jaakko hintikka - existence and predication from aristotle to frege 2006

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Philosophy and Phenomenologicul Research

V o l . LXXII I , N o. 2, September 2006

Existence and Predication from

Aristotle to FregeRISTO VILKKO

University of Helsinki

JAAKKO HINTIKKA

Boston University

One of the characteristic features of contemporary logic is that it incorporates the

Frege-Russell thesis accord ing to which verbs fo r being are multiply ambiguous. This

thesis was not accep ted before the ninete enth century . In Aristotle existen ce cou ld not

serve alone as a predicate term. However, it could be a part of the force of the predi-

cate term, depe nding on the context. For Kant existence could not even be a part of the

force of the predicate term. Hence, after Kant, existence was left homeless. It found a

home in the algebra of logic in which the operators corresp ond ing to universal and par-

ticular judgments were treated as duals, and universal judgments were taken to be rela-

tive to some universe of discou rse. Because of the du ality, existential qu antifier exp res-sions came to express existence. The orphaned notion of existence thus found a new

home in the existential quantifier.

How did modem logic evolve? One of the many interesting aspects about this

question is that i t has not been asked more often and more emphatically even

though there is no clear answer to it to be found in the literature. Some phi-

losophers might say that what we today call logic was discovered by Frege in

1879 and add that of course genuine discoveries cannot in the last analysis be

explained. If so , we presumably ought to emulate Michael Dummett (1973;199 1) and examine Frege's achievement systematically rather than histori-

cally, among other things looking away from its roots in earlier philosophy

and earlier logic. However, this way of looking at Frege's accomplishments

has been challenged repeatedly, most determinately perhaps by Hans Sluga in

his book Gottlob Frege (1980) and by Gordon Baker and Peter Hacker in

their Logical Excavations (1984). Independently of this particular contro-

versy, one's legitimate curiosity should even after a Dummettian putdown be

tickled by the fact that much of the same logic was discovered independentlyand about the same time by Charles S . Peirce. Is this merely a coincidence?

A good historian should not believe in coincidences any more than a good

detective

EXISTEN CE AND PREDICATION FROM A RISTOT LE TO FRECiE 359



Others might prefer to try to trivialize the question. Is not logic one and

the same throughout its history? What is supposed to be so novel in Frege

and Peirce? The stock answer seems to be: the theory of quantifiers. Th is

theory is the gist of what Frege and Peirce independently discovered. How-

ever, it may be objected that quantifiers were studied from the very beginning

of Western logic. Already in Aristo tle‘s logic the main ingredients were theideas of universality (‘every A ’ ) and particularity (‘some R ’ ) . If this is the

main part of the story, the genesis of modern logic should be viewed simply

as a continuation of the older traditions in logic which can be traced back

ultimately to A ristotle rather than as a discovery of something radically new.

This po int of view emphasizes that it was Aristotle who laid the foundations

to formal logic, whereas Frege was in position only to develop logic further.

One reason that some philosophers might have for not examining more

closely that background of modern logic is an underestimation of the substan-

tial differences between today’s mathem atically-oriented logic and traditional

philosophically-oriented logic. There nevertheless are differences, some of

them quite striking. For exam ple, the usual way of understanding logic

merely as the doctrine of the laws of correct inference, that is, as the doctrine

of syntax and semantics of exp licit languages, would not have appealed even

to most of 19th century logicians (see Vilkko 2002).

One more specific difference concerns the counterpart or counterparts in a

logical notation to natural language verbs for being, such as the English is,

the German ist, and the ancient Greek estin. With some exceptions, there has

recently been a consensus to the effect that such verbs are multiply ambigu-

ous between the is of predication, the is of existence, the is of identity, and

the is of subsumption. The assumption of such an ambiguity will be called

here the Frege-R ussell ambigu ity thesis, for indeed the currency of this

assumption is due largely to these two logicians. It is built into the very

notations that have been used in logic since their time, in that the allegedly

different meanings are expressed in the usual logical notations differently. The

i s of identity is expressed by the identity sign a =6 , the is of predication byjuxtaposition, or, more accurately speaking, by a singular term ’s filling the

argument slot of a predicative expression P(a) , he is of existence by the exis-

tential quantifier ( 3 ) P ( x ) , and the i s of subsumption by a general conditional

of the form (Vx)(x E S 3 x E P ) . In a introductory logic course students are

not on ly taught to use this no tation but given to understand that the corre-

sponding distinctions are an unavoidable aspect of all valid logic. It is highly

important to understand what the precise import of the Frege-Russell thesis

is. It is often presented as an eternal and immutable logical truth that anylogician at any stage of the history of logic heeded or ought to have heeded.

For example, there are scholars who have criticized Plato for not distinguish-

ing the is of predication from the is of identity. When Michael Frede (1967)

360 RlSTO VOLKKO A N D J A A K K O HINTIKKA



argued, in his Pradikation und Existenzaussage, that Plato did not, i n the

Sophist, distinguish predicative and existential senses of estin from each

other, at least one reviewer took him to accuse Plato of a major logical blun-

der.

