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Séminaire
Séminaire Philmath
Nous aurons le plaisir d'accueillir : Hidenori Kurokawa (Kobe University)
Titre :
"Wittgenstein’s Diagonal Argument" Revisited: The Overlooked Kreisel Connection
Résumé :
Juliet Floyd has famously argued that Wittgenstein’s 1947 remark on a variant of Cantor’s diagonal proof contains a genuine argument, which she labels “Wittgenstein’s diagonal argument”. Following Floyd, interpreters of “Wittgenstein’s diagonal argument” have focused primarily on what we call the Turing-Watson connection. In this talk, we draw attention to a largely overlooked Kreisel connection. In 1950, Georg Kreisel reported two observations on diagonal definitions made by Wittgenstein in the mid-to-late 1940s, one of which bears a close resemblance to Wittgenstein’s 1947 remark. Throughout his career, Kreisel repeatedly returned to these two observations and explored their relevance to logic and the foundations of mathematics. This talk has three goals. First, we show that Wittgenstein’s reported observations on diagonal definitions indicate both an adequate understanding of Gödel’s incompleteness theorems and an anticipation of Henkin’s problem. Second, we argue that the Kreisel connection reveals a subtle shift in perspective on Cantor’s diagonal proof, namely the recognition of partiality, and we offer a more nuanced treatment of the logical structure of Wittgenstein’s 1947 remark on this basis. Third, we suggest a mutual influence between Wittgenstein and Kreisel. This is joint work with Zhao Fan.
Résumé :
Juliet Floyd has famously argued that Wittgenstein’s 1947 remark on a variant of Cantor’s diagonal proof contains a genuine argument, which she labels “Wittgenstein’s diagonal argument”. Following Floyd, interpreters of “Wittgenstein’s diagonal argument” have focused primarily on what we call the Turing-Watson connection. In this talk, we draw attention to a largely overlooked Kreisel connection. In 1950, Georg Kreisel reported two observations on diagonal definitions made by Wittgenstein in the mid-to-late 1940s, one of which bears a close resemblance to Wittgenstein’s 1947 remark. Throughout his career, Kreisel repeatedly returned to these two observations and explored their relevance to logic and the foundations of mathematics. This talk has three goals. First, we show that Wittgenstein’s reported observations on diagonal definitions indicate both an adequate understanding of Gödel’s incompleteness theorems and an anticipation of Henkin’s problem. Second, we argue that the Kreisel connection reveals a subtle shift in perspective on Cantor’s diagonal proof, namely the recognition of partiality, and we offer a more nuanced treatment of the logical structure of Wittgenstein’s 1947 remark on this basis. Third, we suggest a mutual influence between Wittgenstein and Kreisel. This is joint work with Zhao Fan.