of this, that is, that all the "effects" but these are different. 14 The exception is, of course, his saying, "I feel a pain". 15 Unless Dave's neurological damage is too severe, we could persuade him that he is not in pain at all. We would simply remind him that pain is a distracting, unpleasant sensation that can be debilitating, and so on. 16 And surely Lewis is claiming that pain and mad pain have more in common than that or else he would not say that a credible theory of mind must account for mad pain (in such a way as to treat it as pain). Certainly our theories of finance need not account for river banks.

Dept. of Philosophy Florida State University 203 Dodd Hall Tallahassee, FL 32306 U.S.A.

KENT LINVILLE AND MERRILL RING

MOORE'S PARADOX REVISITED

Wittgenstein "once remarked that the only work of Moore's that greatly impressed him was his discovery of the peculiar kind' of nonsense involved in such a sentence as, e.g., 'It is raining but I don't believe it'''. 1

Present practice is to refer to the difficulties generated by sentences of this form, as well as to sentences of the form "I believe that p but not p", as "Moore's paradox". 2 Despite Wittgenstein's great reputation and regard for the importance of Moore's "discovery", little interest has been generated in the topic. And yet, central issues in epistemology and the philosophy of language are involved in the resolution of this paradox. Since this is not generally appreciated, we begin our discussion by establishing what some of those important issues are, thereby crediting Wittgenstein's assessment of the importance of the paradox. Then, we develop an account of the aberrant nature of Moore's sentences (hereafter labelled "MS") that is indebted to Wittgenstein, and which challenges the assumptions that motivate the standard form of discussion of these sentences initiated by Moore.

Moore says "such a thing as 'I went to the pictures last Tuesday, but I don't believe that I did' is a perfectly absurd thing to say [i.e., assert], although what is asserted is something perfectly possible logically". 3

Moore makes two claims here (besides stating the basic fact that MS would be absurd to assert), claims which have become canonical in subsequent literature. First, the peculiarity or absurdity of MS cannot reside in the sentence itself, since it is not self-contradictory, and second, that its absurdity (therefore) arises only in speech (expressing, as it apparently does, a possibility in thought). So what puzzles Moore and his followers is why the assertion of MS should be absurd, when "what it asserts" might be true.

Explanations offered of that absurdity, with the exception of Wittgenstein's,4 rest on one or another version of the doctrine that saying or asserting implies believing.5 To say "not-p", according to this view, is to imply that one doesn't believe that p; this implied "I don't believe that p" conflicts with one saying "I believe that p", thereby generating the absurdity of such an assertion. And because "I don't believe that


296 KENT LINVILLE AND MERRILL RING

p" is only (non-deductively) implied and not entailed, the assumed non-self-contradictory character of MS is maintained.

Wittgenstein, on the other hand, gives a quite different account of the absurdity of MS. On his view, '''I believe that this is the case' is used like the assertion 'This is the case"';6 that is, "I believe that p" is a form of the assertion that p. Hence, MS conjoins a form of the assertion that p and an assertion that not p and i,ts absurdity arises from that conflict.

Now that we have described these two competing accounts of how the clauses of MS come into conflict, it is obvious each results from a different interpretation of the function of "I believe". In Moorean accounts, that belief phrase is assumed to be self-referential - to say something about, be descriptive of, the speaker. Thus they see the paradox to be that of explaining how a statement such as "I believe it is raining" (understood to be "about the speaker") can conflict with the other clause of MS, since it is clearly about some other (logicallyindependent) subject matter - the weather. Because their response to MS is guided by that question, the explanations they produce involve the prior assumption that "I believe" is self-referential; and that unexamined thought gives rise, in turn, to the other two staples in Moorean discussions: the ideas that MS is not self-contradictory and (therefore) that its absurdity arises only in speech.

Our discussion, following Wittgenstein's lead, argues that the three ideas we have identified as guiding Moorean solutions of the paradox are muddled, so our study, if successful, "dissolves" Moore's paradox by showing it to be the outgrowth of misunderstandings. 7 And since our criticisms aim to show that the philosophical requirements which prompt Moorean invocations of the doctrine that saying implies believing result from antecedent confusion, direct criticism of that doctrine will be ancilliary to our overall strategy, which is designed to show that "I believe it is raining but it's not", for example, is absurd because it consists of two contradictory assertions about the weather.

We begin by locating the ideas motivating standard discussions of Moore's paradox in a different, and undeniable important, philosophical setting.

Wittgenstein hints at the historical significance of the primitive idea in Moorean discussions of MS (that "I believe" is self-referential) in the following remark:

MOORE'S PARADOX REVISITED 297

The significance of such possibilities of transformation, for example of turning all statements into sentences beginning 'I think' or 'I believe' (and thus, as it were, into descriptions of my inner life) will become clearer in another place. (Solipsism)8

The paradigmatic statement of solipsism is of course found at the conclusion of Descartes's "First Meditation", where he vows "resolute attachment" to the thought that I, "having no hands, no eyes, no flesh, no blood, nor any senses, ... [nonetheless] falsely bdieve myself to possess all these things".9 And this is the genesis of the philosophical heritage which informs Moorean sensibilities. For the assumed meaning of "I believe", around which standard discussion of Moore's paradox turns, is also at the heart of the Cartesian enterprise in the Meditations. Indeed, both the skepticism of the "First Meditation" and the cogito of the "Second Meditation" depend upon a self-referential construal of those words. For consider, since Descartes's skeptical hypothesis is intended to immunize him from error, providing an antidote to the threat posed by the malin genie, the "doubt" expressed in the resolution to "consider myself falsely believing" cannot involve full-bodied disbelief; to disbelieve a proposition ("I have hands, eyes ... ," for example) is to believe its contradictory ("I believe that it is not the case I have hands, eyes ... "), and that would leave Descartes equally exposed to error.

So what Descartes's maneuver comes to, what his "hypothesis" requires, is detaching belief from truth. This non-epistemic rendering of "I believe" is spelled out in the Principles, where, explaining the cogito, he characterizes judgments involving perception as though they functioned to describe inner-experience rather than to assert "representational content":

[IJf I say I see, or I walk, I therefore am, and if by seeing and walking I mean the action of my eyes or my legs ... my conclusion is not absolutely certain; because it may be that, as often happens in sleep, I think I see or I walk, although I never open my eyes or move from my place .... But if I mean only to talk of my ... consciously seeming to see or to walk, it becomes quite true because my assertion now refers only to my mind, which alone is concerned with my feeling or thinking that 1 see and I walk. 10

Now we can tie these thoughts of Descartes's directly to the issue at stake in the resolution of Moore's paradox, by imagining an "Eighth Set of Objections" to the Meditations, opening with the following question:

Dear Descartes, in your Meditations you take 'I am seated here by a fire' or 'This is a


hand' to be dubitable; whereas statements such as 'I think (believe/doubt) that this is a hand' you hold to be indubitable. Now you apparently understand this epistemological difference to reflect a semantic contrast, a difference in what is asserted in the two cases. The former assertions go beyond reports or' one's experience, claiming to report an independently existing reality; while the latter assertions, when carefully considered, are seen to be nothing but descriptions of one's own states of mind, and so they are, according to the cogito, indubitable. But then, why can't we assert such a thing as 'I believe I have hands, but I don't'? Surely it would be perfectly absurd to .assert such a thing, although I can't see that it should be, if you are correct in your underStanding of what its conjuncts actually say.

So Descartes, too, might have been called upon to explain the oddness of MS. And with this historical perspective in view, we now return to standard discussions of Moore's paradox, to consider the related claims they make that MS is impeccable in thought, and that it becomes marred only when embodied in speech. For unless the entire thrust of Wittgenstein's later philosophy is fundamentally misguided, it will turn out that precisely because Mooreans are correct in claiming MS is absurd in speech (on permanent holiday, if you will), they are wrong in maintaining its intelligibility in thought. For the claim that an expression's meaning is a function of its having a place, and the place it has in speech and communication is at the center of Wittgenstein's later philosophy. Among the numerous examples we might cite as reminders of this, the following, though long, is especially apt, since it relates that theme directly to Moore's paradox:

How would it be, if a soldier produced military communiques which were justified on grounds of observation; but he adds that he believes they are incorrect. ... The communique is a language-game with these words. It would produce confusion if we were to say: the words of the communique - the proposition communicated - have a definite sense, and the giving of it, the 'assertion' supplies something additional. As if the sentence, spoken by a gramophone, belonged to pure logic; as if here it had the pure logical sense; as if here we had before us the object logicians get hold of and consider -while the sentence as asserted, communicated, is what it is in business. As one may say: the botanist considers a rose as a plant, not as an ornament for a dress or room or as a delicate attention. The sentence, I want to say, has no sense outside the language-game. This hangs together with its not being a kind of name. As though one might say "'I believe ... " - that's how it is' pointing (as it were inwardly) at what gives the sentence its meaning.ll

So the Fregean distinction between assumption and assertion, and the idea of a "pure logical sense", which formal logic is to catch in abstraction from the empirical settings of assertion, is a myth, or so Witt-


genstein maintains. Meaning is inextricably scenic: "Words have their meaning only in the flow of life". 12

Bringing this theme to bear on the useless sentences here at issue, we begin by pressing for a precise characterization of the phenomenology implied by the Moorean claim that "what it [MS] asserts" is a perfectly possible, thinkable state of affairs. Taking "thinkability" literally invites the following question: Can we have the thought "I be~ieve it's raining but it's not" without absurdity? Surely not. If we try to think that MS is so, that strikes us as being every bit as ludicrous as trying to imagine its public declaration; passing it through our head produces the same sense of absurdity as passing it through our lips.

