R A I N E R T R A P P

> > C R E D O * M E * C O G I T A R E E R G O S C I O * M E *

E S S E l / 2 << - D E S C A R T E S ' > > C O G I T O E R G O SUM<<

R E I N T E R P R E T E D 1

ABSTRACT. At first sight one might be tempted to regard Descartes' ~cogito ergo sums< as logically true by existential generalisation. This however would neither exhaust the specific epistemic content of >~cogitor nor reveal the philosophical peculiarities of >>sums< which the author takes to have two ontologically different meanings. The full sense of >,cogito ergo sum~ finally turns out to be "Credo* me* cogitare ergo scio* me* esselt2". Furthermore this proposition can formally be proved to be true by means of epistemic logic.

m .

T h e r e is one thing that is cer tain about the Car tes ian insight p resented in the 4th sect ion of the 'D i scours de la m 6 t h o d e . . . ' of 1637 and in the 2nd sect ion of his 'Medi ta t iones de pr ima phi losophia ' of 1642: This insight, usually summar ised by the Car tes ian formula >>cogito e rgo sum<c, does not only intend to convey that cogito ergo sum. For otherwise it would be der ivable as a simple t ruth of e l ementa ry logic as follows:

I 1 (1) T a >>cogito<< 2(1) v x ( x = a ^ Tx) 3( ) T a - o V x ( x = a)

and thus, by the rule of necessi tat ion,

4( ) I-L(Ta---*Vx(x = a)) >>cogito e rgo suml<~

Let us assume that ' T a ' ( ' I (am) think(ing) ' ) was true by ev idence for Descar tes himself. (The same will be assumed for the respect ive first premises in all the deduc t ions below.) Line 4 is then a formal t ran- script ion of >>cogito e rgo suml~, 2 the index 1 of >>surely< indicat ing that up to now only the existence of the re fe rence ob jec t of T in the sense

o f the existential quanti f ier 'V ' has been deduced . Desca r t e s ' " e g o sum, ego e x i s t o . . , quandiu cog i to ' '3 (my italics) suggests , by the way, to in t roduce also a t ime var iable limiting the time of a ' s existence1 - as far as it is deducib le f rom premise (1) - to the t ime of a ' s reflecting. Only for reasons of simplicity such a var iable is d ropped both here and

Erkennmis 28 (1988) 253-267 �9 1988 by Kiuwer Academic Publishers

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in the subsequent deductions. It could be inserted without impairing in the least the results achieved. Moreover , one might propose to give premise (1) an epistemic logical setting by replacing it by either one of the following propositions (or the like):

1'(1') B(a, M ~ p ) ~I believe that non-p is possible~ (weak doubt as for p);

1"(1") B(a,-np)>~I believe that non-p is true~ (strong doubt as for

P); 1'"(1'") B(a ,~VyVpK(y ,p ) )

>~I believe that nobody knows anything~ (universal scep- ticism)

If for the variable p one substitutes one of the propositions which Descartes in meditation I pretends to radically doubt - such as the existence of external bodies including his own - these formulations of the premise ~cogito~ indeed have the advantage of expressing that the acts of reflection Descartes starts his argument with are acts of doubt. Yet, all these refinements would not change the result that ~cogito ergo sum~ is only an utterly trivial logical truth if ~sumc~ is nothing but the ~suml~ of deduction I.

What makes it recommendable not to stop our reconstructional efforts at this point? Arriving at a logical truth, trivial though it may be, is not the worst thing to arrive at in metaphysics after all. The answer to this is simple. What should make us drive our analysis further here is that Descartes doubtless did not just mean to consider the L-truth in line 4 of I as the Archimedean fulcrum of his metaphy- sics. That this is so becomes obvious already from Descartes ' reaction on Gassendi's critical remarks on the philosophical value of the ~cogito ergo sum~. Gassendi gave this formula a similarly trivial understanding as deduction I did. If Descartes only wanted to assure himself of his existence, Gassendi argued, he might as well have started out from any activity whatsoever. So instead of "I am reflecting" it might also have been "I am taking a walk". 4 It is true that Gassendi in establishing his thesis did not explicitly argue as we did in deduction 1. 5 Nonetheless Gassendi's judgment is, on the basis of taking ~sum~ to be ~suml~, in complete accord with the above reconstruction I. For line 4 of I being L-true and thus even universally generalisable with respect to 'a', it does not at all count how 'Ta ' is interpreted. So it might even be "You are walking". This, however, is

