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Historical Developments and Contemporary Tasks of the Philosophy of Logic and Mathematics in Analytic Philosophy

Research Project

Project/Area Number 03301001
Research Category

Grant-in-Aid for Co-operative Research (A)

Allocation TypeSingle-year Grants
Research Field Philosophy
Research InstitutionHokkaido University

Principal Investigator

YAMADA Tomoyuki  Hokkaido University Faculty of Letters Associate Professor, 文学部, 助教授 (40166723)

Co-Investigator(Kenkyū-buntansha) NAKAGAWA Hajime  Hokkaido University Faculty of Letters Instructor, 文学部, 助手 (40237227)
NAKATOGAWA Koji  Hokkaido University Faculty of Letters Associate Professor, 文学部, 助教授 (20237316)
KANEKO Hiroshi  Senshu University Faculty of Letters Lecturer, 文学部, 講師 (60191988)
ITO Kunitake  Kyoto University Faculty of Letters Associate Professor, 文学部, 助教授 (90144302)
IIDA Takashi  Chiba University, Faculty of Letters Professor, 文学部, 教授 (10117327)
Project Period (FY) 1991 – 1992
Project Status Completed (Fiscal Year 1992)
Budget Amount *help
¥4,200,000 (Direct Cost: ¥4,200,000)
Fiscal Year 1992: ¥2,000,000 (Direct Cost: ¥2,000,000)
Fiscal Year 1991: ¥2,200,000 (Direct Cost: ¥2,200,000)
Keywordsinfinity / self-reference paradox / set theory / intuitionism / theory of meaning / model theory / pragmatism / situation theory / 非古典論理 / 不完全性定理
Research Abstract

This year did we try to make much more study of each of our tasks and to give a synthetic view of our whole task. Concretely, concerning the historical development of the philosophy of logic and mathematics,did we study (1)Frege's conception of generality by looking at his text, (2)Poincare's constructive view of mathematics by reconstruct his argument with Russell and Zermelo, (3)Wittgenstein's criticism to intuitionistic philosophy and (4)Ramsey's theory of truth and belief by pondering his pragmatism. And concerning the contemporary tasks of the philosophy of logic, did we study (5)the radical criticism from the situation theory to the classical theory of truth and semantics, (6)an adaptation of situation theory to the semantics of Japanese and (7)an essential question 'what is a logical constant' by surveying recent researches on this matter. And concerning the contemporary tasks of the philosophy of mathematics, did we study, especially about groundings of set theory, (8)D.Lewis' mereological reconstruction of set theory, (9) M.Dummett's criticism to set theory from his class-monistic point of view. And we made a survey of (10)new developments of the intuitionistic type theory. We, therefore, have gained a new vision of the part which set theory plays in the philosophy of mathematics both in the historical context and in contemporary arguments. And so we have examined constructive views, e.g. intuitionism, both for the philosophy of mathematics and for the philosophy of logic. And we have clarified philosophical tasks which overlap computer science and other empirical sciences.

Report

(3 results)
  • 1992 Annual Research Report   Final Research Report Summary
  • 1991 Annual Research Report
  • Research Products

    (31 results)

All Other

All Publications (31 results)

  • [Publications] 飯田 隆: "真理と意味" 『西日本哲学会会報』. 40. 21-30 (1992)

    • Description
      「研究成果報告書概要(和文)」より
    • Related Report
      1992 Final Research Report Summary
  • [Publications] 伊藤 邦武: "合理性の自然化" 『科学哲学』. 25. 1-13 (1992)

    • Description
      「研究成果報告書概要(和文)」より
    • Related Report
      1992 Final Research Report Summary
  • [Publications] ITO Kunitake: "The Cost of Conflict ;A Note on Risk Analysis" Acta Institutionis Philosophiae et Aestheticae. 10. 75-87 (1992)

    • Description
      「研究成果報告書概要(和文)」より
    • Related Report
      1992 Final Research Report Summary
  • [Publications] 戸田山 和久: "クラスの概念と部分全体関係" 『名古屋大学教養部紀要』. 37. 1-27 (1993)

    • Description
      「研究成果報告書概要(和文)」より
    • Related Report
      1992 Final Research Report Summary
  • [Publications] 中戸川 孝治: "充足列・定義可能性・実質的+全性:A.タルスキー1931年論文について" 北海道大学哲学会『哲学』. 28. 1-12 (1992)

    • Description
      「研究成果報告書概要(和文)」より
    • Related Report
      1992 Final Research Report Summary
  • [Publications] 中川 大: "色彩空間と排中律ー中期ウィトゲンシュタインにおける反直観主義哲学の構想ー" 『北海道大学文学部紀要』. 41-2. 33-56 (1992)

    • Description
      「研究成果報告書概要(和文)」より
    • Related Report
      1992 Final Research Report Summary
  • [Publications] 中川 大: "前提と記述ー真偽二値性へのふたつの態度ー" 『科学基礎論研究』. 80. 65-70 (1993)

    • Description
      「研究成果報告書概要(和文)」より
    • Related Report
      1992 Final Research Report Summary
  • [Publications] KOBAYASI Mitio: "La philosophie raturelle de Descartes" Vrin, (1993)