The Moorean response to this will no doubt be that the intelligibility being claimed for MS is not based on the grounds that we can think it, but rather, that it is possible to imagine (or "entertain" the thought of) oneself believing it is raining, say, and that it's not raining. And this, our objector insists, shows that what MS asserts is perfectly possible logically.

Among traditional philosophers who assume meaning and understanding either are or essentially involve mental states or processes, such appeals are common fare. As a reminder of that, we recall two important examples, the first from Hume, the second from Wittgenstein's Tractatus:

Suppose a person present with me, who advances propositions to which I do not assent, that Caesar dy'd in his bed, that silver is more fusible than lead, or mercury heavier than gold; 'tis evident, that notwithstanding my incredulity, I clearly understand his meaning, and form all the same ideas, which he forms. My imagination is endow'd with the same powers as his.u 'A state of affairs is thinkable': what this means is that we can picture it to ourselves. 14

Of course the Investigations argues that whether or not a sentence has sense and what sense it has is not determined by the products of the imagination:

It is no more essential to the understanding of a proposition that one should imagine anything in connection with it, than that one should make a sketch from iLlS

Nor are such items sufficient to secure understanding; pictures, whether images or sketches, public or private, are themselves signs which can be variously interpreted, so they require rather than produce understanding:


Imagine a picture representing a boxer in a particular stance. Now this picture can be used to tell someone how he should stand, should hold himself; or how he should not hold himself; or how a particular man did stand in such-and-such a place, and so on. 16

But this general and rather abstract discussion will most likely not do to correct the sense that we do have a successful appeal to the imagination in connection with MS, that here "a picture is conjured up which ... [does] fix the sense unambiguously; I •• a picture ... which seems to make the sense of the expression unmistakable". 17 Exposing this apparition of sense to be the result of confusion requires more detailed discussion.

Our beliefs are where we stand cognitively, so to speak; indeed, though this analogy is weak it is not overworked by noting that the verisimilitude of any representation of oneself falsely believing will be limited in a manner akin to a drawing picturing where one is standing:

A painter does not draw the spot where he is standing. But in looking at his picture I can deduce his position by relation to the things drawn. On the other hand, if he puts himself into his picture I know for certain that the place where he shows himself is not the place where he is. 18

Analogously, the person pictured to exhibit what MS asserts is, perforce, a surrogate for "I" in "I believe", and so is subject to its logic. Therefore, if we imagine the person depicted to be believing falsely, we can "deduce" one is not then thinking from within that picture, i.e., from within the "logical space" of "I believe"; for when belief is thus identified ("I believe ... "), one cannot (logically) proceed to indicate that the belief is false - one's current beliefs are one's representation(s) of reality. When we envisage ourselves from afar, as Hume was wont to say, we observe both belief and contrary reality, and so the relevant belief words are observational; but of course "I believe" is not observational. We do not say "I believe it's raining" because we have taken note of ourselves grabbing a raincoat or our saying "I believe it's raining"; even more absurd is the thought that we base those words on what we imagine ourselves to be saying and doing.

This criticism of the Moorean appeal to the imagination - where they assume we find or may produce an exhibit of what MS allegedly asserts -may be thought to mistake epistemological for seman tical differences; that is, a Moorean may object that, of course, "I believe" is not ascribed on the basis of observation, but that's because such ("intentional") states are "known directly", rather than by inference from behavioral


symptoms, as in the case of "You (He) believe(s)". So although it is correct that non-first-person belief words are required to articulate the Moorean thought experiment, still, that in no way shows the thought is not cogent. For making the required correction (substituting the second- or third-person form of words) does not alter the "propositional content" of one's thought.

That something along these lines would be Moore's response is clear in his following comment:

'I went to the pictures last Tuesday, but I don't believe that I did' is absurd to say, although what is asserted is something which is perfectly possible logically: it is perfectly possible that you did go to the picture and yet you do not believe that you did. 19

Of course Moore is not alone in his unselfconscious assumption that changes in pronoun make mere grammatical rather than logical alterations in what is said or asserted (given the "indexicals" are understood to "identify the same referent"). For example, the still widely used canonical "A believes that p" is also employed on the assumption it has the same truth-value, expresses the same proposition, no matter what we substitute for "A". And, the assimilation underlying this practice takes us to an important conceptual source of the thought we earlier identified as basic or primitive in both Descartes's thinking and Moorean accounts of MS, namely, that "I believe" is self-referential. No one will deny that prefixing "You (or He) believe(s)" to a simple assertion such as "It is raining" does change its subject matter - transforming a proposition about the weather into one about the person's belief. And, the assimilation of the first-person to those other forms of the verb leads one to think a similar transformation is effected there, and thus, to suppose those words are self-referential.

In opposition to the assimilation guiding such thinking, Wittgenstein enjoins:

Don't look at it as a matter of course, but as a most remarkable thing, that the verbs 'believe', 'wish', 'will' display all the inflexions possessed by 'cut', 'chew', 'run'. 20

But before we consider how "believes" actually functions in our language, it is important to appreciate the general nature, and thus the full significance, of the presuppositions shaping the "matter of course" (a priori) thinking Wittgenstein warns against. As is made clear by the following questions which he poses in opening the Investigations's discussion of Moore's paradox, those presuppositions are manifes-


tations of the very picture of language his later philosophy labors to show is at the bottom of philosophical perplexity generally:

How did we ever come to use such an expressio~ as 'I believe ... '? Did we at some time become aware of a phenomenon (of belief)? Did we observe ourselves and other people a!1d so discover belief?21

The conception of language, of reality, and qf the relation between them that comes with affirmative answers to Wittgenstein's questions is familiar to readers of the Investigations, which of course opens with a quotation from Augustine illustrating that philosophically bedeviling picture of language. The offending "primitive idea of the way language functions,,22 is, in outline, this: words are names, language functions to report the existence of what is named; and since words only name what is there to be named, the nature of things is independent of and prior to the ways in which we use language to talk about them. Learning the meaning of "believe( s)", then, is learning to identify the phenomenon of human experience it names - belief. "I believe" is the form of words we have for identifying the presence of the phenomenon in oneself; "You" and "He believes" are words and phrases which identify that phenomenon in others. Moreover, when gripped by this model we are inclined to think of sentences as names, too (perhaps along Fregean lines, as a kind of complex proper name). Therefore, since we assume "I believe it is raining" and "It is raining", for example, must name different processes, when one is affirmed and the other denied (as in MS), we think that that can't be a contradiction.

Discussion of the philosophical conception of language and companion metaphysics, we have pointed out in the background of Moorean discussions, is beyond the purview of this brief study. However, there is a direct and untoward consequence of those ideas for first-person belief talk which is perhaps sufficiently jarring to loosen their grip. This consequence is remarked by Wittgenstein in the following comment:

A: 'I believe it's raining'. - B: 'I don't believe so'. Now they are not contradicting each other; each one is simply saying something about himself. 23

Standard discussions of Moore's paradox are focused on the phrases "I believe" or "I don't believe" nested in a single sentence, and thus in one mouth, and so such discussions fail to reveal the implausible consequence which their construal of those words has for an understanding of their role in contexts of interpersonal disagreement in belief.


But as Wittgenstein's above remark calls to attention, the Moorean construal of those phrases effectively elides that role, rendering such remarks bits of autobiography: A: "I feel anxious" - B: "I don't". However, if I say "I believe the Prime Minister will soon fall from office", and an interlocutor responds "I don't believe that he will", there is disagreement.

