Sciences, Philosophie, Histoire – UMR 7219, laboratoire SPHERE

Partenaires

!!! CANCELLED !!!

Tuesday March 17, 2020, 10am–4pm

IHPST
Room of conferences, level 2,
13, rue du Four, Paris 75006

Organised in the framework
of the working group “Axioms & definitions”,
co-steered by
Vincenzo de Risi (SPHERE), Paola Cantù (CGGG), Gabriella Crocco (CGGG) & Andy Arana (IHPST),

a collaboration
of SPHere, the CGGG of Aix-Marseille, & the IHPST

PROGRAM

11:30am-1:00pm

Jeremy Avigad (Carnegie Mellon University)
Formal Methods and the Epistemology of Mathematics

1:00pm-2:00pm Lunchbreak

2:00pm-3:30pm

Ryota Akiyoshi (Waseda Institute for Advanced Study and Keio University)
Takeuti’s finitism in the context of the Kyoto school

ABSTRACTS

Jeremy Avigad (Carnegie Mellon University)
Formal Methods and the Epistemology of Mathematics
In the twentieth-century British-American analytic tradition, two types of questions dominated philosophy of mathematics : What is mathematical knowledge, and what justifies a claim to mathematical knowledge ? What sorts of things are mathematical objects, and how do we (or can we, or should we) come to have knowledge of them ? I will argue that there is a broader array of questions that are interesting and important questions for philosophy of mathematics, and that contemporary developments in logic and computer science offer new analytic tools to address them. I will also argue that, when the questions above are situated in this context, it becomes possible to address them in substantial and satisfying ways.

Ryota Akiyoshi (Waseda Institute for Advanced Study and Keio University)
Takeuti’s finitism in the context of the Kyoto school
Gaisi Takeuti (1926-2017) 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-oder logics, conjecturing the cut-elimination theorem holds for it (Takeuti’s conjecture), and obtaining several stunning results in the 1950—60’s towards the solution of it.
In this talk, we aim to describe a general outline of our project to investigate Takeuti’s philosophy of mathematics. In particular, we point out that there is a crucial difference between Takeuti’s program and Hilbert’s program, which is based on the fact that Takeuti’s philosophical thinking goes back to Nishida’s philosophy in Japan. Additionally, we try to address the issue how Nishida’s philosophy could shape Takeuti’s works in the foundations of mathematics.
This is joint work with Andrew Arana (Paris 1).

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