In this essay, we shall concentrate on the predicative and existential senses

of the verb is and largely disregard the development of the other senses. Any

historical discussion of the central questions of logic will have to be con-

ducted agains t the background of Aristotle 's logic , and we shall accordingly

start with a brief analysis of his treatment of verbs for being. This leads

imm ediately into philosophical questions,

Th e attribution of the Frege-Russell thesis to earlier philosophers, includ-

ing ancient Greek ones, has been encouraged by w hat is known among classi-

cists as Herm ann's rule (Herm ann 1801: 84-85). What i t purports to do is to

use the Greek accent system to make some of the Frege-Russell distinctions

in ancient Greek language. In the beginning of the 19th century the German

philologist Gottfried Hermann drew a distinction between the signification

which requires existence as an additional predicate and the signification which

already contains the predicate. According to Charles Kahn, the former was

expressed by means of th e enclitic accent ( ~ T I ) ,hile the latter one was

expressed by the orthotone accent ( ~ ( JT I ) n the first syllable (Kahn 1972:

420). The reason why Hermann's rule favors the Frege-Russell ambiguity

thesis is that on each occasion it allows only one of the alleged Frege-Russell

senses to be present. Hence it is easily taken to imply an ambiguity betweenseparate senses of estin.

It might nevertheless seem easy to dismiss H ermann 's rule as irrelevant. It

is not controversial to maintain that verbs for being have different uses. What

the Frege-Russell ambiguity thesis amounts to is a proposal to explain these

differences in use as being due to the ambiguity of these verbs, that is, to

their having several separate meanings rather than, e .g . , differences due to the

context. Why could we not simply claim that Hermann's rule is a way of

highlighting unproblematic differences in use? A rejection of the Frege-Rus-sell ambiguity thesis allows for the possibility that in some contexts we

cannot distinguish the allegedly different Frege-Russell meanings from each

other and perhaps are forced to say that more than one alleged Frege-Russell

mean ing is present there. Indeed, Jaakko Hintikka (1979; 1983) has argued for

the former possibility in terms of a game-theoretical treatment of the seman-

tics of is. What is more, we will see that the latter situation can be found i n

Aristotle. We shall return to H ermann 's rule later on.

In view of the widespread acceptance of the Frege-Russell ambiguity the-sis it may be surprising to realize, as Hintikka (1979) has pointed out, that

the Frege-Russell thesis is not an unavoidable part of either logic or the

seman tics of natural language. What is true is that natural language verbs for

EXISTENCE AND PREDICATION FROM ARISTOTLE TO FREGE 361



being are used in several different ways. What the thesis does is to attribute

those differences in use to an ambiguity of a single word, instead of for

instance construing them as being due to differences in the context in which a

verb for being occurs. Hintikka has in fact presented an explicit semantical

treatment of English quantifiers and a number of related notions within the

framew ork of game-theoretical seman tics without assuming the Frege-Russell

thesis. (See Hintikka & Kulas 1985.) He has also pointed out that in some

particular cases the Frege-Russell thesis distinction simply cannot be made,

and also showed that the game-theoretical treatm ent of natura l language quan-

tifiers is closely related to Aristotle's doctrine of catego ries.

What is also striking and what makes these issues relevant to the history

of philosophy and history of logic is the fact that no philosopher before the

nineteenth century embraced the Frege-Russell thesis. Adm ittedly, attempts

have been made to find some of the Frege-Russell distinctions in Plato,

among others by A ckrill (1957) and by van Eck (2000).These attempts have

been persuasively criticized among o thers by Frede (1967) and by Brown (an

unpublished lecture). These discussions have been obscured by the same m-son as the import of Hermann's rule, viz. by a failure to distinguish a words

having different uses from its having different meanings, that is, from its

being ambiguous.

What is more, almost no earlier philosopher even seems to have consid-

ered the Frege-Russell distinction as a possible position. An exception is

Aristotle, who in his Metaphysics does consider the relation of assertions ofpred ication, existence and identity to each other, only to reject any sharp dis-

tinction, writing as follows:

...'one man' and 'man' are the same thing, so are 'existent man' and 'man',and the doubling of the

words in 'one man and one existent man' does not express anything different... and similarly

'one existent man' adds nothing to 'existent man' .. M e t . IV , 1003b26-31.)

Thus Aristotle in effect rejects the Frege-Russell ambiguity thesis. In a full

Aristotelian use of es t in , the first three Frege-Russell senses are present as

components of a single unambiguous force of estin. This leads Aristotle into

difficulties because the different Frege-Russell senses behave differently vis-8-

vis different logical rules. For instance, identity is transitive, while predica-

tion is not always transitive . Part of the way Aristotle tries to cope with

these problems is to admit that on different occasions different Frege-Russe ll

senses m ay be absent from the force of estin. For instance, if I say 'Homer is

a poet' ("Opqpos ~ T T ITO I~T~~S ),t does not imply 'Homer is' ("O~~rpo$

~OTI (V) )

which in the ancient Greek would have been a way of saying 'Homerexists.' (See De int. 11, 21a 20-30.) Here is the existential component of the

former occurrence of estin. Scholars have in fact tried to puzzle out when it is

that Aristotle assumes the existential force to be present. For instance, J. L .

