The Lectures on the Foundations of Mathematics are not formal lectures ; they offer a lot of dialogues between Wittgenstein and his class, and Alan Turing  is obviously the main person spoken to. Wittgenstein fights against his conception of mathematics ; he continually argues against the legitimacy of any theoretical approach to the foundations of mathematics and rejects the very possibility of reducing mathematical calculi to logical calculus. Besides, he stands up against « bolchevism in mathematics » (i.e. « finistism ») and puts forward a subtle view of foundational problems which leaves the last word to practice, and recognizes an autonomy, but no autarky, to formal systems.

Edited by Cora Diamond

Bilingual edition English / French