D E S C A R T E S ' ~ C O G 1 T O E R G O S U M ~ R E I N T E R P R E T E D 255

heavily at odds with Descar tes ' a rgumenta t ion in meditation II. Des- cartes continuously stresses there that it is the peculiarity of his own conscious mental acts like reflecting which gives his a rgument for the undeniability of his existence its very force. Still more it is at odds with what Descartes explicitly writes in answer to Gassendi 's argument : Namely that, because of only his conscious mental acts making his existence certain beyond any doubt, it could only have been his being conscious of his walking but not his walking itself that he might have started his a rgument with. Consequent ly ~ambulo ergo suml~ just does not convey the essence of the proposit ion Descar tes actually strives for in meditat ion II. Still less does ~ambulas ergo esl~.

But what more substantial proposit ion, reformulated in some suit- able formal language, did Descartes have in mind as his basic, in- dubitable truth? A first suggestion might be this of attributing to Descar tes a hidden transcendental insight even before the very term ~>transcendentalism~ came to light. One might say that in reflecting on his being mentally active Descartes recognized that his transcendental Ego as the carrier or (at least co- )producer of all his appearances , thoughts, ideas etc., could not just be itself an appearance , thought, idea beside and epistemologically on a par with the ones produced by it. The Bedingung der M6glichkeit of the mental entities enumera ted - this cognition would amount to in Kantian terms - cannot itself be a mental entity only. It must, so to speak, be ontologically prior to or of >~higher order~ than its products. If one feigns a certain mental entity, conceived as an e lement of one ' s s t ream of consciousness, not to exist this would not automatical ly imply the nonexistence of the transcen- dental Ego as its necessary condition. Yet if, on the other hand, one feigns one ' s t ranscendental Ego not to exist there would a fo r t io r i be no s t ream of consciousness. Put otherwise: The relation " x is a mental object and (co-)product of my E g o " is to be conceived thus that it is not the case that also my Ego is only a mental object and (co-)product of itself. Rather , even if x is only a Ding fi~r reich, my Ego is also a Ding an sich. (Of course, in reflecting about one 's t ranscendental Ego it may also become the object of thought and thus a Ding for mich, but this presupposes the existence of the reflecting Ego as a Ding an sich on a higher level.)

These e lementary Kantian considerations allow to reconstrue the ~cogito ergo sum~ in a less trivial way than above. For >~sum~ can now be taken as an assertion of two modes of existence of the Ego,

256 R A I N E R T R A P P

conceived in Kantian terms as the "transcendental unity of ap- percept ion".

First it exists like anything else does that is in a person's most comprehensive universe of discourse and that therefore may be refer- red to by singular terms of all order. As such it is on a par with external bodies, all kinds of objects of one's reflection, entities that one only hallucinates or dreams of etc. In short, as such it is on a par with entities that might be, or even certainly are, only products of the mind. This first mode of existence of the Ego is expressed by the epistemologically neutral ~suml~ - formally represented by the quantificational term 'Vx(x = a)' we arrive at in deduction I.