36 2 RISTO V O L KK O A N D J A A K K OH I N T I K K A



Ackrill (1963) has criticized the Homer example exactly because of its con-

fusing nature with regard to existential import. Scott Carson (2000) has

defended the importance of this example for its context in De interpretatione

and claimed that it lays stress on certain highly important aspects concerning

the nature of the verb ‘to be’ in ancient Greek philosophy. Hintikka and

Halonen (2000), in their turn, have argued that the presence of existentialforce in a potential syllogistic premise may not depend on this premise alone,

but on the stage of the process of constructing an Aristotelian science which

we are considering.

Likewise, in a syllogistic premise like

every B is A

the verb for being can either have existential force or not. Whether or not it

does depends on the term A . In this sense, in any syllogistic science, existen-tial import commitments are carried by the predicate terms of syllogistic

premises. This import can accordingly be proved by means of an ordinary

syllogism as one of its by-products. In other words, Aristotle could argue as

i t were as follows:

every B is an A (and exists)

every C is B

ergo:every C is an A (and exists)

Here B need not be assumed to have existential force. In contrast, the follow-

ing pattern does not represent a valid syllogism according to Aristotle’s

lights:

every B exists and is an A

every C is a B (and exists)

e r go : every C is an A (and exists)

Hence, in a syllogistic science existence need to be assumed only for the wid-

est (generic) term characterizing the purview of that sc ience . For all other

terms in that science, existence can be proved syllogistically. And this is

precisely what Aristotle says in his Analytica posteriora (A 10, 76a 31-37;

B 7, 92b 12-23). Whether or not the predicate term of given syllogisticprem ise of an Aristotelian science can be assumed to have ex istential force

therefore depends on whether the scientist has already proved this force , as

Hintikka and Halonen (2000) have argued.




What this means is that in Aristotelian scientific statements, i . e . syllogis-

tic premises, the existential force was canied by the predicate term. In this

sense, existence was for A ristotle a predicate or, rather, a part of the force of a

predicate. This force depends on the context. Existence could not serve alone

as a predicate term, but this was only because it would have been too broad a

term, not restricted to any one category and hence not an essence of anything.

In so many words: “Existence is not the ousia of anything” (An . post . B 7 ,

92b 13-15).

This statement calls for an explanation. The usual translation of ousia

(ojaia) is essence, and hence the quoted passage might seem to say merely

that mere existence does not distinguish the properties of any class of entities

from those of the others. However, Aristotle’s reasons for his statement are

quite different. For Aristotle, an essential predication is one that specifies the

class of entities to which it applies. Existence cannot be an essence of any-

thing, because a ll existing entities would form a class comprehending entities

from different categories. And such classes are for Aris totle conceptually

impossible, for the categories are precisely the largest classes that we can

coherently consider.

In order to avoid misunders tandings, it m ay be in order to point out that

we are employing the term ‘existen tial force’ in a sense different from its

most comm on use to indicate the nonem ptiness of a term . Here it means the

presence of the existential sense of a verb for being. In a syllogistic context,

i t amounts to the claim that all (possible) instances of a term actually exist.Since predicatively used terms did not always have existential force, the

Aristotelian quantification phrase ‘for some’ did not express actual existence.

If Aristotelian syllogistic was translated into modern logical notation and

interpreted in the same way as this notation, particular quantifier phrases

could only be taken to range over some kind of merely possible objects, not

necessarily over any existing ones.

But it is not the only remarkable fact here that in Aristotle’s syllogistic

logic the predicate term carries some of the existential force of a judgment.An equa lly remarkab le fac t here is that it carries in som e sense and with cer-

tain qualifications all of the ex istential force. One qualification needed in this

statement is that it has to be restricted to actual existence. A ristotelian quanti-

fier phrases like ‘every B’ or ‘some C’ should not in the first place be

thought of as m odern quantifiers ranging over the class of B’s or the class of

C‘s, much less over the class of all actually existing entities of the appropri-

ate category. When Aristotle puts forward a syllogistic premise like ‘every B

is A ,’ he does not mean merely that every actually existing B is A . If we triedto think anachronistically of Aristotle’s syllogistic premises in terms of quan-

tifiers ranging over certain entities, we would have to say that their values are

some sorts of possible individuals. How ever, this is not how Aristotle looked

364 RISTO VOLKKO A N D J A A K K O HI N T I KKA



upon h is syllogistic premises. For him, they expressed primarily relations of

the forms expressed by the subject and the predicate. A premise like ‘every B

is A ’ says that it is a fact about the form expressed by the term B that it is

always accompanied by the form expressed by A . And since a premise like

‘every B is A’ is thus thought of as dealing in the first place with relations of

forms, the sets of entities instantiating these forms becom e largely irrelevant.

Th e force of such a prem ise certainly is not exhausted by speaking of rela-

tions of inclusion between the se t of entities actually satisfying B and the set

of entities actually satisfying A . Hence the twentieth-century logical nota-

tion, which is based on the idea of quantifiers ranging over a class of values,

can be applied to Aristotle only with considerable care.