Once we turn from the monolithic view of meaning and reference which arises from a "name-thing" (" 'Fido'-Fido") conception of language, we see quite clearly "I believe" and "He believes" do not have the same function. Wittgenstein expresses their salient difference this way: "'I believe that this is the case' is used like the assertion 'This is the case'; and yet the hypothesis that I believe this is the case is not used like the hypothesis that this is the case". 24 That is, "I believe that the Prime Minister will fall from power" takes a position on, makes a truth-claim about, the Prime Minister; whereas "He believes that the Prime Minister will fall from power" takes no such stand (as witnessed by the fact "He believes the Prime Minister will fall from power, but he won't" is an impeccable assertion).

Wittgenstein brings out the conceptual difference in those belief phrases from yet another angle, by asking the following:

I say of someone else 'He seems to believe ... .' and other people say it of me. Now, why do I never say it of myself, not even when others rightly say it of me? - Do I myself not see and hear myself, then? ... 25

The short answer is "seeing and hearing myself" is irrelevant, because "I believe that p" announces a verdict about the truth-value of p; not the condition of the person rendering that verdict;26 and others can say of me that I seem to believe because their words - "He seems to believe that p" (said of me) - do form a hypothesis about me, not a verdict aboutp.

In sum then, "I believe" and "He believes" are different instruments which perform functions as distinct as that made familiar by John Austin between "I promise" and "He promises". "I believe", rather than altering the subject matter of assertions, attenuates or otherwise modifies statements. One form this takes is brought out in Urmson's classic article "Parenthetical Verbs", in which he compares "I believe that p" to "It is probable that p".27 Though again, one sometimes offers up a proposition on the platter of "I believe" as a matter of conversational form, thereby acknowledging that p is controversial (that others may


doubt or deny it), though nonetheless, certain of it oneself. In neither case, though, is one adverting to a state or condition of the speaker; as'Wittgenstein cautions: "Don't regard a hesitant assertion as an assertion of hesitancy". 28

We must now anticipate and defend against various objections to our account of "I believe", objections motivated by the thought that in saying "I believe" surely something gets said abput the speaker. Such criticisms can be developed in numerous ways. We concentrate here on central examples, leaving it to the reader to adapt the principle guiding our responses to those further cases. The error in all such objections is the same: recognizing that information about the speaker is made available by his speaking, the attempt is made to locate that information in his words "I believe", whereas properly it should be assigned elsewhere.

Starting with a simple case, of course a person can be saying something about himself when using "I believe". "Can you run a mile in six minutes?" - "Yes, I believe I can". But that this remark is about the speaker is not a function of the words "I believe", but of the second occurrence of the pronoun. Or again, we answer questions like "Do you believe Gorbachev will succeed in reforming the Soviet economy?" by saying "Yes, I believe he will", or "No, I don't believe he will". Don't such answers show we are saying something about ourselves? The erroneous assumption here is that the question is about the respondent. But surely the question is about Gorbachev, though of course addressed to the respondent. Again: "If you say 'I believe he's happy', inferences about your behavior are possible. Doesn't that show something gets said about the assertor?" No, inferences about my behavior can also be made on the basis of my saying "He's happy", but it doesn't follow that that assertion is about the speaker. Of course if you assert "I believe ... ", that is your assertion and inferences about you are possible. But that you have spoken and thereby opened up the possibility of inferences being made about yourself is not the same thing as asserting something about yourself.

Similar kinds of confusion arise from projecting features of the context of utterance onto the use of "I believe". Someone applying for Conscientious Objector status, for example, may well say to officials, "I believe violence is evil". But it is not that his words are about himself, rather he is the object of inquiry, an inquiry in which the authorities are interested in the person. Their pursuing the question of


whether violence is evil, even had the applicant said straight off "Violence is evil", would be out of place in such proceedings. The following observation of Wittgenstein's helps clarify what is at issue here, which is how words that are about some other subject matter can, nonetheless, be spoken to provide information about oneself:

The language-game of reporting can be given such a turn that a report is not meant to inform the hearer about its subject matter but about the person making the report.

It is so when, for instance, a teacher examines a pupil. (You can measure to test the ruler.)29

In asking, "Who discovered America?" the teacher is seeking to learn something about the pupil. Yet the student can only perform successfully by using words which are not about himself, by saying, for example, "Columbus, I believe".

Finally, further occasion for the misinterpretation of the logic of assertions arises when traditional talk of truth conditions is applied to propositions modified by "epistemic verbs". This kind of difficulty is illustrated by David Lewis, when he states:

If someone says "I declare that the Earth is flat" (sincerely, not play-acting, etc.) 1 claim that he has spoken truly: he does indeed so declare. 1 claim this not only for the sake of my theory but as a point of common sense. Yet one might be tempted to say that he has spoken falsely, because the sentence embedded in his performative - the content of his declaration, the belief he avows - is false. Hence 1 do not propose to take ordinary declaratives as paraphrased performatives ... because that would get their truth conditions wrong.30

Applying Lewis's reasoning to Moore's sentences of course inclines one to hold that the assignment of conflicting truth values to its clauses poses no problem of logical consistency. But this inclination and Lewis's claim, that it is supported by common sense, are clearly wrong. The truth is, rather, to the contrary, as George Lakoff observes:

Note that in statements it is the propositional content, not the entire sentence, that will be true or false. For example, if 1 say to you 'I state that 1 am innocent', and you reply That's false', you are denying that 1 am innocent, not that 1 made the statement. That is, in sentences where there is an overt performative verb of saying or stating or asserting, the propositional content, which is true or false, is not given by the sentence as a whole. 3 !

Of course "believe" is not a performative verb, but Lakoff's point holds there, too. Lewis is confusing sincerity conditions with truth conditions, conflating questions of truth with questions of truthfulness; these are two different language-games or modes of assessment, both


of which can be engaged in with respect to "I declare", "I state", or "I believe" statements, unlike "I have pain" statements, for example.

Before we conclude with a final criticism of standard treatments of Moore's paradox, we should make note of one implication of this study for studies of belief. Our account of the uselessness of MS, if correct, inverts orthodox treatments of belief. This reorientation requires independent development, of course, but we can sket,ch how the developed story would parallel Wittgenstein's well-known "reversals" of the traditionally held primacy of appearance language over physical object language,32 or of doubt over belief. 33 On the account of believing developed here, belief is not, as traditionally assumed, the source of assertions (a mental reservoir, a neural network, or whatever from which assertions flow); rather, belief is itself "a new joint in", an elaboration or modification of, the concept of assertion.

To this point in our discussion, our criticism of the standard account of the absurdity of Moore's sentences has attacked the ideas which motivate it; we have said nothing about the Moorean solution itself, about their saying-implies-believing doctrine. We close by showing why that doctrine, though perhaps true,34 does not explain the infelicity of MS.

Those who maintain that saying implies believing gloss "implies" in terms of what might be called the associated rights of "givings" and "takings" in communication. Moore writes in explanation, "If we hear a man say ... , we should all take it that ... ".35 Toulmin claims that a forecaster's "It will rain" is about the weather and only "implies, or gives people to understand" what his beliefs are. 36 Again, NowellSmith develops a notion of contextual implication, which he explains in terms of justified takings: "A statement p contextually implies a statement q if anyone ... would be entitled to infer q from p in the context in which they occur". 37 In sum, the idea that there is an implication relation between saying and believing is explained as amounting to the claim that there is an inference ticket from asserting to a state of the assertor.

As a principle of inference, however, the doctrine saying-impliesbelieving is not something that a person can employ about himself. We do not infer what we ourselves believe from what we say; we cannot say "I said 'p', therefore (ceteris paribus), 'I believe p'''. Saying does not imply believing, it implies "He believes": "'He said p', so (ceteris paribus) he believes p". To make the principle here relevant to MS,


one must stretch it to include our taking the same interest in our own words as another can. But when one works out that possibility, the data which the principle is being invoked to explain (viz., the absurdity of asserting MS) disappears:

If I listened to the words of my mouth, I might say someone else was speaking out of my mouth.

'Judging from what I say, this is what I believe.' Now, it is possible to think out circumstances in which these words would make sense.

