| Project/Area Number |
17H02263
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| Research Category |
Grant-in-Aid for Scientific Research (B)
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| Allocation Type | Single-year Grants |
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| Section | 一般 |
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| Research Field |
Philosophy/Ethics
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| Research Institution | Kobe University |
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Principal Investigator |
Kikuchi Makoto 神戸大学, システム情報学研究科, 教授 (60273801)
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| Co-Investigator(Kenkyū-buntansha) |
岡本 賢吾 東京都立大学, 人文科学研究科, 教授 (00224072)
岡田 光弘 慶應義塾大学, 文学部(三田), 名誉教授 (30224025)
三好 博之 京都産業大学, 理学部, 教授 (60286135)
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| Project Period (FY) |
2017-04-01 – 2022-03-31
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| Project Status |
Completed (Fiscal Year 2022)
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| Budget Amount *help |
¥16,640,000 (Direct Cost: ¥12,800,000、Indirect Cost: ¥3,840,000)
Fiscal Year 2021: ¥4,160,000 (Direct Cost: ¥3,200,000、Indirect Cost: ¥960,000)
Fiscal Year 2020: ¥2,990,000 (Direct Cost: ¥2,300,000、Indirect Cost: ¥690,000)
Fiscal Year 2019: ¥2,990,000 (Direct Cost: ¥2,300,000、Indirect Cost: ¥690,000)
Fiscal Year 2018: ¥2,990,000 (Direct Cost: ¥2,300,000、Indirect Cost: ¥690,000)
Fiscal Year 2017: ¥3,510,000 (Direct Cost: ¥2,700,000、Indirect Cost: ¥810,000)
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| Keywords | 数学の哲学 / 論理学の哲学 / 計算の哲学 / 数学基礎論 / 証明論 / 集合論 / 数理論理学 / 哲学 |
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| Outline of Final Research Achievements |
There are four principles in the modern philosophy of mathematics: (1) reduction of mathematics to arithmetic and set theory, (2) axiomatization of set theory by the first-order logic, (3) formalization of the concept of proofs by the first-order logic, (4) characterization of computability by Turing machine. The aim of this research is giving new developments of the philosophy of mathematics and philosophical explication of the concepts of computation, inference, and information, by investigating the relationship between these four principles and the modern standard view of mathematics and mutual relationship between the four principles. In this research project, we have analyzed the influence of Kant's philosophy to the modern logic, the possibility of new interpretations of Frege's logic, philosophical significance of mathematical results of Gaisi Takeuti, and the relationship between the modern logic and Dummett's philosophy of mathematics.
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| Academic Significance and Societal Importance of the Research Achievements |
数学の哲学の中核には計算，推論，情報といった概念があり，数学の哲学は情報科学や計算機科学の起源の一つである．数学の哲学の新たな展開はこれらの概念の本質的な見直しに繋がるもので，社会的な影響が極めて大きい．本研究による数学の哲学の四つの原理の分析は数学の哲学の発展に留まらず，数学の哲学と数学それ自身の関係を再構築し，数学それ自身や情報科学の革新へ貢献することが期待される．また，本研究によって現代の論理学の発展は古典的な哲学の問題の展開と深く関わっていることが示された．数学，情報科学，数学以外の哲学のいずれにおいても，本研究の成果がさらに発展させられることが強く期待される．
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