It may be true that Aristotle’s logic, like modem logic, dealt with quanti-

fiers, as we have already seen. But what we have seen shows that he dealt

with them in a way radically different from ours, in particular as far as the

relation of quantifiers to the ideas of actual existence and actual universality

are concerned.

This analysis of Aristotle’s logical assumptions puts into perspective one

of the major questions concerning the origins of twentieth-century logic.

Even though the development of modern logic certainly “cannot be seen as a

tree growing from a single seed,” as Volker Peckhaus (2000) has recently

written, it has become commonplace to say that the starting point of modem

logic is the discovery of quantifiers by Frege in 1879 and by Peirce during the

early 1880s. Among other scholars, W. V. Quine (1995) has dated modemlogic from here. According to him, logic became a substantial branch of

mathem atics only with the emergence of general theory of quantification. But

what can be meant by the discovery of quantifiers? Quantifiers are roughly

speaking the logical counterparts to the expressions ‘for every’ and ‘for

som e.’ But the behavior of such expressions were part and parcel of what

Aristotle was trying to study in his syllogistic. Hence we face the question:

What else is new here? Aristotle already studied quantifiers, how could they

be the great novelty of F rege’s and Peirce’s logic?Here a contrastive comparison with Aristotle shows what the so-called

discovery of quan tifiers really amounted to. Earlier i t was seen that according

to him in a premise of a scientific syllogism the existential force (if any) was

carried by and large by the predicate term. The particular quantifier of Aristo-

telian logic was not for him really an existential quantifier. In Frege and his

successors the ex istential force was canied by and large by the ex istential

quantifier. One reason for the second qualification is that in Frege and most of

his imm ediate successors existen tial force was also carried by singular termslike proper names, which were assumed to be nonempty. This unnecessary

assumption was eliminated when logicians began to develop, in the late

EXISTENCE AND PREDICATION FROM A RISTOT LE TO FREGE 365



1950s, so-called free logics, beginning with H intikka (1959), and Leblanc and

Hailperin (1959).

The essential novelty of Frege‘s new log ic is therefore not the notion of

quantifier but the location of the existential import in a logical formula. In

the form of a suggestive but oversimplified slogan, one can say that for Aris-

totle existential import was carried by the predicate term while for the mod-

erns it is cam ed by the existential quantifier. This is crucial difference

between Aristotelian logic and modern logic. The profound character of this

difference cannot be exaggerated. There are reasons to be deeply skeptical in

most cases about presumed cases of conceptual incom mensu rability of scien-

tific, mathematical or logical theories. Here we nonetheless have a fairly clear

example where the same words are used so differently in two theories that no

direct comparison of the two theories is possible. Y et there is no insuperable

difficulty about discussing both of them rationally and even relating them to

each other in more complex ways.

Now how did this fundamental change come about? In order to answer this

question, it is helpful to use as a clue the question of the developm ent of an

apparently different aspect of contemporary logic, viz . of the Frege-Russell

thesis of the ambiguity of verbs for being. This thesis is sometimes attrib-

uted to Kant. In his book Kant’s Analyt ic (1966), Jonathan Bennett goes so

far as to speak of the ‘Kant-Frege thesis.’ H e claim s that “the quantified

treatment of existence-statements, formalized by Frege a century later, was

largely pioneered by K ant in the Dialectic” (p. 199). This attribution is inap-propriate i n the literal sense of the thesis. Kant never claimed that verbs for

being like the Germ an ist are ambiguous. Indeed, in addition to the notions of

‘existence’ (‘Dasein,’ ‘Existenz’) ,‘being’ (‘Sein’) ,and ‘is’ (‘ist’) , one finds

from his vocabulary also the unambiguous notion of ‘positing’ (‘setzen’).

Already in 1763 Kan t declared that “the notion of positing is quite simple and

altogether of one kind w ith the notion of being” (K ant 1763: 73), and later,

in the First Critique, he wrote that

‘Being’ s obviously no t a real predicate; that is, it is not a conce pt of something which could be

added to the concept of a thing. It is merely the positing of a thing, or of certain determinations,

as existing in themselves. Logically, it is merely the copula of a judgment. The proposition,

‘Cod s omnipotent‘, conta ins two conc epts, e ach of which has its object-God and om nipo-

tence. The sm all word ‘is’adds no new predicate, but only serves to posit the predicate in its

relation to the subject. ( K rV , B626-627.)

This implies among other things that ‘God is omnipotent’ does not logically

imp ly for Kant that ‘God is.’ What is more, in the title of the f irst paragraph

of the aforementioned precritical essay of 1763 Kant puts i t short and clear:“Existence is by no means a predicate or a determination of any particular

thing” (K ant 1763: 72; cf. Hintikka 1981).

366 RISTO V O L K K O A N D JA A K K O H I N T I KK A



The distinction between predication and Existenzaussage was for Kant a

difference betw een two uses of the notion of being-a relative and an absolute

one. This is not only different from the distinction of Frege and Russell; it is

incompatible with their distinction.