Yet beyond this philosophically ~trivial~ mode of existence the ~transcendental Ego~ has to be conceded also a second mode of existence - a mode that can only be represented by a particular existence2 predicate E. This predicate would be one of the several possible predicates which some logicians suggested in order to be able to attribute particular additional modes of existence to singular entities existing~ in or constructible within a given universe of discourse. 'E ' in particular would have to denote indubitable existencez in itself - ~indubitable~ meaning that the very act of denying this mode of existence2 presupposes it and thus falsifies the contents of the doubt. This predicate would be analytically implied by being a transcendental Ego consciously performing a ~cogitatio~ of whatever kind and only by being such an entity. For my respective transcendental Ego, consciously performing some mental activity - one might put forward to justify this latter restriction also in Cartesian terms - is the only thing which in reflecting I clare et distincte recognise not to be (only) a product of my mind. So it is the only thing in itself which I positively know to exist2 (also) as a thing in itself. All other entities which I might refer to by singular terms of my language and which I consider to exist2 also as things in themselves might after all not exist2 - howso- ever indubitably they exists. So at this stage of the reflection in meditation II, I am entitled to doubt the truth of 'Ex' for all entities x(x ~ a*) - a* denoting my respective transcendental Ego. Doubting also the truth of 'Ea*' , once 'Ta* ' is introspectively experienced to be evidently true, would run up to stripping this very act of doubting of one of its transcendental presuppositions ("Bedingungen der M6glich- keit"). The latter, being nothing but a special case of necessary conditions, can formally be presented by some kind of implication.

D E S C A R T E S ' ~ C O G I T O E R G O S U M ~ R E I N T E R P R E T E D 257

There are good reasons that this implication is, in terms of possible- worlds-semantics, at least of the strength of a subjunctive implication. For the result to be aimed at here it will suffice, however, to only reconstrue it as a material implication. So this ~transcendentak~ in- terpretation of the ~cogito ergo sum~ amounts to deduce it in the following way:

I! l ( l ) Ta* ~cogito*~ 2(2) Ta* --~ Ea* ~cogito* ergo sum2~ 3(1,2) V x ( x = a* ^ Ex) ~suml,2~ 4(2) Ta*---~ V x ( x = a* A Ex) ~cogito* ergo suml/2~

Note that 'ambulare ' , in contradistinction to 'cogitare' , can no longer be reconstrued as a predicate of Descartes ' Ego a* in the restricted transcendental sense which we now assume for 'Ego' . In deduction I the individual constant ' a ' still denoted 'I' in a broad sense according to which I can be said to think as well as to walk. 'Ta ' (~cogito~) or 'Aa ' (~ambulo~) would accordingly express something like this: " (A suitable part of) my person a - which includes my body and my mind - performs activity T or A, respectively". In contrast to this 'Ta* ' now stands for "My mind or only this part of my person which comprises its non-physical component and is a transcendental presupposition of all my mental activities is reflecting". That the notion of Ego has to be restricted in this Kantian interpretation of the ~cogito ergo sum~ is beyond ,doubt : One just cannot arrive by the transcendental arguments given above at the existences/2 of an Ego denoting one's whole person. Ego a* might well feign by assumption not to have a body at all that exists2. The possibility for a* to accept 'Ta*' as evidently true would not be undermined by this. In addition, this restriction of Ego in reconstruction I to Ego* in reconstruction II nicely accords with Descartes ' considering himself only as a part of res cogitans and not as an ~integer homo~ in this foundational stage of his metaphysics.

Note, moreover , that Descartes could of course also include his restricted Ego* separately in his original universe of discourse. So a*'s simple existence1 in the sense of the quantifier still continues to be deducible in line 4 of II in addition to that further mode of existence2 that 'E ' purports to express. Let us indicate this restricted understand- ing of T and the two senses of existence in the interpretation of the ~cogito ergo sum~ by the asterix and two indices already used in

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deduction |I. So what we now have shown is that >>Cogito* ergo sum*u2r is true provided premise (2) is true. Quite apart from the fact that ~ambularer162 could no longer be meaningfully attributed to a* - i.e., that ~ambulor could not also be >>ambulo*<~ - 'Aa*' would not permit to gain 'Ea*' from line 2 of II. So in gaining line 4 of II the peculiarities of mental activities in contradistinction to non-mental ones indeed count in accordance with Descartes ' argumentation.

Furthermore, >~cogito* ergo suml/2*<r is no longer an elementary L-truth and thus trivial. For the truth of line 4 in II still depends on premise (2), which is not an axiom or principle of whatever system of logic. On the other hand, it is not an empirical hypothesis, either. Its status as a transcendental truth rather qualifies it as a premise that is "clare et distincte" recognisable, informative in a not only structural sense and yet undeniable. Hence, according to Descartes ' own cri- teria, it can be used as a tool in deriving the desired insight which resists all the possible kinds of doubts exposed in meditation I. So deduction lI in fact seems to be a first way of making the >>cogito... ~ appear less trivial than it is at first sight.

