Wittgenstein, Turing, and the Intelligence of Games

One of Wittgenstein’s most quoted passages from his Remarks on the Philosophy of Psychology concerns Turing’s “machines” and says verbatim: “These machines are humans who calculate. And one might express what he [Turing] says also in the form of games.” This passage not only captures the kernel of Turing’s conceptual argument for the adequacy of his definition of “computability”, as presented in his article On Computable Numbers (1936), but also helps clarify Turing’s idea of “mechanical intelligence.” Indeed, the notion of game provides an ideal means to focus on similarities and differences between Turing and Wittgenstein’s views of mechanical procedures, mathematical understanding, and thinking activity. The live encounter between Ludwig Wittgenstein and Alan Turing took place in Cambridge in 1939, when Wittgenstein’s Lectures on the Foundations of Mathematics were regularly attended by Turing. Interestingly, during the conversations between the two, Turing seems to play the role of the Wittgenstein of the Tractatus, to allow the present Wittgenstein to reassess what he deplores as mistaken or misleading in his early work. As for Turing himself, his reflection on thinking machines from the late 1940s demonstrates the significance of his dialogue with Wittgenstein.