New Developments in the Philosophy of Formalism: Through the Elucidation of Gaisi Takeuti's Logical Philosophy

2023 Fiscal Year Final Research Report

• Project/Area Number: 19K00022
• Research Category: Grant-in-Aid for Scientific Research (C)
• Allocation Type: Multi-year Fund
• Section: 一般
• Review Section: Basic Section 01010:Philosophy and ethics-related
• Research Institution: Waseda University
• Principal Investigator: Akiyoshi Ryota 早稲田大学, 高等研究所, その他(招聘研究員) (20587852)
• Project Period (FY): 2019-04-01 – 2024-03-31
• Keywords: 数学の哲学 / 論理学 / 証明論 / 京都学派 / 西田幾多郎 / 自己 / デジタルツイン / 志向性

Outline of Final Research Achievements

The purpose of this study is to shed light on and elucidate new aspects of formalism by approaching Gaisi Takeuti's logical philosophy, the greatest postwar logician produced in Japan. Until now, Takeuti has been treated exclusively as a mathematician, but this study has revealed the connection with the Kyoto School philosophy represented by Nishida Kitaro. In addition, a mathematical result was obtained by reconstructing Takeuti's proof of the well-foundedness of ordinal numbers. Relatedly, we were able to advance a comparative study with Feferman, who represents the postwar proof theory in the West. As an unexpected byproduct, we were also able to advance research on the application of the philosophy of the self in Eastern philosophy to the philosophy and logic of the digital twin.

Free Research Field

数学・論理学の哲学

Academic Significance and Societal Importance of the Research Achievements

本研究によって、戦後最大の論理学者である竹内外史の論理哲学と西田幾多郎に代表される京都学派の哲学の繋がりが明らかになってきたことで、形式主義の新たな側面に光を当てることができた。これは、数学・論理学の哲学の新たな方向性を指ししており、西洋哲学と東洋哲学の新たな接点を提供する意義ももっている。また、デジタルツインの研究は、東洋的な自己観の応用哲学へのさらなる適用可能性を意味している。