On Wittgenstein's transcendental deductions

Abstract

In this paper, I aim to shed light on the use of transcendental deductions, within demonstrations of aspects of Wittgenstein's early semantics, metaphysics, and philosophy of mathematics. I focus on two crucial claims introduced by Wittgenstein within these transcendental deductions, each identified in conversation with Desmond Lee in 1930-31. Specifically, the claims are of the logical independence of elementary propositions, and that infinity is a number. I show how these two, crucial claims are both demonstrated and subsequently deployed by Wittgenstein within a series of transcendental deductions, a series which begins with extensionalism as a generalized condition of sense on propositions, and in the context of which are then derived various, further, significant and unobvious presuppositions generated by that generalized condition of sense. In addition to clearing up deductions of these two, aforementioned claims, I also elucidate deductions of the subsistence of objects, and of logical space as an infinite totality.