It is often said that Kant rejected the idea tha t ‘existence is a predicate.’ In

a strictly literal sense, this marks no difference from Aristotle, for whom

existence could not be the essence of anything. But there is a fundamental

difference between the two. Existence could not be a predicate for Aristotle

because it was too general a notion not restricted to any one category, i.e . , to

any one class ofp red icabilia as any decent predicate must. In contrast, if we

examine what Kant meant, we can see that his claim was far stronger than

what the slogan ‘existence is not a predicate’ expresses. He argued that exis-

tence cannot even be a part of the force of a predicate term. As he put it, exis-

tence does not add anything to the concept expressed by the predicate. Hence,

in a judgment of existential, e . g . ‘God exists,’ a subject is taken as i t was

ready made with its essential predicates and merely assert that this particular

complex of predicates is in fact instantiated in reality. As Hintikka has writ-

ten: “Here existence is not one of the configurations of predicates; i t is what

is asserted of the configuration” (Hintikka 1981: 134).

Still other aspects of Kant’s philosophy are relevant here. The history of

the interrelation of the ideas of existence and predication is connected with the

history of the theory of categories . In Aristotle, his theory of categories

encourages strongly the idea that the existential and predicative uses of verbsfor being are parallel. But what precisely is his theory? The answ er is not

obvious, and it is not even obvious what it is that his categories are supposed

to categorize. The distinction between the different categories appears some-

times in Aristotle as a distinction between the largest genera w hose m embers

we can consider together (see, e . g . , Met. IV, 1003b 19-20; An. post . A 2 2 ,

83b, 10-17). If so , different categories mark different uses of existence and

presumably also different uses of identity. These different uses are held

together only by a dependence on one particular type of being, v i z . the beingof substances. But sometimes the distinction appears to separate the different

things that we can predicate of an object (Cut. 4). Categories thus seem to be

the different kinds of predicabilia, and in different categories w e therefore seem

to be dealing with different varieties of predication. At other times Aristotle

correlates the category distinction with a distinction between the different

question words of the ancient Greek, to the extent of using question words

and phrases as labels of the different categories (T op . I, 9). Which one of

these does Aristotle really mean? Scholars have defended strikingly differentlearned opinions on this point. For example, Adolf Trendelenburg (1846)

considered Aristotle’s categories above al l as the most general predicates, ad

Hermann Bonitz (1853) as the largest genera of entities. Jaakko Hintikka

EXI STENC E A N D PR EDI C ATI ON FROM ARISTOTLE TO FREGE 367



(1986), in his turn, has analyzed the question from the vantage point of the

logic of quantifiers as it is incorporated in natural languages. He has been led

in this way to the answer: all of the above. In the logic of natural language,

at least of such natural languages as English and Greek, the semantics of

quantifier phrases forces these apparently different distinctions to be paralle l.

(Ibid., 96-103.)

This parallelism made it natural for Aristotle to think that the existential

and the predicative senses of einai-if they are different senses in the first

p l a c e d o go together. When they do not, for instance, when the existential

predicative and identificatory senses exhibit different logical behaviour, para-

doxes come about. How Aristotle dealt with them, is a story for another

occasion.

Thus in Aristotle, the category distinctions do not separate the allegedly

different Frege-Russell senses of being from each other. Rather, they separate

the parallel uses of eina i in one category from their u ses in another category.

There is nothing that disallows one and the same use of a verb like einai to

carry both an existential force and a predicative force as long as these two

forces are compatible categorially. Existence is not a predicate for Aristotle,

not because existence and predication are categorially different, but because

existence is used in all the different categories, and hence is not one of the

legitimate category bound predicabilia. The upsho t is an Aristotelian universe

which is split up into different larges t classes of beings. In different classes of

such kind, that is, in different categories, different things can be said of itsmembers, and their members are identified differently.

This overall picture changes radically when we move to Kant’s theory of

categories. Kant says that he is in his theory doing the same thing as Aris-

totle ( K r V , B105), but it is not clear what he means by that statement. It is

perhaps good to keep in mind that evidently Kant‘s knowledge of Ar istotle

was mostly based on such rather inadequate textbooks as Jacob Brucker’s His-

toria critica philosophie (1742-1744). Indeed, ccording to Peter Petersen,

after Melanchthon and before Trendelenburg there was no significant A r i s -

totle-reception (Petersen 1913 : 124-138). One possible answer in any case is

that Kant is, like Aristotle, concerned with the different kinds of questions

that we can raise about the world. But in Kant these differences between dif-

feren t questions do not merely reflect the objective differences between the

different realms of being that we might be talking about. They are differences

between different questions I must ask in order to integrate the messages that

my senses convey to me into a body of my knowledge. In Kant’s phrase, we

are in the category distinctions dealing with distinctions between different“pure concepts of understanding which apply a priori to objects of intuition

in general” (KrV, B105). They correspond to different “logical functions in all

possible judgments” (zbid.). A comparison with Aristotle shows remarkable

368 RISTO V O L K K O AN D J A A K K O HI N T I KKA



differences. In so far differen t Kantian categories correspond to different kinds

of questions. The answers to questions show up in different aspects of the

logical form of all propositions. They are not questions that can be only

about a certain genus of entities, as Aristotelian categorial questions. They

are questions that arise in connection with any judgment.

The crucial difference between Aristotle and Kant for our present purposes

concerns the status of questions of ex istence and predication in Kant's theory.

