Takeuti's proof theory in the context of the Kyoto School


Authors
Andrew Arana
University of Paris 1 Panthéon-Sorbonne
Abstract
Gaisi Takeuti (1926–2017) is one of the most distinguished logicians in proof theory after Hilbert and Gentzen. He extensively extended Hilbert's program in the sense that he formulated Gentzen's sequent calculus, conjectured that cut-elimination holds for it (Takeuti's conjecture), and obtained several stunning results in the 1950–60s towards the solution of his conjecture. Though he has been known chiefly as a great mathematician, he wrote many papers in English and Japanese where he expressed his philosophical thoughts. In particular, he used several keywords such as "active intuition" and "self-reflection" from Nishida's philosophy. In this paper, we aim to describe a general outline of our project to investigate Takeuti's philosophy of mathematics. In particular, after reviewing Takeuti's proof-theoretic results briefly, we describe some key elements in Takeuti's texts. By explaining these texts, we point out the connection between Takeuti's proof theory and Nishida's philosophy and explain the future goals of our project.
Keywords Philosophy of mathematics  Proof theory  Japanese philosophy  Kyoto School  Nishida  Hilbert
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References found in this work BETA

Grundlagen der Mathematik.D. Hilbert & P. Bernays - 1940 - Journal of Symbolic Logic 5 (1):16-20.
On the Theory of Ordinal Numbers.Gaisi Takeuti - 1959 - Journal of Symbolic Logic 24 (1):67-67.

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