And then it would also be possible for someone to say 'It is raining and I don't believe it', or 'It seems to me that my ego believes this, but it isn't true.' One would have to fill out the picture with behaviour indicating that two people were speaking through my mouth. 38

NOTES

1 Norman Malcolm: 1958, Ludwig Wittgenstein: A Memoir, London, p. 177. 2 This practice probably derives from Wittgenstein; cf. his discussion of these sentences in Ludwig Wittgenstein: 1968, Philosophical Investigations, 3d ed., trans. G. E. M. Anscombe, New York, Part II, pp. 190-92. 3 G. E. Moore: 1942, "A Reply to My Critics", The Philosophy ofG. E. Moore, ed. P. A. Schilpp, Evanston, pp. 542-43. 4 In addition to Wittgenstein's extensive discussion of the paradox, both in the Investigations and elsewhere (cited below, note 11), this discussion draws on Kent Linville and Mervill Ring: 1972, "Moore's Paradox: Assertions and Implication", Behaviorism I, pp. 87-102. 5 For an extensive bibliography of the major writings on Moore's paradox, see Jaakko Hintikka: 1962, Knowledge and Belief, Ithaca, p. 64, footnote. To that, add Hintikka's own work in that book, pp. 64-76; J. L. Austin: 1962, How to do Things with Words, Cambridge, pp. 48-49; Norman Malcolm: 1963, Knowledge and Certainty, Englewood Cliffs, pp. 16-17; P. H. Nowell-Smith: 1954, Ethics, London, pp. 80-81; B. C. van Fraassen: 1984, "Belief and the Will", Journal of Philosophy 81, pp. 235-56; and Bernard Williams: 1973, The Problems of the Self, Cambridge, p. 137. Considerations of length lead us to only assert the basic sameness of these accounts, leaving verification to the reader. 6 Wittgenstein, op. cit., p. 190. Cp.: "The sentence 'I want some wine to drink' has roughly the same sense as 'Wine over here'!" Ludwig Wittgenstein: 1980, Remarkson the Philosophy of Psychology, trans. G. E. M. Anscombe, eds. G. E. M. Anscombe and G. H. von Wright, Chicago, vol. I, section 469. 7 "Something surprising, a paradox, is a paradox only in a particular, as it were, defective, surrounding. One needs to complete this surrounding in such a way that what looked like a paradox no longer seems one". Ludwig Wittgenstein: 1978, Remarks on the Foundations of Mathematics, 3d ed., Oxford, section VII, no. 43. 8 Wittgenstein, Investigations, Part I, p. 24.


9 Rene Descartes: 1967, The Philosophical Works of Descartes, trans. Haldane and Ross, Cambridge, vol. I, p. 148. 10 Ibid., p. 222, emphasis added. 11 Wittgenstein, Remarks on the Philosophy of Psychology, vol. I, sec. 487-88. 12 Ludwig Wittgenstein: 1980, Remarks on the Philosophy of Psychology, trans. C. G. Luckhardt and A. E. Aue, eds. G. H. von Wright and Neikki Nyman, Chicago, vol. II, sec. 687. 13 David Hume: 1967, A Treatise of Human Nature, ed. Selby-Biggs, Oxford, p. 95. 14 Ludwig Wittgenstein: 1963, Tractatus Logico-Philosophicus, trans. D. Pears and B. McGuinness, London, 3.001. 15 Wittgenstein, Investigations, Part I, p. 396. 16 Ibid., note p. 11. 17 Ibid., pp. 426, 352. 18 Simone Weil: 1970, First and Last Notebooks, trans. Richard Rees, London, p. 146. 19 Moore, op. cit., p. 542. 20 Wittgenstein, Investigations, p. 190. Cp.: "Must the verb 'I believe' have a past tense form? Well, if instead of 'I believe he's coming' we always said 'He could be coming' (or the like), but nevertheless said 'I believed ... ' - in this way the verb 'I believe' would have no present. It is characteristic of the way in which we are apt to regard language, that we believe that there must after all in the last instance be uniformity, symmetry: instead of holding on the contrary that it doesn't have to exist". Wittgenstein, Remarks on the Philosophy of Psychology, vol. I, sec. 907. 21 Wittgenstein, Investigations, p. 190. 22 Ibid., Part I, p. 2. 23 Wittgenstein, Remarks on the Philosophy of Psychology, vol. II, sec. 419. 24 Wittgenstein, Investigations, p. 190. 25 Ibid., p. 191. 26 "That he believes such and such, we gather from observation of his person, but he does not make the statement 'I believe .. .' on the grounds of observation of himself. And that is why 'I believe p' may be equivalent to the assertion of p. And the question 'Is it so?' to 'I'd like to know if it is so?,". Wittgenstein, Remarks on the Philosophy of Psychology, vol. I. sec. 504. 27 J. O. Urmson: 1952, "Parenthetical Verbs", Mind LXI, reprinted in Essays in Conceptual Analysis, ed. A. Flew (London, 1956). 28 Wittgenstein, Investigations, p. 192. 29 Ibid., pp. 190-91. 30 From David Lewis: 1972, "General Semantics", in Harman and Davidson, eds. Semantics for Natural Language, Dordrecht, p. 210, as quoted in, George Lakoff: 1975, "Pragmatics in Natural Logic", in E. L. Keenan, ed., Formal Semantics of Natural Language, Cambridge, p. 256. 31 Ibid., p. 257. 32 Ludwig Wittgenstein: 1967, Zettel, eds. G. E. M. Anscombe and G. H. von Wright, trans. G. E. M. Anscombe, Oxford, sec. 413-26. 33 Ludwig Wittgenstein: 1969, On Certainty, eds. G. E. M. Anscombe and G. H. von Wright, trans. Denis Paul and G. E. M. Anscombe, Oxford, sec. 115, 160. 34 We use "perhaps true" advisedly; ct. Henry A. Alexander Jr.: 1967, "Comments on Saying and Believing", in Epistemology: New Essays in the Theory of Knowledge, ed. Avrum Stroll, New York, pp. 159-78.

MOORE'S PARADOX REVISITED

35 Moore op. cit., p. 543. 36 Toulmin, op. cit., pp. 52, 85. 37 Nowell-Smith, loco cit. 38 Wittgenstein, Investigations, p. 192.

Linville: Dept. of Philosophy Oxford College/Emory University Oxford, GA 30267 U.S.A.

Ring: Dept. of Philosophy California State University Fullerton, CA 92634 U.S.A.

309

THEODORE R. SCHATZKI

ELEMENTS OF A WITTGENSTEINIAN PHILOSOPHY

OF THE HUMAN SCIENCES

ABSTRACT. In this paper, a Wittgensteinian account of the human sciences is constructed around the notions of the surface of human life and of surface phenomena as expressions. I begin by explaining Wittgenstein's idea that the goal of interpretive social science is to make actions and practices seem natural. I then explicate his notions of the surface of life and of surface phenomena as expressions by reviewing his analysis of mental state language. Finally, I critically examine three ideas: (a) that the goal of interpretive inquiry is realized through a descriptive, context-constructing method that enables investigators to grasp the instincts, mental states, and experiences ("Geist") expressed in surface phenomena; (b) that uncovering rules plays a minor role in this enterprise; and (c) that surface phenomena not only can be made natural but also have causes and are subject to causal explanation.

Only to a limited extent did Wittgenstein explicitly advocate a definite conception of the Geisteswissenschaften. It is possible, however, to extract from his later works a consistent, albeit partial, account of this field of knowledge. For the notions of the surface of human life and of surface phenomena as expressions provide a guiding link with which his ideas on a number of topics can be interrelated and their significance for the human sciences established. This paper aims to carry out this synthesis. I shall first discuss Wittgenstein's naturalistic conception of the goal of interpretive social investigation, introducing notions such as instinct-behavior and commonalities in human existence which will subsequently receive greater concretization. Following this, I shall describe his notion of the surface of human life, and then analyze the expressivity of surface phenomena by reviewing his analysis of mental state language. The remaining sections will examine, with reference to surface phenomena and their expressivity, Wittgenstein's views on: (a) how to realize the goal of interpretive inquiry; (b) the roles played by rules in such inquiry; and (c) the proper focus of the causal investigation and explanation of human life.

1. THE GOAL OF INTERPRETIVE SOCIAL INVESTIGATION

Most of Wittgenstein's remarks that pertain explicitly to human science concern so-called "interpretive" inquiry. Interpretive inquiry comprises


312 THEODORE R. SCHATZKI

those investigations that aim to render at first strange, unfamiliar, or puzzling actions and practices understandable (verstiindlich). Such efforts are found predominantly in history and social anthropology, but also in sociology, political science, and psychoanalysis.

