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The Search Jor Logically Alien Thought: Descartes, Kant, Frege, and the Tractatus1

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PHILOSOPHICAL TOPICS VOL. 20 NO. 1, FALL 1991 The Search Jor Logically Alien Thought: Descartes, Kant, Frege, and the Tractatus1 James Conant University ofPittsburgh [I]n order to draw a limit to thought we should have to be able to think both sides ofthis limit (we should there­ fore have to be able to think what cannot be thought). The limit can, therefore, only be drawn in language and what lies on the other side ofthe limit will be sim­ ply nonsense. -Ludwig Wittgenstein2 The only proper way to break an egg is from the inside. -Parva Gallina Rubra3 This essay is about three things: Wittgenstein's ideas conceming the question of the possibility of illogical thought, the sources of those ideas (especially in Kant and Frege), and Putnam's recent interest in both of these matters. Along the way, this paper briefly sketches the broad outlines of two almost parallel traditions ofthought about the laws oflogic: one rather long and complicated tradition called the History of Modem Philosophy, and one rather short and complicated one called Hilary Putnam. Here is a thumb­ nail version ofhow these two traditions align: Descartes thought the laws of logic were only contingently necessary; not so recent Putnam agreed. 8t. Thomas Aquinas believed that they were necessarily necessary; relatively recent Putnam agreed (this is only confusing ifyou think Aquinas should not 115 be a step ahead of Descartes). Kant thought they were simply necessary. Frege wanted to agree-but his manner of doing so raised the worry that there was no way in which to express his agreement that made sense. Wittgenstein agreed with the worry. He concluded that sense had not (yet) been made ofthe question to which our two traditions sought an answer; very recent Putnam agreed. HISTORICAL PREAMBLE: A DIFFERENT KIND OF CARTESIANISM What is the status of the laws of logic, the most basic laws of thought? Wherein does their necessity lie? In what sense does the negation of a basic law of logic represent an impossibility? The Scholastics were forced to think hard about these questions since they believed in the existence of an omnipotent God for whom all things are possible. If God is omnipotent does that mean that He has the power to abrogate the laws oflogic? The Scholastics, on the whole, were quite reluc­ tant to draw this conclusion. But does that then mean that God is not all­ powerful, that there is a limit to his power, that there is something he can­ not do? That is a conclusion that the Scholastics were, on the whole, at least equally as reluctant to draw. Posed here in a theological guise is aversion of a question that has continued to haunt philosophy up until the present: do the laws of logic impose a limit which we ron up against in our thinking? If so, what kind of a limit is this? Do their negations represent something that we cannot do or that cannot be? If so, what sort of "cannot" is this? Here is Aquinas's attempt to reconcile the omnipotence of the Divine Being with the inexorability of the basic principles of Reason: All confess that God is omnipotent; but it seems difficult to explain in what His omnipotence precisely consists. For there may be a doubt as to the precise meaning ofthe word "all" when we say that God can do all things. If, however, we consider the matter aright, since power is said in reference to possible things, this phrase, God can do all things, is rightly understood to mean that God can do all things that are possible; and for this reason He is said to be omnipotent. Now ... a thing is said to be pos­ sible in two ways. First, in relation to some power ... If, how­ ever, we were to say that God is omnipotent because He can do all things that are possible to His power, there would be a vicious circle in explaining the nature of His power. For this would be saying nothing else but that God is omnipotent because He can do all that He is able to do. It remains, therefore, that God is called omnipotent because He can do all things that are possible absolutely; which is the 116 second way ofsaying a thing is possible. For a thing is said to be possible or impossible absolutely, according to the relation in which the very terms stand to one another: possible, if the pred­ icate is not incompatible with the subject, as that Socrates sits; and absolutely impossible when the predicate is altogether incompatible with the subject, as, for instance, that a man is an ass. ... Therefore, everything that does not imply a contradic­ tion in terms is numbered among those possibles in respect of which God is called omnipotent; whereas whatever implies con­ tradiction does not come within the scope of divine omnipo­ tence, because it cannot have the aspect of possibility. Hence it is more appropriate to say that such things cannot be done, than that God cannot do them. Nor is this contrary to the word ofthe angel, saying: No word shall be impossible with God (Luke i.37). For whatever implies a contradiction cannot be a word, because no intellect can possibly conceive such a thing.4 Aquinas is caught here between the Charybdis of asserting a mere tau­ tology (God can do everything within His power) and the Scylla of implic­ itly ascribing a substantive limit to God's power (by declaring God can do all those sorts ofthings which fall under a certain general description X, and hence apparently implicitly declaring: He cannot do those things which do not fall under X). One way out-a way out which, as we shall see, is grad­ ually refined in the course of these two traditions of thought about logic­ would be for this description (of those things which God cannot do) to turn out not to be a genuine description at all. Aquinas, indeed, tries to argue that those things which fall under the (apparent) description things which God cannot do are not, properly speaking, things which can be done at all. These are things which "cannot have the aspect of possibility." Of these, Aquinas says, "it is more appropriate to say that such things cannot be done, than that God cannot do them." But the worry arises: hasn't Aquinas just offered us a redescription of what kind of a thing a logically impossible sort of a thing is? It would seem that we still have here to deal with a certain (albeit remark­ able) kind 0/a thing. If so, the question remains: what sort of a thing is this and is it something not even God can do? Even ifwe concede to Aquinas that perhaps, strictly speaking, we should not speak of it as if it were a doable kind of a thing, nevertheless, there certainly still appears to be an "it" here that our words are straining after and which has formed the subject of our thought throughout the preceding paragraph. Aquinas appears to be on his strongest ground when he tries to make out that the "it" which falls under these descriptions-"that which is logically impossible," "that which even God cannot do"-is not a kind of a thing at all. What we have here instead is an attempt to conceive ofa kind ofa thing which "no intellect [i.e., not just a human intellect] can possibly conceive;" 117 it is an attempt to speak a word "which cannot be a word." In order to set up this way ofdissolving the appearance ofan "it" (which not even God can do), Aquinas invokes Aristotle's distinction between those things which are impossible in relation to some power and those things which are impossible absolutely. It is not clear, however, that this distinction really helps. It threat­ ens to recreate the appearance that we have to do here with two different kinds ofthings, belonging to two distinct orders ofimpossibility: the merely impossible and the absolutely impossible. Just as it is natural to picture that which is possible for a finite being (such as man) as contained within the space ofthat which is possible for God, it can seem natural to take Aristotle's distinction as marking an analogous boundary, only at a higher level. One pictures the distinction in terms of two degrees of impossibility: things belonging to the second degree (the absolutely impossible) are situated on the far side ofthe outer limit which encompasses things belonging to the first degree (the merely impossible). So now it seems that although God never chafes against anything which lies within the circumference of this exterior circle, nonetheless, Great as He is, that is as far as He can go--even He must remain within this circle. This picture of a circle (circumscribing the limits ofthat which is absolutely possible) lying within a wider space (the space of the absolutely impossible) inevitably leaves us with the feeling that we have, after all, succeeded in describing a genuine limit to His power. The existence of this outer space of absolute impossibility seems to settle the question in precisely the contrary direction from the one in which Aquinas had hoped to lead uso The apparently innocent step ofpicturing the space ofabsolute pos­ sibility as bounded by a limit seems to have led us to the opposite conclu­ sion about God's omnipotence.5 What sort ofa thing lies beyond the limit ofGod's power? Answer: the sort which is absolutely impossible.
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