B.

There is, however, still quite a different and in a sense more natural possibility of reconstruing the >>cogito... << in a nontrivial way. It is more natural in that it does not rely on transcendental arguments but instead only makes formally explicit what is implicit in Descartes ' texts themselves. For it becomes conspicuous from many formulations both in the 'Discours' and in the "Meditationes" that what Descartes actually is after is not only proving his existence from his thinking, but proving from this premise his knowledge of his existence as a firm and un- deniable basis for gaining further knowledge. So what he is after is not that >~cogito ergo sum~<~ but at least - as we shall see in section C of this paper - the stronger insight that ~>cogito ergo scio (novi) me esse1<<. 6 Being stronger >>scio me esse1<< implies >>sum1<<; so >>cogito ergo scio me esse1<< implies >>cogito ergo sum~<; thus it would, if it could be proved, be indeed mo.re informative.

Reformulating the original >>cogito...<< in this way, of course, presupposes the use of epistemical notions. In the sequel it will be shown that this variant of the >>cogito<< can in fact be proved to be true by relatively modest means taken from standard epistemic logic.

D E S C A R T E S ' ~ C O G I T O E R G O S U M ~ R E I N T E R P R E T E D 259

Beyond this, it can be demonstrated that even the premise ~credo me cogitare~ which prima vista seems to be epistemically weaker than ~cogito~ suffices to arrive at the conclusion ~scio me essel~ and thus a l s o a t ~ s u m l ~ .

For deducing this 7 we need the following axioms of rational belief plus a definition of knowledge: (These basic principles form a proper subset of the set of axioms of Lenzen's and yon Kutschera 's system of elementary epistemic logic, which in turn is developed on the basis of Hintikka's pioneering considerations in (1962).) 8

AI: If p is analytically true then B(x, p) is true. - Analytical (and a fo r t i o r i logical) truths are believed by

rational individuals. A2: B(x, p ~ q) A B(x, p) ~ B(x, q) Epistemical modus ponens

If x believes that if p then q, and fur thermore believes that p, then x also believes that q.

A3: B(x,p)--~B(x,B(x,p)) - If x believes that p, then x also believes that x believes

that p.

(Of course, one could - and actually should - put universal quantifiers in front of the formulas A~, A2, and A3. But to avoid tedious universal specifications in applying these axioms in the proofs beyond I drop universal quantifiers already here. Mind also that subsequently these axioms should implicitly be transformed into corresponding rules of epistemic logical deduction supplementing the usual rules of deduction for standard logic construed as a Gentzenian calculus of natural deduction. 9 This will further facilitate proofs.)

Moreover , we need one the following definitions of knowledge:

df Do: Ko(x, p): = B(x, p) A p

- Knowledge is true belief. One might like to see added to Do the usually accepted third conjunct 'F(x, p)' which states that p has been justified or rationally established by x:

df Dr: Kr(x, p) := B(x, p) A F(x, p) A p.

In the subsequent deductions we may work with only Do but also with the more demanding version DF. 1~ Whenever we shall proceed from

2 6 0 R A I N E R T R A P P

individual a 's belief that p and the truth of p, definition Do will be formally applicable. At the same time the truth of p will - in all cases we consider - have been gained by individual a only via logical deduction from premises which, expressing a certain belief of a's, are evidently true. So also F(a, p) will hold in the strongest possible form of justifying a true belief. Consequently also Dv will be applicable throughout the cases where we shall pass over from true belie[ to knowledge.

Mind secondly that in all the following deductions I shall represent the starting premise ~cogito<~ not only by 'Ta ' or 'Ta*' as I did in deductions I and II; instead I shall use version 1' (i.e., weak doubt) of the doubt-expressing belief sentences I introduced on p. 254 as best representing what kind of mental activities Descartes had in mind by ~cogito~. I could, however, as well use premise 1" (strong doubt) or premise 1" (universal scepticism). The desired conclusion ~scio me esse~(~ can be reached by either starting point.

