Man and Machine, Machine and Man: Wittgenstein and Turing

Abstract

Ludwig Wittgenstein and Alan Turing met in Cambridge in 1937, both of them working on the foundations of mathematics at the time. The exchange of ideas between them took place at Wittgenstein’s 1939 lectures. The article discusses the main topic of this exchange, namely the problem of contradiction in mathematics, and posits that Wittgenstein accepted the version of Cantor’s diagonal proof used by Turing in his On Computable Numbers (1936). He disagreed, however, with Turing’s interpretation and answer to the question: „Can machines think?”.