The difference is that in Kant questions of existence and questions of inher-

ence and subsistence belong to different categories: the former to the category

of m odality and the latter to the category of relation. Hence, no logical func-

tion can express both. Consequently existence is not only not a predicate, i t

cannot be a part of the force of any predicate .

All this necess itated a radical reinterpretation of the semantics of syllogis-

tic premises. For on e thing, predication and ex istence had to be distinguished

from each other. However, it was not obvious how to conceptualize the rela-

tion of the two. Maybe they were not two meanings of a single word, but

they were not obviously two components of the meaning of a single unam-

biguous word, either. What is crucial, the existential force (i f any) of a syllo-

gistic premise becam e an orphan. It could no longer be im ported to the mean-

ing of the premise by the predicate term. And it was seen that in Aristotelian

logic, the particular quantifier did not necessarily express actual existence,

either.

Kant's influence makes understandable the problem situation in which

thinkers found themselves in the early nineteenth century. They had to keep

apart the existen tial and the predicative uses of verbs for being, whether or

not they were inclined to freeze the distinction into an ambiguity of a single

word or not. This problem situation was not restricted to professional phi-

losophers, either. A case in point is the aforementioned Herm ann's rule. We

are now able to see what there is to be said about it. Around the turn of the

19th century, under the influence of K ant's philosophy, Hermann w as project-

ing the sharp distinction between the different uses of verbs for be ing back tothe Greeks. But the variety of such a projection depends on there actually be-

ing a sharp distinction present in ancient writers, including the major Greek

philosophers. Hence, Hermann's rule cannot be used as evidence for the pres-

ence of the Frege-Russel1 distinction in ancient Greek philosophers. Instead,

the unmistakable absence of any such distinction in writers like Aristotle

should make us wary of the historical accuracy of Hermann's rule. On the

other hand we must acknowledge that Herm ann's rule was already anticipated

by some Byzantine scholars whose motivation was of course not philosophi-cal. Their concern seems to have been at least partly phonetic rather than

semantical, which reduces the interest of their distinction for the purposes of

the history of philosophy.

EXISTENCE A N D PREDICATION FROM ARISTOTLE TO FREGE 369



If the situation into which Kant had thrust all thinkers was thus felt out-

side philosophy, it is only to be expected that it was perceived independently

and more or less simu ltaneously by several different philosophers. O ne way

of trying to cope with it is to make the Frege-Russell distinction, or some

part of it. Thus it is not at all surprising to find parts of Frege-Russell thesis

put forward by D e Morgan , Peirce, and quite likely still others . Frege’s new

logic was therefore not in all respects a unique discovery that could have been

made by a genius like Frege at any time. His distinctions between allegedly

different senses of being were made very much in a particular historical situa-

tion. As Gordon Baker and Peter Hacker have said, “if Frege had not made the

decisive breakthrough in 1879, others would have made it along the same line

within his lifetime (and nobody had been in a position to do so significantly

earlier)” (Baker&Hacker 1984: 16). It was no accident that Frege‘s philoso-

phical education (such as i t was) was almost exclusively Kantian. Hans Sluga

(1980) has it right: it is important to realize that both Frege’s logical and

philosophical ideas had their ancestry.

These coincidences are not really coincidences. They become even less

surprising when we note that for logicians there existed an obvious way of

finding a home to the orphaned existential force, even in the case of syllogis-

tic premises. This way was to assign it exclusively to the particular quantifier

expression, which was thus turned into our now familiar existential quanti-

fier. This transfer was further encouraged by other facts. For mathematicians

like Augustus De Morgan and George Boole, universality came to mean uni-

versality in some universe of discourse which is the ultimate subject of the

discourse. In virtue of the duality of the universally and particularly quantified

statem ents reflected in their interdefinability, this meant that the particular

statements cam e to express existence in the same universe. Admittedly, Jean

van Heijenoort (1967) has said that Boole’s logic did not have much onto-

logical import. This has to be understood in the right way. The telltale

notion in Boole is the notion of the universe of discourse. By this he did not

mean the actual universe but whatever system of ob jects we choose to speakabout. In his 1847 mathematical analysis of logic Boole understood the uni-

verse as comprehending

every conceivable class of objects whether actually existing or not, it being premised that the

same individual may be found in more than one class, inasmuch as it may possess more than

one quality in comm on w ith other individuals. (Boo le 1847: 15.)