Wittgenstein never indicated exactly what sorts of questions and perplexities rendering practices understandable resolves. He was clear, however, that, in most cases, making a practic,e intelligible does not mean seeing the rationality in it. For, in his eyes, rationality is but an occasional feature of life that presupposes a nonrational foundation. Most practices, accordingly, do not make sense in the sense of being rational. Rendering a practice intelligible means, instead, making it seem natural. For Wittgenstein, a practice seems natural when an investigator locates it within the range of the humanly familiar, usually by comprehending it as an expression or development of something common to all mankind and occasionally by relating it to what he or she has learned about the vicissitudes of human life. As this formulation implies, Wittgenstein was not the relativist that many of his interpreters portray him as being. He was a staunch exponent of an extensive commonality in human situations and ways of acting and being which not only grounds but also constitutes interpersonal and intercultural comprehensibility. As he writes:

One sees how misleading Frazer's explanations are - I believe - by noting that one could very easily invent primitive practices oneself, and it would be pure luck if they were not actually found somewhere. That is, the principle according to which these practices are arranged is a much more general one than in Frazer's explanations and it is present in our own minds, so that we ourselves could think up all the possibilities. (Wittgenstein 1979, pp. 65-66; hereafter RFGB)

In fact, if the "meaning" (RFGB, p. 69) of a practice is what is grasped when that practice is rendered intelligible, then in the majority of cases the meaning of a practice consists in concretizations or elaborations of elements of human commonality.

Wittgenstein's criticisms of Frazer exemplify this conception of the task of interpretive social science. Frazer is convicted of two central mistakes. First, he misunderstands the nature of ritual in general, that is, he misidentifies the general element of commonality of which it is an elaboration. Frazer interprets ritual as instrumental action, thus viewing it as an elaboration of the purposiveness found in human existence, whereas Wittgenstein believed that ritual should be viewed

ELEMENTS OF A WITTGENSTEINIAN PHILOSOPHY 313

as "instinct-behavior" (RFGB, p. 72) expressive of certain aspects of the instinct component of our common humanity (see also Wittgenstein 1966, p. 53ff.; hereafter LC). Second, Frazer fails to make specific practices, e.g., the Beltane Fire Festivals, intelligible. When attempting to come to grips with what is going on when children ceremoniously "mak[e] a show" of burning a human being, Frazer retreats into a hypothesis about the historical origin of this practice. According to Wittgenstein, a historical hypothesis might fail to resolve Frazer's perplexity. Such a hypothesis brings historically antecedent phenomena into association with the festivals. In doing so, however, there is no guarantee that it will reveal the elements of commonality concretized or elaborated in the festivals, and this is what it must accomplish if it is to succeed in making these practices intelligible. Moreover, and most importantly, if the hypothesis does accomplish this, it is not the fact that the festivals originate in certain phenomena, but the resemblance of these antecedent phenomena to the festivals that is responsible for this success (see Section 3). In other words, if a historical hypothesis makes a practice intelligible, it does so not because it is a historical hypothesis, but because it happens to construct a context in which the practice can be seen as natural. Historical origins qua origins cannot make practices intelligible.

Of course, a social scientist might be interested in historical origins simply because he or she is interested in knowing where a practice or institution came from. More generally, an investigator might be interested in what brings certain phenomena about, i.e., their causes. An investigator who pursues these interests does not aim to make practices intelligible, but instead, to explain them causally. I do not think that Wittgenstein saw anything wrong with causal explanation and the search for origins and causes. He often characterized psychology and physiology, for instance, as investigations of the causes of activity. What Wittgenstein clearly did oppose is searching for causes when engaged in the interpetive enterprise.

2. SURFACE PHENOMENA AND EXPRESSIONS

The guiding element in my synthesis of Wittgenstein's idea is his notion of the surface of human life. Wittgenstein used the term "phenomenon" (usually Erscheinung, sometimes Phanomen) as a general expression for anything encounterable in experience. He wrote, for example, of


phenomena of electricity, of language, and of personal experience, where, in each case, the phenomena of X are the experientially encounterable appearances of X. The "surface of human life" is comprised, accordingly, by the phenomena of human life, the aspects of human life that are encounterable as such in experience. It embraces speech acts, behavior, gestures, and facial expressions, on the one hand, and thought experiences (e.g., Wittgenstein 1969, p. 8, hereafter BB), pains (e.g., Wittgenstein 1967, sec. 288; hereafter PI), and other conscious mental processes (seelische Vorgiinge), on the other.

By acknowledging the latter entities as surface phenomena, Wittgenstein differentiated himself from behavioralism, which restricts the surface of human life to behavior, the spatial-temporal appearances of human life in the external world. More like Kant, the surface of life comprised for Wittgenstein the totality of inner and outer, i.e., mental and behavioral appearances of life. Each individual, moreover, has sole experimental access to those elements of the mental surface of his own life that are not simultaneously expressed in behavioral phenomena. In outline, therefore, Wittgenstein followed tradition in acknowledging a fundamental duality among the appearances of life. He differed from tradition in arguing, first, that access to the mental surface of one's own life is an ability engendered through and certified by social interaction, and second, that mental phenomena such as feelings and pains must not be assimilated to external objects. It should be mentioned that Wittgenstein neither critically analyzed the idea that certain aspects of life are encountered as such in experience nor defended his views on which aspects these are. 1 Moreover, his notion of the surface of life does not obviously apply to the experience of acting.

An important feature of the phenomena of human life is that they express (ausdriicken) mental states, instincts, and experiences. Mental states such as beliefs, expectations, moods, and emotions are not, like conscious mental processes, surface appearances, that is, they are never encountered as such in experience: "The psychological verbs to see, to believe, to think, to wish, do not signify phenomena" (Wittgenstein 1970, sec. 471; hereafter Z); "'But "joy" surely designates an inward thing'. No. "Joy" designates nothing at all. Neither any inward or any outward thing" (Z, sec. 487). Mental states are, instead, expressed by surface phenomena (cf. Z, sec. 506). This means, first, that surface phenomena are the experiential, temporal or spatial-temporal appearances of these states and, second, that what there is in the world to


mental states is nothing beyond these phenomena.Wittgenstein described this relation by saying that appearances, in the circumstances in which they occur, are what such states "consist in". For example, what John's expecting Paul consists in, what there is in the world to his being in this state, might be his pacing to and fro in his living room, feelings of excitement and tension, and glances thrown at the clock on the wall. In general, mental state concepts reflect the interest that a group of people takes in certain patterns (Muster,' PI, p. 174), or looks, that reappear in the surface appearances of their lives. When a particular pattern appears in a given life, members of this group say that the person is in such and such a state. This state, however, is nothing above and beyond the appearances involved. Mental state concepts are simply linguistic expressions for how it is with people whose lives display certain looks (cf. PI, sec. 571).2

Surface phenomena are also able to express other surface phenomena. In such cases, the entities expressed are something above and beyoild the appearances that express them, and hence do not merely "consist in" the latter. The two most prominent examples of this second class of expressed entities are instincts and states of consciousness. For Wittgenstein, instincts are not "inner" states but primitive, pre-linguistic reactions (cf. Z, sec. 545; Wittgenstein 1975, sec. 545 (hereafter ~C); and Z, sec. 540-541). As such, they lie on the surface, and certain more complex nexes of action and speech are extensions and developments ofthem (Z, sec. 545; Wittgenstein 1976, p. 420; hereafter CE). These more complex nexes can be called "expressions" of these instincts, as suggested by Wittgenstein's description of ritual as ,"instinct-actions". Similarly, mental processes such as sensations of sound and taste, conscious thoughts (cf. Z, sec. 493), and pains (cf. Z, sec. 485) are surface phenomena, though not, like instincts, external behavior. They, too, however, can be expressed in behavior (cf. PI, sec, 288), especially in linguistic behavior such as "Oh, how beautiful!" or "Boy, that smarts".

A final important feature of Wittgenstein's picture of the surface of human life is that the phenomena of X form a particular sort of unity. In his words, they have a particular face (Gesicht), or physiognomy (on this topic, see Finch 1977, Chapter 11). When, for instance, Wittgenstein wrote that belief (Z, sec. 514) or doubt (CD, p. 419) has a particular physiognomy, what he meant was that the appearances of belief or doubt, in the circumstances in which they occur, have a certain

316 THEODORE R. SCHA TZKI

look to them (cf. PI, p. 174 on grief, and Wittgenstein 1983, vol. VII, sec. 17 (hereafter RFM) on experimentation). This thesis is an instance, of course, of the wider doctrine that instances of a given concept share a certain look, or face (cf. Z, sec. 376), by virtue of a host of similarities and resemblances between them.

Now, an important issue in the philosophy of the human sciences concerns the propriety of using one's own ordinary language mental state and action concepts when describing lives in other cultures. This issue seems to arise in an acute fashion on Wittgenstein's account of such concepts. For according to him, which faces strike (beruhren, Z, sec. 376) the members of a linguistic community in the phenomena of life (thus, coordinately, what mental state/action concepts they employ) depends on their needs and interests. If, consequently, basic or widespread needs and interests vary from community to community, the physiognomies that the members of different communities see in the appearances of life will similarly vary. But if so, then the faces that an investigator encounters in the lives of the people she studies may differ from the faces they encounter there. And if this is the case, then, since the use of mental states and action language reflects and itself propagates the physiognomies people see in appearances, the mental state and action concepts in terms of which her subjects carry out their lives will not correlate with her own such concepts. Describing their lives with her own such concepts, consequently, would only seem to misconstrue what they're about.

