descartes' »cogito ergo sum« reinterpreted
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ME* SUM~cogitor nor reveal the philosophical peculiarities of >>sums,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 o n e thing that is certain a b o u t the Cartesian insight p r e s e n t e d in the 4th section of the ' D i s c o u r s de la m 6 t h o d e . . . ' of 1637 and in the 2nd section of his ' M e d i t a t i o n e s de prima philosophia' of 1642: This insight, usually s u m m a r i s e d by the Cartesian f o r m u l a >>cogito e r g o sum>cogito>cogito e r g o suml>cogito e r g o suml~, 2 the index 1 of >>surely< indicating that up to now only the existence of the r e f e r e n c e o b j e c t of T in the sense o f the existential quantifier ' V ' has b e e n d e d u c e d . D e s c a r t e s ' " e g o sum, e g o e x i s t o . . , q u a n d i u c o g i t o ''3 (my italics) suggests, by the way, to i n t r o d u c e also a time variable limiting the time of a ' s existence1 - as far as it is deducible f r o m premise (1) - to the time of a ' s reflecting. O n l y for reasons of simplicity such a variable is d r o p p e d both here andErkennmis 28 (1988) 253-267 9 1988 by Kiuwer Academic Publishers
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') 1"(1") 1'"(1'") B(a, M ~ p ) ~I believe that non-p is possible~ (weak doubt as for p); B(a,-np)>~I believe that non-p is true~ (strong doubt as for P);
B(a,~VyVpK(y,p))>~I believe that nobody knows anything~ (universal scepticism)
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 metaphysics. 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 " Y o u are walking". This, however, is
heavily at odds with Descartes' argumentation in meditation II. Descartes continuously stresses there that it is the peculiarity of his own conscious mental acts like reflecting which gives his a r g u m e n t 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 r g u m e n t with. Consequently ~ambulo ergo suml~ just does not c o n v e y the essence of the proposition Descartes actually strives for in meditation II. Still less does ~ambulas ergo esl~. But what m o r e substantial proposition, reformulated in some suitable formal language, did Descartes have in mind as his basic, indubitable truth? A first suggestion might be this of attributing to Descartes a hidden transcendental insight even before the very term ~>transcendentalism~ c a m e 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 c o - ) p r o d u c e r 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. T h e Bedingung der M6glichkeit of the mental entities e n u m e r a t e d 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 element of o n e ' s stream of consciousness, not to exist this would not automatically imply the nonexistence of the transcendental E g o as its necessary condition. Yet if, on the other hand, one feigns o n e ' s transcendental E g o not to exist there would a f o r t i o r i be no stream of consciousness. Put otherwise: T h e relation " x is a mental object and (co-)product of my E g o " is to be c o n c e i v e d thus that it is not the case that also my E g o is only a mental object and (co-)product of itself. Rather, e v e n if x is only a Ding fi~r reich, my E g o is also a Ding an sich. (Of course, in reflecting about one's transcendental E g o it may also b e c o m e the object of thought and thus a Ding for mich, but this presupposes the existence of the reflecting E g o as a Ding an sich on a higher level.) T h e s e elementary Kantian considerations allow to reconstrue the ~cogito e r g o 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,
conceived in Kantian terms as the "transcendental unity of apperception". First it exists like anything else does that is in a person's most comprehensive universe of discourse and that therefore may be referred 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 ' V x ( 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 - howsoever 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 M6glichkeit"). T h e latter, being nothing but a special case of necessary conditions, can formally be presented by some kind of implication.
T h e r e are good reasons that this implication is, in terms of possibleworlds-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~ interpretation of the ~cogito ergo sum~ amounts to deduce it in the following way: I! l ( l ) 2(2) 3(1,2) 4(2) Ta* ~cogito*~ Ta* --~ Ea* ~cogito* ergo sum2~ V x ( x = a* ^ Ex) ~suml,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 " M y mind or only this part of my person which comprises its non-physical c o m p o n e n t 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. T h e 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 understanding 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
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*>cogito... ~ appear less trivial than it is at first sight. B. T h e r e 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 undeniable basis for gaining further knowledge. So what he is after is not that >~cogito ergo sum~cogito ergo scio (novi) me esse1scio me esse1>sum1cogito ergo scio me esse1>cogito ergo sum~>cogito...>cogito 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*,
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)
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.
This is 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) by A1 from 10 by Az from 12, 13 14(1, 2) >~scio* me* essel,2r by Do from 15(1, 2) 4, 14--->V x ( x = a * ^ Ex)) B(a*, A x ( x = a * ^ Ex)) K(a*, V x ( x = a * ^ Ex))
As line 14 is established by purely logical deduction from (1, 2), also = a * ^ Ex))' is true so that line 15 could as well be gained by the stronger definition Dr. By conditionalisation we finally get:"F(a*,Vx(x
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
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 r e c o m m e n d this restricted interpretation; 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 truth" in the formulation of At to just those analytical truths to which A~ is actually applied in this paper. This restriction will, moreover, positively 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 transcendental c o m p o n e n t 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-
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 f o r t i o 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 " V x ( x = a ^ Ex)' i.e., at >>ergo suml/2~~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 sleepwalk 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 A a . T h e 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 believing 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~