NECESSITY AND PROVABILITY WITTGENSTEIN'S PHILOSOPHY OF NECESSITY

SHELLEY LIANE TRIANOSKY-STILLWELL, Purdue University

Abstract

Wittgenstein's philosophy contains many rich discussions of necessity. In his early work (Tractatus Logico-Philosophicus) he provides a truth-functional account of necessity which is undoubtedly anti-relativistic. The account, that is, makes any proposition's necessity wholly independent of contingent matters. But the later work (Remarks on the Foundations of Mathematics) is less clear in its import. Virtually all commentators think the later work includes an account of necessity which relativistic: that the account makes a proposition's necessity to depend on our language, and specifically on the nature of the proof-procedures we employ. I think this kind of interpretation is seriously mistaken. The aims of this dissertation are twofold: First, to show that the later work does not commit Wittgenstein to a relativism about necessary truth, and moreover that he holds a proposition's necessity to be "absolute"; Second, to explain why the later philosophy appears to be relativistic and to destroy the basis of relativistic interpretations. All told, my position is that the later work of Wittgenstein contains an intriguing account of necessity, and especially of the relation between necessity and provability. His account offers an important alternative to the doctrine of platonism, on the one hand, and to constructivism, on the other. I carry out the most central part of my project in Chapters I and III. I present strong evidence for holding that Wittgenstein's later account of necessity is anti-relativistic. Specifically, I argue that that account is every bit as "absolutistic" as the positions of philosophers such as Kripke and Plantinga, because the account is, like theirs, an S5-account of necessity. My argument for this is double-edged: On the one hand, I appeal to Wittgenstein's metaphors; These he uses to characterize our concept of necessary truth as the concept of something which cannot possibly fail to be necessary; The significance of the metaphors has been overlooked, in part because of the predilection of commentators to construe the passages in which they occur as mere attacks on platonism in logic and mathematics; While Wittgenstein does indeed attack the doctrine of platonism in these passages, he never wants to undermine our own "preanalytical platonism" (the "absolute" character of necessity as we conceive of it); Secondly, I investigate the point of Wittgenstein's numerous examples of "alternative proof-procedures"; Usually these examples are interpreted as suggestions that what we know to be necessary might have been false, since alternative proof-procedures would have shown other propositions to be necessarily true; I argue that, on the contrary, Wittgenstein advanced such examples in order to exhibit the "conceptual gap" between what we believe to be possibly provable and what we know to be necessary; The examples show only how other propositions might have been provable, had alternative proofs been constructed. Thus Wittgenstein held an important and original "Conceptual Gap Thesis": that the concept of provability does not include that of necessity (I defend this thesis in Chapter III by reference to formal results in modal logic; the results are laid out in Chapter IV). In Chapter V, I conclude by defending Wittgenstein from the charge that, on his view, we can never know any proposition to be necessary. I argue that in fact his account is an anti-sceptical account of necessity.

Degree

Ph.D.

Subject Area

Philosophy

COinS