Atelier : perspectives philosophiques sur des théories formelles jeudi 28 février 2019, 9h30 - 13h IHPST, salle de conférences (13, rue de Four, Paris, 75006, 2ème étage) Organisateur : Andrew Arana, philosophie, Univ. Paris 1 Panthéon-Sorbonne, IHPST ([email protected])
9h30 - 11h Walter Dean (Philosophy, University of Warwick, UK) "Undecidability and intensionality via arithmetized completeness" 11h - 11h30 Pause 11h30 - 13h Ryota Akiyoshi (Waseda Institute for Advanced Study, Japan, Keio University, Japan) "Takeuti’s finitism revisited" Resumés : Walter Dean (Philosophy, University of Warwick, UK) "Undecidability and intensionality via arithmetized completeness" Abstract: This talk will refine and generalize a method for obtaining formally undecidable arithmetical statements via the formalization of familiar paradoxes originally developed by Georg Kreisel and Hao Wang. A central tool will be the arithmetized completeness theorem which will be employed to obtain first-order interpretations of second-order theories in which various “paradoxical notions” may be formalized. Connections to the treatment of the paradoxes by Hilbert and Bernays (1939) and to the intensionality of arithmetization in the sense of Feferman (1960) will also be explored. Ryota Akiyoshi (Waseda Institute for Advanced Study, Japan, Keio University, Japan) "Takeuti’s finitism revisited" In this talk, we address several mathematical and philosophical issues of Gaisi Takeuti’s proof theory, who is one of the most distinguished logicians in proof theory after Hilbert and Gentzen. He furthered the realization of Hilbert’s program by formulating Gentzen’s sequent calculus for higher-order logics, conjecturing that the cut-elimination holds for it (Takeuti’s conjecture), and obtaining several stunning results in the 1950-60’s towards the solution of his conjecture. This talk consists of two parts. (1) To summarize Takeuti’s background and the argument of the well-ordering proof of ordinals up to ε0 , (2) To evaluate it on philosophical grounds. Also, we will explain several mathematical and philosophical issues to be addressed. This is joint work with Andrew Arana. -- Pour toute question, la FAQ de la liste se trouve ici: https://www.vidal-rosset.net/