The problem with this argument, theoretically speaking, is that it fails to distinguish between describing people's lives and capturing what it is like to be one of them (see Runciman 1983). I shall not, however, elaborate this claim, because from Wittgenstein's point of view there is a tough of unreality to this theoretical discussion. As mentioned, he believed that human beings share an extensive array of situations and of ways of acting and being. From his remarks, mostly on Frazer, we can gather that he viewed this commonality as consisting in at least: (1) common basic needs and emotions; (2) similar physical environs (phases of the moon, seasons, and animal and plant life); (3) common facts of life (birth, death, and sex); (4) common gestures and primitive reactions; (5) common goals and interests; (6) environmental entities having the same significance (e.g., lions and thunder as threatening); and (7) common practices (e.g., teaching, disciplining, and celebrating). Where such commonalities are at work in the lives an investigator


studies, it follows: first, that faces familiar to the investigator from her own linguistic community often will appear in these lives; second, that this occurs because the same sort of thing is going on in these lives as goes on in lives in the investigator's community when the same face confronts her there; third, that the faces that strike the investigator will also most likely strike them; all meaning, fourth, that there is no problem with using the investigator's mental state anQ action language to describe their lives - doing so neither falsifies the appearances nor distorts what it is like to be one of them. Making these points leaves open, of course, the exact extent to which they are true in any particular situation. Since Wittgenstein, however, believed in extensive commonalities, he thought that cross-cultural description and understanding are far less problematic than they are sometimes portrayed as being (cf. PI, sec. 206). For him, phenomenal physiognomics does not relativistically confine mental state/action language to the linguistic community within which it has organically grown.

However, it is not clear whether Wittgenstein is entitled to assert the existence of most of these commonalities. If apprehension of physiognomies is relativized to a community's interests and needs, it is not obvious how an investigator can know that the familiar look she apprehends in a foreign community is not merely the projection of her own community's ways of understanding and seeing. Unless it is possible to transcend this relativization, it is impossible to be certain that most of the above commonalities exist. As we shall see in Section 3, Wittgenstein's account of understanding does not allow for such transcendence.

3. SPIRIT AND OVERVIEW

Making a practice intelligible requires uncovering the instincts, mental states, and experiences that are expressed in the surface phenomena constituting it. Wittgenstein formulated this idea by writing that what must be grasped in order to make a practice intelligible is the spirit (Geist) expressed in it (the "inner nature" of the practice, RFGB, p. 74). This spirit is not the significance the practice has for its participants (Cioffi 1981, p. 215), but the central instincts, mental states, and experiences it expresses. The reason why grasping spirit makes practices intelligible is that the instincts, etc., comprising it are, by and large, concretizations and elaborations of types of instincts, etc., shared by the investigator. Usually, therefore, grasping spirit is a means of "redis-

318 THEODORE R. SCHA TZKI

covering the I in the Thou" and thus of locating the practice within the range of the humanly familiar.

How did Wittgenstein think a social scientist should go about grasping the spirit expressed in a practice? He suggested that she observe the same procedure recommended to philosophers who seek to understand concepts and essence: constructing overviews (ilbersichtliche Darstellungen). The social scientist should collect toget)1er different practices related to the one to be understood in such a surveyable fashion that she sees the connections among them, that is, how they hang together: "This overview brings about the understanding which consists precisely in the fact that we see how [these practices] hang together (die Zusammenhdnge sehen). Hence the importance of finding connecting links" (RFGB, p. 69; translation modified).3 Underlying this recommendation is the idea that practices are "associated", that, e.g., the Fire Festivals of Europe, or the practices found in a given society, form "a multiplicity of faces with co, 'lmon features which continually emerge here and there" (RFGB, p. 74; translation corrected). Associated practices display a common physiognomy, and one grasps this physiognomy by gaining an overview over the practices. Grasping this physiognomy, however, is the same as grasping spirit. Thus, the inner nature of a practice is unveiled either by placing the practice in the context (Zusammenhang) of the wider culture in which it occurs, or by juxtaposing it alongside similar practices in different cultures (cf. RFGB, pp. 75-76). Notice that grasping the spirit of a practice does not require penetrating or digging below the surface phenomena of life. It requires, instead, gaining a proper overview of the surface. Notice, too, that, unbeknownst to Wittgenstein, it will sometimes be difficult for an investigator to construct an overview. In order to construct one, she must know which practices are "related" to the one under investigation; in many cases, she will know which practices these are only by understanding the spirit expressed in her object; and she can grasp this spirit only by constructing the overview.

This exposition reveals that Winch's analysis of cross-cultural understanding, in his article "Understanding a Primitive Society", does not describe Wittgenstein's views on this topic. Winch begins from the assumption that each society has its own concept of (or rules for) the intelligibility of human proceedings. He then argues that cross-cultural understanding requires that the social anthropologist bring his concept of intelligibility into relation with that of the society under investigation


in such a way as to create "a new unity for the concept of intelligibility having a certain relation to [his] old one" (Winch 1977, p. 176). In other words, understanding foreign practices necessitates achieving a wider view of human life which incorporates the subjects' and the investigator's ways of understanding human activity into a new perspective that goes beyond while retaining features of both. Hence, on Winch's account, commonalities serve merely as a ground upon which more expansive ways of understanding are erected. C~mmonalities do not suffice to ensure understanding but only make adequate, nonethnocentric understanding possible.

For the most part, this account is clearly not Wittgenstein's. As we have seen, in that majority of cases where the spirit of a foreign practice consists of elements or types of elements shared by the investigator, this commonality guarantees that grasping spirit is possible and that accomplishing this makes the practice intelligible. In this vein, Wittgenstein wrote:

All these different practices show that it is not a question of the derivation of one from the other, but of a common spirit. And one could invent (devise) all these ceremonies oneself. And precisely that spirit from which one invented them would be their common spirit. (RFGB, p. 80)

Further, when the spirit contains unshared elements or types of elements, then commonality, in conjunction with the investigator's knowledge of the vicissitudes of human life, will usually suffice to ensure that spirit can be grasped and that understanding can thereby be achieved. Only when the spirit is so incongruous with any sort of thinking the investigator knows of could there be room, in Wittgenstein's scheme, for Winch's Hegelianesque transformation of the investigator's concept (or principles or rules) of intelligibility. It is significant, however, that, although Wittgenstein considered (imaginary) cases of extremely opaque practices, he never suggested that we react to these practices by carrying out this sort of transformation. He suggested, instead, that we either renew our efforts to make sense of them using our old concept of intelligibility or abandon the effort and admit that we cannot understand them (see, e.g., his discussion of the wood trade at RFM, vol. 1, sec. 143ff.). To state Wittgenstein's views baldly: there is either sufficient commonality and hence understanding or insufficient commonality and, as a result, no understanding.

Wittgenstein's claim about insufficient commonality is obvious. Sub-


suming practices under universal features of human life, however, cannot provide much in the way of understanding. Such features are extremely general, and many different practices instantiate anyone of them. Acquiring more particularized and robust understandings of individual practices, consequently, requires some other, perhaps dialogical, process. This conclusion is even more compelling in cases where the spirit to be grasped contains unshared elements. ~oreover, as intimated at the end of Section 2, Wittgenstein's account of mental state concepts, when combined with the absence of a transformational model of understanding, makes it impossible both in general and in practice to distinguish between the apprehension of commonality and the projection of one's community's ways of understanding and seeing.

4. RULES

My discussion of Wittgenstein's views on rules focuses on the scope he accorded rules in human life. My aim is to show that interpretive social science, as he conceived it, is concerned with rules only to a limited extent. Wittgenstein's ideas on rules have been the subject of intense discussion; I shall make no effort, however, to respond to the literature. I shall also not examine the topic addressed by most of his remarks on rules, viz., what it is to follow an explicitly formulated rule, for instance, a rule of calculating.

