Wittgenstein and ‘tonk’: Inference and Representation in the Tractatus

Wittgenstein’s reflections on color exclusion and other related difficulties lead him to abandon the Tractarian conception of the nature of the proposition. And what finally happens is not that he replaces it with some other general account of what it is for a proposition to state how things are. Rather, he abandons the very idea that reflections on the general nature of truth and falsity can provide us with a universally valid account of our concepts of description, proposition, language and logic. Indeed, even if we lay down that a proposition is whatever can be true or false, our concept of truth and falsity cannot thereby serve to determine what is and is not a proposition. This seems to be the point, or one point, of the difficult paragraph 136 in the Philosophical Investigations. In this paragraph, Wittgenstein notes that the concepts of truth and falsity are not given antecedently to, but together with, the concept of a proposition, and, hence, “the proposition that only a proposition can be true or false can say no more than that we only predicate ‘true’ or ‘false’ of what we call a proposition.” (PI 136)

One thing that makes this paragraph particularly difficult to understand, if one is interested in the relation between early and later Wittgenstein, is that, as it stands, early Wittgenstein would probably have wanted to agree with what his later self is saying there. Indeed, my description of how early Wittgenstein would have criticized a “semantic” account of the connectives such as Stevenson’s ascribes to him precisely the view that our “use of ‘true’ and ‘false’ “belongs to our concept ‘proposition’ but does not fit it” (PI 136). And yet, later Wittgenstein seems to be suggesting that the author of the Tractatus has not taken the “internal” relation between our concepts of truth and falsity and our concept of a proposition seriously enough. According to later Wittgenstein, the Tractarian conception of truth is in fact developed and defended in complete isolation from any careful investigation of what it actually means to “describe the world” in real life. So, later Wittgenstein’s target is not the Tractarian idea that the concept of truth and the concept of a proposition are internally related. Rather, his criticism of the Tractatus is that if one really thinks through that idea one will realize that the internal relation between the concept of truth and the concept of a proposition cannot serve as the basis for a uniform account of the form of a proposition.

Where does this leave us with ‘tonk’? With what right can later Wittgenstein now say that the rules for ‘tonk’ necessarily describe the use of two logically distinct connectives? What if someone denies this? With what right can later Wittgenstein say that such a denial is incompatible with ‘tonk’ being a logical expression at all? If there is no general, once and for all settled determination of what a proposition is, and no general, once and for all settled determination of what constitutes the domain of the logical, then aren’t we defenseless against someone who insists that ‘tonk’, as defined by the introduction rule and the elimination rule given by Prior, belongs to this domain of the logical? And doesn’t this show that Prior, after all, has put his finger on a weak spot in Wittgenstein’s conception?

I think Wittgenstein answer is that we will look defenseless only on a certain conception of what a defense here would have to look like, and that it is one of his central aims precisely to reject that sort of conception. The sort of view against which Prior’s ‘tonk’-example has genuine force is an inferentialism of an explanatory kind – a inferentialism meant to account for how a logically inert raw material of mere shapes or ‘sign-designs’ can, as it were, get beefed up so as to achieve logical potency; an inferentialism according to which rules of inference make it the case that already identified, orthographically individuated units come to stand in logical relations to one another. Wittgenstein never aspired to provide such an explanation. On the contrary, he always thought that this sort of aspiration was fundamentally misguided. Indeed, I think he would say that if we try to give rules of inference this sort of explanatory role, any attempt to find a defense against Prior’s ‘tonk’-example has to fail. Which means that, strictly thought through, this explanatory form of inferentialism does away with logic; or, better, it never gets the domain of the logical into proper view at all.

Instead, Wittgenstein thinks we can get logic into proper view only if we start from that familiarity with inferential practice that we already have as competent speakers and thinkers. That is, we must occupy a standpoint from which the units that figure in inferences are already given as logical units, units whose very identity is tied to the rules according to which they are being employed. It is only through logic that we can determine whether two occurrences of one and the same orthographic shape – say, ‘p tonk q’ – can also be occurrences of one and the same logical unit, or whether they must have different logical functions. An account that takes logic for granted in this sense, and therefore shuns away from the sort of explanatory aspiration described before, will not be vulnerable to Prior’s criticism.