Thus, B oole’s universe is the only class which contains all the individuals

that exist in any class. This is in perfect agreement with De Morgan’s notionof the universe of discourse. In his Formal Logic (1847), which was pub-

lished almost simultaneously with Boole’s Mathematical Analysis of Logic,

De Morgan characterized the universe as a range of ideas which is either

370 KIST0 VOLKKO A N D J A A K K O H IN T IK K A



expressed or understood as containing the whole matter under consideration,

i e . , “merely the whole of w hich we a re considering parts” ( ib id . , 38). In his

greatest work, An Investigation oft h e Laws of Thought (1854), Boole refined

his conception of the universe and wrote that “whatever may be the extent of

the field with in which all the objects of our discourse are found, that field

may properly be termed the universe of discourse” ( ib id . , 42). What is more,

in his late manuscript “Logic and Reasoning,” which was probably a sketch

for an introduction to a nonmathematical exposition of the basic ideas of the

Luws of Thought,Boole says short and clear that the limiting conceptions of

universe and nothing express simply the ideas of exis tence and nonexistence

(Boole 1952 : 218). Rush Rhees has claimed that this was a late change, and

that there may be important reasons for i t (Boole 1952: 30). Indeed, this was

an important change but i t was not as late as Rhees likes to suggest. Boole

did express the is of existence by x = 1 for ‘Something exists’ and respec-

tively x =0 for ‘Something does not exist’ already in his Investigation of the

Laws of Thought (Boole 1854: 189-190). In any case, i t is interesting to

compare this late definition of the universe as expressing simply the idea of

existence to the earlier 1847 definition, where the un iverse covered every class

of objects whether ac tually existing or not.

All in all, what Boole had in mind with his notion of the universe of dis-

course w as that logical truths do not convey any information about th e actual

world, since they are calculated to apply to any old universe of discourse. But

applied to one such dom ain the universal quantifier expresses universality andthe existential quantifier expresses existence with respect to the given

domain.

After Kant and before Frege the most far reaching development in logical

theory was the algebra of logic and theory of re lations that originated around

the mid-19th century with Boole and De Morgan. The following two ideas

came to the forefront. First, the operators corresponding to the syllogistical

standard forms of universal and particular judgments were treated as duals.

Second, universal judgments were taken to be relative to some universe ofdiscourse, and were inevitably taken as the nonexistence of exceptions in that

domain. But because of the duality, existential quantifier expressions came to

express existence. Boole differed from today’s notation of Boolean algebra

only in his use of the unnecessary elective symbol v to denote ‘some’ (thus,

e . g . ,x =vy reads ‘X is some y’ ) . The orphaned notion of existence thus found

a home, no longer in the predicative is but in the existential quantifier. This

helps in explaining the independent discovery of quantifiers by Frege in 1879

and by Peirce in the early 1880s.If De Morgan’s achievem ents seem insignificant from today’s perspective,

i t is because Boole ’s novel and successfu l ideas resulted in logic taking a

totally new direction. What is more, whereas Boole’s notation became widely

EXISTENCE A N D PREDICATION FROM ARISTOTLE TO FREGE 371



recognized, De M organ’s notation soon fell ou t of date. Undoubtedly Boole

was a more original thinker than De Morgan. In G. C. Smith’s words,

“[Boole] chose interesting and important topics, had new ideas to express

about them, and communicated these incisively. De Morgan, on the other

hand, often wrote at great length without quite reaching the heart of the mat-

ter, although what h e had to say contained interesting-often vividly

expressed-remarks” (Smith 1982: 121).

One historical question concerns the level of B oole’s and De M organ’s

knowledge about the previous achievements in the field of logic. Both of

them became exceptionally well educated by different routes. Their correspon-

dence, for instance, provides good evidence for both of them having been

quite well informed about the previous developments in the field of logic (see

Smith 1982). How ever, Boole did not, for exam ple, know about Leibniz’s

pioneering results in logical calculi. What about Kant, then? Kant’s most

important works were well available in any decent university library and both

De M organ and Boole mastered the German language. Moreover, their contri-

butions contain remarks on what Kant had to say about, e . g . , categories,

hypothetical propositions, or the theory of syllogistic reasoning. However,

the only definite reference (Boole 1854: 239) is made to the so-called Jiische-

Logik (Kant 1800). In other words, the only definite reference is to a secon-

dary source which did not originate from Kant’s hand only , but also from

notes and remarks of his colleagues and students who attended his lectures .

Indeed, Terry Boswe ll(1988) has traced the Jiische-Logik back to four differ-

ent sources: (1) students’ notes, (2) Kant’s own reflections on logic, (3)

Gottlob Benjamin Jasche’s editorial additions, and (4) material from Georg

Meier’s Auszug uus der Vernunftlehre (1752), which Kant used as manual

during his lectures. Although authorized by Kant himself, the Jusche-Logik

is an unreliable source to Kan t’s logic.

De Morgan seems to have been very sensitive with regard to semantical

issues, perhaps even more sensitive than Boole. For example, in a letter to

Boole on February Ist, 1862, De Morgan criticized Sir W illiam Ham ilton’suse of the term ‘some,’ distinguished three different senses of this term, and

claimed that Hamilton had completely confused them (Smith 1982: 87).

How ever, of more importance for our story was his scrutiny of the verb is i n

his Formal Logic (1847).

In the third chapter of his Formal Logic De Morgan discusses first the

general characteristics of the terms of a proposition, as wanted for the abstract

forms of inference, and concentrates thereafter on those of the connecting

copulae is and is not. He sums up the most common uses of the verb is asfollows (ibid.,53):

( 1) Absolute identity, as in ‘The thing he sold you is the one I sold him;’

37 2 RlSTO VOLKKO AND JAAKKO HlNTlKKA



(2) Agreement in a certain particular or particulars und erstood , as in ‘He is a Caucasian’ said

of a European in reference to the color of his skin;

(3 ) Possession of a quality, as in ‘The rose is red;’ and

(4) eference of a species to its genus, as in ‘Man is an animal.’