Now ~cogito ergo scio me esse~ is easily provable thus:

III 1(1) B(a, M-qp) ~cogito~ 2(1) Vx[x = a ^ B(x,M-~p)] 3(1) Vx(x = a) ~suml~ 4( ) B(a,M-qp)---~Vx(x = a).

Line 4 is nothing but a variant of our initial ~cogito ergo s u m ~ of deduction I.

Now we go beyond this aiming at ~>scio me essel~

5( ) B[a, B(a, M-~p) ~ Vx(x = a)] by A1 from line 4, which is L-true

6(1) B(a, B(a, M-qp)) by A 3 from line 1 7(1) B(a, Vx(x = a)) ~credo me essel~ by A2 from lines 5, 6 8(1) K(a, Vx (x = a)) ~scio me essel~ by Do or DF from lines 3,

7 9( ) B(a, M-qp) ~ K(a , V x ( x = a)) by conditionalisation

from lines 1, 8. Q.E.D.

As said at the beginning of section B it would be possible to conclude ~scio me esse~ even from the epistemically weaker premise ~credo me cogitare~:

IV 1(1) B(a, B(a, M-qp)) ~credo me cogitare~

D E S C A R T E S " ~ > C O G I T O E R G O SUM<< R E I N T E R P R E T E D 261

2(1) V x [ x = a A B(x, M-Tp))] 3(1) Vx(x = a) >>sum1<< 4( ) B(a ,B (a ,M-7p ) ) - - ->Vx(x = a).

Line 4 is not necessary for the further deduction. It only was added to show that also >>credo me cogitare ergo suml~< is most easily derivable. Now we again aim at >>scio me essex<<

5(5) 6(5) 7(5) 8( ) 9( )

10(1) 11(1)

12( )

So we also

B(a, M--7p) V x[x = a ^ B(x, M ~ p ) ] V x ( x = a) B(a, M-7p)---> V x ( x = a) B[a, B(a , M-Tp) ---> V x ( x = a)] by AI from line 8, which is L-true B(a , V x ( x = a)) by A2 from lines 1, 9 K(a , V x ( x = a))>~scio me essel<~ by Do or DF from lines 3, 10 B(a , B(a , M-7p))---> K ( a , V x ( x = a)) by conditionalisation from lines 1, 11. Q.E.D.

have established ~credo me cogitare ergo scio me essel~c.

C.

Now the idea suggests itself to still enrich the philosophical substance of this result somewhat by combining it with transcendental insight condensed in premise (2) of deduction II. More precisely put, one might try to further remove >>cogito ergo sum<< f r o m its face value interpretation in deduction I by reconstruing it as a formula analogous to line 12 of deduction IV with the only difference of strengthening its consequent by the particular existence predicate 'E ' introduced in deduction II. This, of course, requires as an additional predicate an epistemic logical anaiogon of the >~transcendental truth<~ 'Ta*--> Ea*' used in deduction II. Being a clare et distincte realisable a priori truth of non-tautological character it seems not only justified to fall back on it in this context but also to apply axiom A t to it thus treating it on a par with analytical truths. ~1 If both steps are granted the suggested further enrichment of the ~>Cogito... ~ can be achieved by the subsequent deduction. (Due to the contents of the crucial premise (2) the sense of 'Ego ' has, of course, again to be restricted from a to a*,

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as it had to in deduction II):

V 1(1) 2(2) 3(1,2) 4(1, 2) 5(5) 6(2, 5) 7(2, 5) 8(2) 9( )

lo( )

11(2)

