Mon Apr 4, 2016
20 Barrows, 4:10–6 PM
|Alfred Tarski Lectures
William W. Tait (Professor Emeritus, Department of Philosophy and CHSS, University of Chicago)
On Skepticism about the Ideal
There is a historic skepticism about mathematics that hangs on the fact that the objects of mathematics, structures and their elements—numbers, functions, sets, etc., are ideal, i.e. that empirical facts, facts about the natural world, have no relevance to the truth of propositions about them.
Of course, the view that ‘existence’ simply means empirical existence, so that the term is misused as applied to ideal things can be countered only on pragmatic grounds, that we use the term in other contexts and that it is very useful there. The rejection of ideal existence becomes meaningful only if one has a transcendental ground on which to stand and judge applications of the term. I believe that the ground, at least implicitly, has been a wrong thesis about how language works, namely the view that genuine reference to objects presupposes a non-linguistic interaction with them. And that is what I want to talk about. My argument draws on a reading of Wittgenstein’s Philosophical Investigations, a reading which is more positive than a more common one according to which he, himself, was a skeptic.