数学と論理の哲学セミナー Mathieu Marion教授 講演会
“WITTGENSTEIN ON TURING’S DIAGONAL, RULES, AND CONTRADICTION”
- 日時 / Date
- 6月26日 (火) 18:10-19:30 June 26, Tues.,
- 場所 / Venue
Classroom 313, 1F of Graduate School Building, Mita Campus of Keio University. (Number 8 of the Campus Map)
- 講演者 / Speakers
- Mathieu Marion教授 （ケベック大学モントリオール校哲学科教授）
Prof. Mathieu Marion (Professor, Department of Philosophy, Université du Québec à Montréal)
- 題目 / Title
- Mathieu Marion 教授 講演会
“WITTGENSTEIN ON TURING’S DIAGONAL, RULES, AND CONTRADICTION” (Joint work with Mitsuhiro Okada, Keio University)
アブストラクト / Abstracts
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.
- Copeland, B. J., 2004, ‘Computable Numbers: A Guide’, in B. J. Copeland (ed.), The Essential Turing, Oxford, Clarendon Press.
- Floyd, J., 2012, ‘Wittgenstein’s Diagonal Argument: A Variation on Cantor and Turing’, in P. Dybjer, S. Lindström, E. Palmgren & G. Sundholm (eds.), Epistemology versus Ontology: Essays on the Philosophy and Foundations of
Mathematics in Honour of Per Martin-Löf, Berlin, Springer, 25-55.
- Kreisel, G., 1950, ‘Note on Arithmetic Models for Consistent Formulae of the Predicate Calculus’, Fundamenta Mathematicae, vol. 37, 265-285.
- Marion, M. & M. Okada, 2013, ‘Wittgenstein on Contradiction and Consistency: An Overview’, O Que No Faz Pensar, vol. 33, 52-79.
- Turing, A. M., 1936, ‘On Computable Numbers with an Application to the Entscheidungsproblem’, Proceedings of the London Mathematical Society, 2nd series, vol. 42, 230-65.
- Watson, A. G. D., 1938, ‘Mathematics and its Foundations’, Mind, vol. 47, 440-451.
- Wittgenstein, L., 1967, Zettel, Oxford, Blackwell.
- Wittgenstein, L., 1979, Ludwig Wittgenstein and the Vienna Circle. Conversations recorded by Friedrich Waismann, Oxford, Blackwell.
- Wittgenstein, L., 1980, Remarks on the Philosophy of Psychology, vol. 1, Oxford, Blackwell.