This is

B(a*, B(a*, M~p)) ~credo* me* cogitarer162 Aq(B(a*, q)---~Ea*) >~cogito* ergo sum2*~ Ea* univ. inst., mod. pon. from 1, 2 V x ( x = a * A Ex) 3 B(a*, M--qp) assumption Ea* univ. inst., mod. pon. from 2, 5 V x ( x = a * ^ Ex) 6 B(a*, M~p)---> V x ( x = a* ^ Ex) conditionalisation, 5, 7 Vq(B(a*, q) ---> Ea*) --~ [B(a*, M-qp) ---> V x ( x = a* ^ Ex)] conditionalisation, 2, 8 [Aq(B(a*, q)---)Ea*) A B(a*, M~p)] ---> V x ( x = a * ^ Ex) 9 B(a*, A q(B(a*, q) ---> Ea*)) by AI from 2.

the crucial step alluded to above. Premise (2) being an undeniable a priori truth, in line 11 a rational individual is assumed to consider it as true just as he is assumed to consider any analytical truth whatsoever as true.

12(1, 2) B[a*, A q(B(a*, q)----> Ea*) ^ B(a*, M-rip)]

'B(x, A) ^ B(x, B)--* B(x, A ^ B)' being derivable from A1 and A2 line 12 immediately follows from lines 11 and 1.

13( ) B(a*, Aq(a*, q) ---> Ea*) ^ B(a*, M--qp) ---> V x ( x = a * ^ Ex)) by A1 from 10

14(1, 2) B(a*, A x ( x = a * ^ Ex)) by Az from 12, 13 15(1, 2) K(a*, V x ( x = a * ^ Ex)) >~scio* me* essel,2r by Do from

4, 14

As line 14 is established by purely logical deduction from (1, 2), also " F ( a * , V x ( x = a * ^ Ex))' is true so that line 15 could as well be gained by the stronger definition Dr. By conditionalisation we finally get:

16(2) B(a*, B(a*, M--qp))--> K(a*, V x ( x = a * ^ Ex)).

Since line 16 still depends on line 2, which is not logically true in either of the two systems we used, ),credo* me* cogitare ergo scio me* essel/2(r can - contrary to ))credo me cogitare ergo scio me esselr162 in line 12 of deduction IV - not be considered as provable within

D E S C A R T E S ' ~ C O G I T O E R G O S U M ~ R E I N T E R P R E T E D 263

standard logic plus epistemic logic alone. Yet being an a priori truth premise (2) does not injure the fact that this final and presumably most adequate interpretation of Descartes ' ~Cogito ergo sum~ is itself an a priori truth.

It is easy to see that - as was desired in view of the triviality of I - in all the ~non-trivial~ reconstructions II-V the first premise has to express some kind of mental act of a (or a*, respectively) and not any act whatsoever. (For the sake of the argument let us interpret B(a . . . . ) and B(a* . . . . ) in the first lines of III-V as being closer in kind to 'Ta ' and 'Ta*' than the normal interpretation of belief would suggest. In particular, let us in these lines not just take belief to express a latent disposition. Instead we should interpret ' a (or a*) believes t h a t . . . ' as ' a (or a*) believes consciously and actively, t h a t . . . ' Descartes ' own arguments recommend this restricted inter- pretation; for it is his performing consciously mental acts and not his latently having beliefs that makes him arrive at ~ergo sum~. One might object here that under this restriction axiom A~ is no longer plausible, since even by a rational individual not all analytical truths of some complexity are automatically also consciously believed to be true. This has quite certainly to be admitted. Yet recall that in this paper we made only a very limited use of axiom At. When we ascended from a certain analytical truth p to a 's (or a*'s) belief that p we always presupposed in line l of the respective deduction that it is a (or a*) himself who performs a certain mental act and that a (or a*) himself gains insight into p by analysing the logical consequences of his performing this original mental act. We did not also presuppose that a gains insight into an infinity of analytical truths. So A~, as we use it in this paper, does not presuppose a 's (or a*'s) active logical omniscience. (To make this argument water proof against any such criticism we could simply restrict the notion of "analytical t ruth" in the formulation of At to just those analytical truths to which A~ is actually applied in this paper. This restriction will, moreover , posi- tively enhance the plausibility of A~ as far as it is used in the present context.)

