This paper is meant as a commentary on Remarks on the Philosophy of Psychology, vol. 1, §§ 1096-1097. These paragraphs contain Wittgenstein’s only comments on A. M. Turing’s 1936 paper, ‘On Computable Numbers with an Application to the Entscheidungsproblem’ as well as a mention of Alistair Watson, whose 1938 paper in Mind is of help to understand Wittgenstein’s remarks. We shall focus on the diagonal argument § 1097 (also reprised as Zettel § 694 as well as in a footnote to (Kreisel 1950, p. 281)), which was correctly identified by Juliet Floyd (2012) as a version of Turing’s own use of Cantor’s diagonal in § 9 of his 1936 paper, in order to prove a negative solution to what Copeland (2004) calls the ‘Satisfactoriness Problem’: to find a procedure for enumerating computable sequences in a finite number of steps. Our main interpretative claim is that, in § 1097, Wittgenstein merely couched Turing’s diagonal argument in terms of rules. We will thus be able to find a place Wittgenstein’s variant within his thinking on contradiction (see (Marion & Okada 2013)). Wittgenstein believed that “a contradiction can only occur among the rules of a game” (Ludwig Wittgenstein and the Vienna Circle, p. 124), i.e., that it would be like suddenly facing a configuration where the rules of the game does not tell one what to do next, and the variant of Turing’s diagonal is precisely an instance of this. Finally, we will point out that the latter confirms his view that a ‘hidden contradiction’ can do no harm before it occurs.
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