It has become' dogma among some interpreters that Wittgenstein, although he never explicitly indicated this, thought that all language use, indeed, all behavior, is rule-governed. This dogma is a mistake. The idea that all behavior is rule-governed exemplifies a rationalist, or intellectualist, view of life. Wittgenstein, however, believed that underlying and running through the layers and realms of rational, intellectually-governed human conduct are a bedrock and veins of nonrational proceedings: ordinary life is incompletely governed by logoi. This thesis is reflected in his constant reminders that action, not thought, underlies language (e.g., GC, sec. 475; Z, sec. 391; and RFM, vol. VI, sec. 39), and that action is what underlies thought, observation and reason (e.g., Z, sec. 8; PI, sec. 456; GC, sec. 110, 204). Since action underlies reason, it follows that reason is not the measure of practices (CE, p. 417). This viewpoint also animates, of course, Wittgenstein's account of what it is to follow a rule: following a rule does not require an intellectual act (e.g., an intuition or interpretation)


concerning how to act, nor does it involve following a second rule that governs the application of the first. Rather, it simply consists in going on (reacting) in particular ways within certain "surroundings", i.e., in the context of what others do and the sort of instruction and correction that pertain to the behavior in question (see RFM, vol. VI, sec. 42; for an interpretation of rule-following similar to mine which also develops ideas resembling those discussed at the end of this section, see Hintikka, 1989). In any case, to view all behavior and/or language use as rulegoverned is to see a core of ratio lying below the surface of human life, and thus, to contravene Wittgenstein's admonishments in this context not to dig below the surface (RFM, vol. VI, sec. 31). Let us consider more precisely what his remarks imply about the scope of rules.

They suggest that Wittgenstein would have restricted the expression "following a rule" to situations in which either an explicitly formulated rule is "involved in" (BB, p. 13) behavior - e.g., consulted in the course of acting - or action results from training (instruction and correction) in which explicit rules are cited (cf. RFM, vol. VI, sec. 45). After all, he wrote that "following a rule is a particular language-game" (RFM, vol. VII, sec. 52, my emphasis) and that following a rule has a particular physiognomy (RFM, vol. VII, sec. 60). Wittgenstein recognized, however, that behavior and language use can be and are sometimes executed and learned without consultation with or citation of rules (e.g., DC, sec. 95, 140). Much of the time, accordingly, people are incorrectly described as "following rules". Some of what they do on those occasions, however, might still be, in Wittgenstein's words, "in accordance with a rule" (BB, pp. 87-98; and PI, sec. 54). For the notion of a rule is connected to the notion of a regularity (e.g., PI, sec. 208) and in at least two places, Wittgenstein acknowledged that it is correct to describe a practice as proceeding according to rules when "an observer can read these rules off from the practices of the game - like a natural law governing the play" (PI, sec. 54; and cf. BB, p. 98). In other words, behavior proceeds according to rules when it is possible to codify behavioral regularities in the form of rules. 4 Of course, a regularitycodifying rule, as Wittgenstein painstakingly worked out, is not the same as a description of a regularity. It is a proposition, merely with the form of a description, that is treated as a specification of how actions must turn out if they are to count as correctly performed.

The key point about regularity-codifying rules is that they often, if not usually, are not formulable. Wittgenstein explicitly drew this


conclusion in the case of the use of ordinary language concepts (e. g. , PI, sec. 84; and Z, sec. 350) on the grounds that any rule, formulated either by an actor or by an observer ,on the basis of a finite number of uses of a concept, will be unable pre facto to cover all possible acceptable uses. 5 Moreover, since any finite chunk of behavior displays an indefinite number of regularities, it accords with an indefinite number of "law-like" rules (see Rosen 1983). This meflns, however, that the behavior is no more in accordance with anyone or other of these rules (BB, p. 13). These arguments apply to all behavior regardless of whether it results from or involves explicit rules or is interwoven with correction and instruction that do not cite rules. Action cannot be encompassed by rules, and not only, as Winch claims, because what it is to follow a rule cannot be understood as grasping a rule for the application of the rule (Winch 1958, p. 55).

Since observation does not usually yield rules governing language use, and since actors are unable to formulate such rules (BB, p. 25), Wittgenstein asked, "What meaning is the expression 'the rule by which he proceeds' supposed to have left to it here?" (PI, sec. 82). In other words, hasn't it become pointless to describe the actions concerned as proceeding according to rules? Of course, one might feel compelled, especially in the presence of correction and instruction, to insist that there must be rules at work keeping us consistent with and intelligible to one another. This temptation merely expresses, however, our dissatisfaction with the surface phenomena. Instead of being content simply to note the surface and to say "This is what we do", we insist on penetrating the surface to uncover the logos that secures our performances. For Wittgenstein, however, there is no such stratum of reason. There is only the surface (and a physical substratum). "Our mistake is to look for an explanation where we ought to look at what happens as a 'primordial phenomenon' (Urphanomen). That is, where we ought to have said: this language-game is played" (PI, sec. 654; translation amended).

For Wittgenstein, therefore, neither linguistic nor nonlinguistic behavior is generally governed by rules. (It is possible to construct an argument pertaining to nonlinguistic behavior that parallels the one just presented concerning linguistic behavior.) People follow rules when rules are an explicit feature of the surface; and people can be said to act in accord with rules in the exceedingly rare cases where behavioral regularities are subject to comprehensive codification in a set of unique


rules. Notice that it follows, I do not think paradoxically, that in most of the cases where people follow rules, they do not act in accordance with rules.

Incidentally, I think that the strongest argument for the ubiquity thesis is grounded in the connections Wittgenstein drew between language and regularities (e.g., PI, sec. 207), on the one hand, and between regularities and rules (e.g., PI, sec. 208), on tqe other. If anything is to be recognizable by us as language it must display regularities; and, as we've seen, one type of rule is regularity-codifying formulations. It seems to follow, accordingly, that rules exist wherever there is language (cf. DC, sec. 61-62; and also Z, sec. 612). This argument fails, however, to confront the above problem: How does one formulate unique sets of rules that cover all possible (acceptable) uses of a given concept? It might also be mentioned that John McDowell has pointed to the following statement (at RFM, vol. VI, sec. 28) as evidence for the ubi4uity claim: "Following according to the rule is FUNDAMENTAL to our language-game. It characterizes what we call description" (McDowell 1984, p. 341; see also Kerr 1986, p. 110). However, the opening paragraph of this section addresses the issue of how someone knows that the color he sees is red; and, in the Blue Book, Wittgenstein characterized an ostensive definition of the word "yellow" as a "rule of the usage of the word" (BB, p. 12, cf. p. 90). Now, an ostensive definition is an example of an explicit rule that is cited in the teaching of language. Using color words, accordingly, is correctly described as "following a rule". Hence, I do not think that Wittgenstein was making a general point about all description whatsoever, merely one about the description of colors in particular.

The consequences of this discussion of rules for interpretive social science are straightforward. Explicitly formulated rules are surface phenomena. As such, they help comprise the set of surface phenomena, the spirit of which an investigator aims to grasp. I do not think that it is correct, however, to construe either explicitly formulated rules or regularity-codifying rules as part of the spirit of any practice. Not only did Wittgenstein nowhere write or imply that surface phenomena "express" rules of any sort, but regularity-codifying rules do not pertain to surface phenomena until they are formulated. Thus, although rules are part of interpretive social science's object of study, they are not part of what the social scientist aims to grasp (spirit) in order to understand this object. Making practices intelligible, an enterprise which, as


we've seen, is keyed to the surface, thus concerns itself with rules only to the extent that rules are surface phenomena.

This conclusion runs counter to the most widely acknowledged "Wittgensteinian" philosophy of social science, that of Winch's (see also, e.g., Apel 1967). In Winch's account, understanding a practice requires a grasp of the usually nonexplicit rules governing it. For, a practice is defined as a regularity in action; regularities are "constant recurrence[s] of the same"; what counts as the same is determined by rules; and the identity-establishing rules definitive of any given practice are the largely nonexplicit ones followed by the people carrying it out. In Winch's view, therefore, understanding a given surface phenomena (a practice) requires a grasp of something beneath the surface which governs it (nonexplicit rules) (Winch 1958, pp. 83-87). Winch is wrong, however, to maintain that, in Wittgenstein's account, nonexplicit rules govern practices, more specifically, that what practices are is defined by nonexplicit rules that determine what counts as "the same". Essentially the only rules that pertain to practices are explicit ones. And even where explicit rules are at work, it is action (what we do) that ultimately determines what "the same" is (e.g., RFM, vol. VII, sec. 40). To state all this in terms of meaning: since interpretive social science aims to uncover meaning, it does not strive to uncover rules, for rules do not determine the meanings of practices.

5. CONCLUSION: DESCRIPTION AND EXPLANATION

As we have seen, the comparative, context-constructing method Wittgenstein advocated for interpretive social science is descriptive in nature. Executing it consists in arranging descriptions of phenomena that are related to the practice under investigation in such a way that there results a grasp of the spirit of the practice and the practice is thereby rendered natural. This procedure does not require explanations or hypotheses about origin, although as indicated, explanations and hypotheses can help construct the context (see Cioffi 1981, pp. 219-20). Furthermore, since Wittgenstein tied theories to hypotheses and explanations (see, e.g., PI, sec. 109; and BB, p. 18), it follows that theories, too, are not required in interpretive social science.