Now it is quite obvious why, contrary to deduction I, it is essential that mental (and not e.g., physical acts such as walking) form the starting points of the reconstructions II-V. In view of the transcen- dental component Ea* in II and V it is clear anyway that the premises 'Ta*--~ Ea* ' and 'A q(B(a*, q ) -~ Ea*) would make no sense for non-

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mental acts, since ' a* ' denotes the arguer 's respective transcendental Ego*. As for the starting points 'B(a . . . . )' in III and IV it is the very notion of believing that which is analysed by the belief operator and the axioms governing it and not any other notion. So one might not argue that deductions III and IV, and a fo r t io r i the belief involving final deduction V, still make sense and even remain logically true if B(a . . . . ) and B(a* . . . . ) are taken to express whatever non-mental act. Summing this up one may say that starting out from >>ambulo~< one would not arrive, at "Vx(x = a ^ Ex)' i.e., at >>ergo suml/2~<. This is so already for the reason that the analogon of the crucial premise (2) of II, namely 'Aa----~ Ea' would not be true; even less would we arrive from >~ambulo(< at K(a . . . . ) let alone K(a* . . . . ). For 'Aa' does not imply 'B(a, Aa)' and therefore not 'K(a , Aa)'. (A person can sleep- walk and thus make 'Aa' true without believing that (s)he sleep-walks; (s)he can do so in a weak and in strong sense of not believing that Aa . The first only implies that (s)he might sleep-walk without believing that (s)he sleep-walks while (s)he performs the act of sleep-walking; the second implies that (s)he may even sleep-walk without ever believ- ing anything again after this act. Imagine (s)he falls from a roof without regaining consciousness.)

The utmost we can reach for a physical act like the one referred to by 'Aa' would be this: Replacing the argument 'B(a, M-7p)' in the first premise of deduction IV, i.e. in 'B(a, B(a, M-Tp)) by 'Aa' we might arrive at

B(a, Aa)--~ K(a, V x(x = a)),

i.e., at >>Credo me ambulare, ergo scio me essel~<. But firstly a 's knowledge of his existence~ in the consequent of this implication has not been deduced from a physical act but from believing that a physical takes place and hence from a mental act; secondly this result is only slightly more interesting then the trivial reconstruction of the >~Cogito... << given in deduction I.

Let me draw the reader 's attention to one final aspect: All the reconstructions offered comply with the four well known, very general methodological rules presented by Descartes in section II of the "Discours". This is of interest in so far as Descartes claims not to transgress these rules in laying the ground for his metaphysics. It can, I think, be convincingly shown that he by far transgresses these rules in proving the existence of God or of the res cogitans qua substance.

D E S C A R T E S " ~ C O G I T O E R G O S U M ~ R E I N T E R P R E T E D 265

He also does so, notwithstanding his claim to the contrary, in his examples of possible applications of these rules to selected problems of physics and medicine. For his ~analyses~ there draw heavily on empirical hypotheses postulating certain causal connections; these hypotheses definitely do not stem from a priori ~evidence~ and merely logical analysis of ~evident~ truths. So he there just does not decom- pose such truths into its components, further process these by purely analytical means and then recompose the new components thus gained as the rules of the "Discours" allow it. Yet, Descartes would not infringe the latter in proving that from his initial doubt he can arrive at the undubitable truth that he knows to existl/2. It is true that Descartes himself probably did not yet recognize clare et distincte what Kant recognised later as for the particular mode of existence2 of transcendental subjects; it is also true that he did not yet dispose of the logical tools of analysis employed above. Notwithstanding this it can be argued that both any logical means whatsoever and nontautological a priori truths are prototypes of tools admissible within the limits of Descartes ' four rules of analysis. So in all our reconstructions we did not go beyond the methodological boundaries Descartes set to himself in seeking a firm ground for his metaphysics.

A concluding remark concerns t h e claim of this paper. I did not argue that what Descartes in fact intended to aim at was ~credo* me* cogitare ergo scio* me* essel/2~ and that he only failed to make this clear enough by pressing the result of his initial step into the formula ~cogito ergo sum~. What I rather claim are only the following two things:

(1) From the point of view of very elementary parts of modern standard and philosophical logic plus an evident nonlogical a priori truth he would have been justified in arguing for this logically stronger and philosophically more substantial proposition.