Here we in effect have the Frege-Russell distinction before Frege and Russell.

De Morgan also pointed out that all these uses are independent of the use of

the verb ‘alone,’ i.e.,of the is of existence, as in the expression ‘Man is (i.e.

exists).’ In all these senses, as well as in all such senses which might be

added consistently with the aforementioned conditions, some propositions

sometimes admit of having the sense of is shifted, and some do not. Thus, in

the case of negative propositions it is always possible to reduce the is of

agreement in particulars into that of identity by alteration of the predicate.

For example, if ‘N o A is B in color,’ then absolutely ‘No A is B.’ However,

‘Every A is B in color’ does not give ‘EveryA is B.’ But the first pair might

be connected by a syllogism. (Ibid., 53.)

De Morgan’s idea of a shift in the sense of is is an interesting one, and

deserves more attention than it has received. It is not even clear whether the

shift fails i n universal premises for logical reasons. It may be mentioned that

in the Finnish language there is a construction more generally applicable than

De Morgan’s which can perhaps be thought of as implementing the kind of

shift De Morgan is considering. It is illustrated by the following groups of

synonyms:

Lippu on punainen

Lippu on vj:rilaj:n punainen

Lipun vari on punainen

Han on suomalainen

Hl n on kansalaisuudeltaan suomalainen

H ln on Suomen kansalainen

Hanen nimensj: on Samuel

Han on nime ltlln Samuel

The flag is red

The flag is red in color

The color of the flag is red

He is a Finn o r He is Finnish

He is a Finn by nationality ur

His nationality is Finnish

He is a Finnish national

His name is Samuel

He is Samuel by name

In the last group we are obviously dealing with the identity sense of i s . The

relevant construction can be used also in general statements. More discussion

is nevertheless needed here.

To return to De Morgan, within a few pages of his Formal Logic (49-54)

he manages to write about the different senses, the different meanings, and the

different uses of the verb i s . Even thought he clearly had a sharp sight with

regard to semantical nuances, it seems as if he did not have a clear opinion

about whether the differences in the use of the verb is are due to the multiple

ambiguity of a single word or differences in the context in which it occurs.




The third use of verbs for being, the identity sense, became prominent when

relations and functions were included among the notions studied in logic. In

Aristotelian syllogistic, it did not make much difference whether a phrase like

‘some women are wise’ was in effect parsed as ‘some women are identical

with members of the class of wise people’ or ‘some women have the predi-

cate of wisdom .’ But relational expressions like ‘the teacher of Alexander the

Great’ could not be accommodated in this way. The situation in logic was

correctly perceived to be like the situation in algebra, where identities and

predications had to be distinguished from one another. T his development was

connected with the gradual change of the notion of relation from a relational

predicate (e.g. ‘a brother’) to a genuine entity linking its two terms. (On th is

use of the verb is, see Hintikka, forthcoming.)

The fourth alleged Frege-Russell meaning, the is of subsumption, was

promoted-or necessitated-by the categorical articulation of the reality

described in a logical language into individuals, their properties and relations,

possib ly properties and relations of properties and relations, and so on. A

sharp form of this articulation was Frege’s distinction between saturated enti-

ties (‘objects’) and unsaturated entities (‘functions’). Such articulation was

not peculiar to Frege, bu t foreshadowed in the tradition of the algebra of

logic.

Many philosophers have seen in this categorical articulation the crucial

step in the genesis of modem logic. Be the justification of this claim as it is,

on the level of actual logical rules a related change is more conspicuous. It isthe breakup of what Russell called denoting phrases in th e logical notation.

For instance, when ‘every man is m ortal’ is expressed as ‘(Vn)(x is a man 3

is mortal),’ the phrase ‘every man’ disappears altogether as a whole. ‘Every’

goes into ‘(Vx)’ and ‘man’ becomes the predicate term of the antecedent. This

led to introduction of bound variab les, which do not have any counterpart in

natural languages.

In a historical perspective, this distance between logical and ‘natural’ lan-

guages mean in effect that it was not immediately clear that logical notation,for instance the first-order notation, could actually express the same things as

ordinary discourse. Frege claimed such universality for his Begrzffssschrift,

but did little to demonstrate it or to illustrate it. He did not even emphasize

that quantifiers could serve to define (a la Weierstrass) the basic concepts of

analysis such as continuity and differentiability. A large part of the argumen-

tation needed to persuade philosophers of the expressibility was in fact carried

out by Russell, culminating in his famous essay “On Denoting” of 1905.

Russell even said that the distinction we have associated with his name (andFrege’s) marks “the first real progress in logic since the days of the Greeks.”

He was not right in the sense that the distinction is not an eternal truth about

all possible logics ready to be carved in stone. However, there may be a large

374 RlSTO VOLKKO A ND JAAKKO HINTIKKA



grain of truth in Russell’s boast. In a deeper sense enhanced awareness of the

different uses of verbs for being and of their differences means genuine pro-

gress in our understanding of logic.’

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