This does not mean, however, that Wittgenstein opposed the use of explanations, hypotheses, and theories in the human sciences. Both overviews and theoretical explanations have secure places in the


Geisteswissenschaften if different components of this enterprise strive to realize different cognitive achievements. And sure enough, Wittgenstein acknowledged that physiology and psychology have legitimate explanatory work to perform. What he opposed was the idea "that these explanatory sciences provide the sort of comprehension sought after in interpretive social science (or in aesthetics and philosophy). I want to conclude by suggesting how the above account of the sprface of human life identifies the focus of these explanatory efforts.

The surface phenomena of human life that Wittgenstein construed as expressions of mental states and processes have causes, where by "cause" Wittgenstein meant a connection, possibly not open to view (BB, p. 6), that is established either by experiment and statistics or by tracing a mechanism (LC, p. 13f.; and CE, passim.). He spoke, in this vein, of the causes of behavior (BB, pp. 11-12, 15), the causes of word association (PI, p. 216), the causes of pain (Wittgenstein 1968, sec. 235; hereafter NFL), and the causes of the experience of seeing an aspect (PI, p. 193, ct. pp. 201, 205). All these effects are surface phenomena. He also spoke of the causes of certainty (RFM, vol. VI, sec. 47; DC, sec. 429; and PI, sec. 325), of being able to follow a rule (PI, sec. 217), of belief (Z, sec. 437), of fear (PI, sec. 476), and of sadness (Z, sec. 509). In these cases, I take him to have been speaking of the causes of those surface phenomena that are expressions of these mental states. Since attributions of causality are, for Wittgenstein, hypothetical explanations (BB, pp. 15,88; and PI, sec. 475), by using the notion of cause as he did, he indicated that the entire apparatus of hypothesis, explanation, theory, experimentation, and statistics can be brought to bear on surface phenomena. We thus find him referring in a matter-of-fact and uncritical manner to psychological and physiological experiments, explanations, and causation (e.g., PI, sec. 412, 493, pp. 203,212; BB, pp. 6,88; LC, p. 20; and NFL, p. 235).

As is well known, the major question Wittgenstein raised about these sciences is whether they can become systematic. In any science, the "craving for generality" expresses itself in the desire to reduce the explanation of events to the smallest number of primitive laws (BB, p. 18). Against this, Wittgenstein stressed the variety of causes, e.g., of dreams, play, and punishment (LC, pp. 47, 49, 50). There also exists the familiar issue of whether there is any regularity to the causes of the variety of phenomena that count as expressions of a given mental state; that is, whether there exist type correlations between, say, physiological


processes and instances of people being in that state. Wittgenstein was skeptical about the likelihood of such correlations. Our use of mental state and action concepts is keyed to physiognomic features of the surface, and these concepts are learned through observation, participation, training, and correction, all of which are likewise keyed to the surface. It is true that some of the causality at work in human activity also lies on the surface, e.g., training bringing <;lbout "the phenomena of understanding, obeying etc." (BB, p. 12, see also p. 111). But to the extent that this causality lies below the surface, as for instance, in the case of physiological causality, we should not expect physiological regularities to correlate with physiognomies and the patterns of phenomena that are expressions of a given mental state.

Earlier I criticized Wittgenstein's accounts of what is involved in and how social scientists should go about understanding actions and practices. I also indicated possible problems with his notion of the surface of life. I believe he is correct, however, that at least most of the rules governing human life are explicit and that behavior and conscious mental phenomena have causes.

APPENDIX: WITTGENSTEIN AND GERMAN PHILOSOPHY

The sketch of a philosophy of the human sciences presented in this paper substantiates and further develops the idea that Wittgenstein was a twentieth century descendent of what Karl Mannheim called (early nineteenth century) "conservative thought" (Mannheim 1971, Chapter 5; see Nyiri 1976 and 1982; and Bloor 1983, Chapter 8). Of the features attributed by Mannheim to this style of thought, those most prominently displayed by Wittgenstein's views on human-social reality and human science are emphases: on physiognomic as opposed to constructive understanding; on concreteness as opposed to abstractness; on particularity as opposed to systems; on the nonrationality as opposed to the rationality of human life; and on understanding norms (rules) via the actual instead of vice versa.

Moreover, since Mannheim identified Lebensphilosophie as the central late nineteenth and early twentieth century descendent of conservative thought, it is of particular interest to note the apparent influence exerted upon Wittgenstein by this school of thought. Lebensphilosophie was influential in the German-speaking world, both when Wittgenstein grew up and when he lived in Austria in the teens and twenties. One


of its prominent doctrines was the neo-Hegelian idea that the products and sensible appearances of life manifest, embody, or make present mental/spiritual/intellectual contents and states. Wittgenstein's idea that surface phenomena "express" mental states is a version of this doctrine (though he did not follow most life-philosophers in according these contents and states an "ideal" existence in contrast to the "real" existence of their spatial and temporal bearers). Wittgenstein even occasionally used one of this school's terms of art: "L~bensiiusserung" (e.g., Z, sec. 110,534).

It seems likely, furthermore, that the life-philosopher Oswald Spengler, whose direct influence Wittgenstein acknowledged (Wittgenstein 1980, p. 19), was the concrete link between Wittgenstein and Lebensphilosophie. Wittgenstein appears to have derived (at least) two important notions from Spengler: the idea that the appearances of X have a particular physiognomy, or look, and the idea that comprehending a practice is accomplished by grasping, through the construction of an overview, the spirit expressed in it. The first idea strongly resembles Spengler's notion of the "habitus" of X: "the type of external appearance pertaining to X alone", the "character and style of X's stepping-into" the spatial realm of what has become (Spengler 1918, p. 158). The second idea resembles Spengler's notion of physiognomics (cf. RFGB, p. 69), a procedure in which the meaning of an individual entity, the element of the "inner soul" it expresses, is grasped by incorporating the entity into a living, inwardly felt unity constructed by comparative methods (RFGB, pp. 146-54).6

NOTES

1 Wittgenstein did not make any specific comments about the notion of a phenomenon. He seems to have believed, however, that the appearances encountered in experience are in some way independent of the linguistically-expressed conceptual resources of, and hence the descriptions given by, the people who encounter them. Appearances, that is, are entities with a being of their own. Moreover, people can apprehend what these appearances in themselves are. One of the many remarks suggesting that this was Wittgenstein's view is the famous passage (at PI, sec. 90) where he equated the possibilities of phenomena with the kind of statements we make about them. At first sight, this passage appears to contravene my reading. Notice, however, that Wittgenstein wrote, "the kind of statements we make about phenomena" (my emphasis). This formulation implies that appearances are some way and that we make statements about them on the basis of this. The kind of statements we make about phenomena do not define the possibilities of how phenomena in themselves are, but instead, the possibilities of what for us these phenom-


ena are instances of, given how they in themselves are. How appearances in themselves are also determines what aspects of life are encountered as such in experience. 2 It is worth adding that Wittgenstein maintained that it is possible to see in appearances the mental states they express. It is usually not the case, consequently, that a person learns that someone else is in a given state by first observing an appearance and then making an inference to the presence of the state (though, of course, this process also at times occurs) (See Z, sec. 220, 225). 3 Incidentally, similar ideas appear in Wittgenstein's remarks on psychoanalysis (see Le, pp. 45-51). 4 I am unclear whether Wittgenstein thought that only those regularities that occur in certain surroundings, e.g., amid correctional and instructional behavior, can be correctly codified in rules. 5 This argument implies that at least most of the rules cited when teaching language do not adequately represent the linguistic practice they are used to help inculcate. I write 'most' because passages, such as PI, sec. 558 and Z, sec. 350, suggest that Wittgenstein thought that rules can sometimes be formulated. 6 An earlier version of this paper was presented in May 1988 at the Inter-University Center of Postgraduate Studies in Dubrovnik as part of a course on Wittgenstein and the Philosophy of Culture. I wish to thank the course participants for their comments and the course organizers, Tore Nordenstam and Kjell Johannessen, for the invitation.

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Bloor, David: 1983, Wittgenstein: A Social Theory of Knowledge, Columbia University Press, New York.

Cioffi, Frank: 1981, 'Wittgenstein and the Fire-Festivals', in Irving Block (ed.), Perspectives on the Philosophy of Wittgenstein, MIT Press, Cambridge.

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Department of Philosophy and Committee on Social Theory University of Kentucky Lexington, KY 40506-0027 U.S.A.

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