(2) In arguing for this proposition he would have remained within the limits he posed himself by his methodological rules in the "Discours".

The formula this paper dealt with at first sight turned out to be a true but rather poor philosophical insight. Also the scrutiny to which it was subjected here did not reveal it to be really rich in substance. Nonetheless one may resume that it demonstrated the possibility of

266 r A ~ n E r TRAPP

reconstruing the ~ c o g i t o . . . ~ in such a way that it c o n v e y s much m o r e than appears at a first g lance .

N O T E S

t The following reflections were indirectly motivated by a stimulating talk that Profes- sor Wolfgang R/Sd Ilnnsbruck) presented on quite different aspects of Descartes ' philosophy and by the subsequent discussion I had with him and with Professor Arend Kulenkampff (Frankfurt/M). So I owe thanks to both of these gentlemen. 2 Notwithstanding the reasons brought forward for the thesis that ~ergo~ in the Cartesian formula does not stand for any kind of implication, with which logic deals, I hold throughout the reconstructional alternative proposed here that ~ergo~ can be considered as such. The best reason for justifying this seems to me the following: The substance of the following interpretations of the ~cog i to . . .~ I shall carry out proofs in pretation of the >~Cogito... r contains all the philosophical gist of this formula and yet treats ~ergoc~ as (at least) a material implication. 3 Cf. e.g., Meditation II, p. 27. 4 See the beginning of section 1 of Gassendi 's objections against meditation I1; p. 259 of Descartes (I 904).

Gassendi does not base his argument for his thesis that Descartes might have concluded his existence from any other of his activities on mere logical grounds by pointing to somewhat that in modern terms would be the L-validity of existential generalisation. Rather he argues that "whatever has an effect must exist". 6 Cf. e.g., Meditation I1, pp. 27-28. 7 In order to facilitate the reading of the subsequent passages as much as possible also to readers who - without being familiar with epistemic logic - are interested in the substance of the following interpretations of the & c o g i t o . . . ~r I shall carry out proofs in more detail than the expert in the field will deem necessary. Correspondingly, more was said in favour of the crucial Kantian premise (2) in I1 than will be indispensable in order to convince a sworn Kantian of its truth.

See von Kutschera (1976, chap. 4) and Lenzen (1980) for systematic expositions of epistemic logic and its semantics. For the following also the concise survey in chapter 1 of yon Kutschera (1982) will give a sufficient basis. 9 See e.g., Essler (t983), chapters III to X, where the Gentzen approach was chosen in erecting standard logic. lo I do not enter here into E. Gett ier 's arguments in his often quoted and much discussed paper of (1963) according to which knowledge is not yet sufficiently defined as true, justified belief. One may easily evade these arguments by appropriately charac- terising the notion of justification. 11 In other words, it seems justified to extend the class of analytical truths as referred to in axiom A~ in such a way that it also comprises the transcendental a priori truth mentioned.

D E S C A R T E S ' >>COGITO E R G O SUM~ R E I N T E R P R E T E D 267

R E F E R E N C E S

Descartes: 1904, Oeuvres edited by C. Adam and P. Tannery, Vol. VII, Cerf, Paris. Essler, W. K. and R. F. Martinez Cruzado: 1983, Grundziige der Logik I, Klostermann,

Frankfurt. Gettier, E. L.: 1963, 'Is Justified True Belief Knowledge?', Analysis 121-23. Hintikka, J.: 1962, Knowledge and Belief, Cornell University Press, Ithaca. v. Kutschera, F.: 1976, Intensionale Semant/k, de Gruyter, Berlin. v. Kutschera, F.: 1976, Grundfragen der Erkennmistheorie, de Gruyter, Berlin. Lenzen, W.: 1980, Glauben, Wissen, Wahrscheinlichkeit, Springer Verlag, Wien.

Manuscript received 20 May 1987

Fachbereich Philosophie, Universit~it Frankfurt Dantestr. 4-6 D-6000 Frankfurt 1 F.R.G.