    • Description
      「研究成果報告書概要(和文)」より
    • Related Report
      1992 Final Research Report Summary
  • [Publications] IIDA,Takashi: "Truth and Meaning" Proceedings of the West-Japan Philosophical Society.40. 21-30 (1992)

    • Description
      「研究成果報告書概要(欧文)」より
    • Related Report
      1992 Final Research Report Summary
  • [Publications] ITO,Kunitake: "The Naturalization of Rationality" Philosophy of Science.25. 1-13 (1992)

    • Description
      「研究成果報告書概要(欧文)」より
    • Related Report
      1992 Final Research Report Summary
  • [Publications] ITO,Kunitake: "The Cost of Conflict; A Note on Risk Analysis" Acta Institutionis Philosophiae et Aestheticae.10. 75-87 (1992)

    • Description
      「研究成果報告書概要(欧文)」より
    • Related Report
      1992 Final Research Report Summary
  • [Publications] TODAYAMA,Kazuhisa: "The Concept of Class and Part-Whole Relation" Research Bulletin; series A (College of General Education Nagoya University).37. 1-27 (1993)

    • Description
      「研究成果報告書概要(欧文)」より
    • Related Report
      1992 Final Research Report Summary
  • [Publications] NAKATOGAWA,Koji: "Satisfaction sequence, definability and material adequacy in A.Tarski's paper published in 1931" Annals of the Philosophical Society of Hokkaido University.28. 1-12 (1992)

    • Description
      「研究成果報告書概要(欧文)」より
    • Related Report
      1992 Final Research Report Summary
  • [Publications] NAKAGAWA,Hajime: "Color Space and the Law of Excluded Middle -Middle Wittgenstein agaist Intuitionism-" Annual Report on Cultural Science(Faculty of the Letters Hokkaido University).41-2. 33-56 (1992)

    • Description
      「研究成果報告書概要(欧文)」より
    • Related Report
      1992 Final Research Report Summary
  • [Publications] NAKAGAWA,Hajime: "Presupposition and Description -Two Attitudes toward Bivalence-" Journal of the Japan Association for Philosophy of Science.80. 65-70 (1993)

    • Description
      「研究成果報告書概要(欧文)」より
    • Related Report
      1992 Final Research Report Summary
  • [Publications] 飯田 隆: "真理と意味" 『西日本哲学会会報』. 40. 21-30 (1992)

    • Related Report
      1992 Annual Research Report
  • [Publications] 伊藤 邦武: "合理性の自然化" 『科学哲学』. 25. 1-13 (1992)

    • Related Report
      1992 Annual Research Report
  • [Publications] ITO,Kunitake: "The Cost of Conflict;A Note on Risk Analysis" Acta Institutionis et Aestheticae. 10. 75-87 (1992)

    • Related Report
      1992 Annual Research Report
  • [Publications] 戸田山 和久: "クラスの概念と部分全体関係" 『名古屋大学教養部紀要』. 37. 1-27 (1993)

    • Related Report
      1992 Annual Research Report
  • [Publications] 中戸川 孝治: "充足列・定義可能性・実質的十全性:A.タルスキー1931年論文について" 北海道大学哲学会『哲学』. 28. 1-12 (1992)

    • Related Report
      1992 Annual Research Report
  • [Publications] 中川 大: "色彩空間と排中律 ー中期ウィトゲンシュタインにおける反直観主義哲学の構想ー" 『北海道大学文学部紀要』. 41-2. 33-56 (1992)

    • Related Report
      1992 Annual Research Report
  • [Publications] 中川 大: "前提と記述 ー真偽二値性へのふたつの態度ー" 『科学基礎論研究』. 80. 65-70 (1993)

    • Related Report
      1992 Annual Research Report
  • [Publications] KOBASI,Mitio: "La philosophie nature de Descartes" Vrin, (1993)

    • Related Report
      1992 Annual Research Report
  • [Publications] 飯田 隆: "不完全性定理はなぜ意外だったのか" 科学基礎論研究. 第77号(Vol.20.No3). 7-13 (1991)

    • Related Report
      1991 Annual Research Report
  • [Publications] 金子 洋之: "意味の理論はいかにして言語の知識を特徴づけるかーダメットのデイヴィドソン解釈をめぐってー" 専修人文論集. 49号. 161-177 (1992)

    • Related Report
      1991 Annual Research Report
  • [Publications] Kunitake Ito (伊藤 邦武): "Fusion of Personal Identity?" Acta Institutionis Philosophiae et Aestheticae. Vol.9. 9-20 (1991)

    • Related Report
      1991 Annual Research Report
  • [Publications] 中戸川 孝治: "A. Tarskiにより定義された論理的導出関係:J. Etchemendyによる再構成と批判" 筑波哲学. 3号. 1-8 (1992)

    • Related Report
      1991 Annual Research Report
  • [Publications] 岡本 賢吾: "無限の理論の系譜学 ー実体のシステムから集合のシステムへー" 現代哲学の昌険(9) ゲ-ムと計算 (岩波書書). 167-238 (1991)

    • Related Report
      1991 Annual Research Report
  • [Publications] 伊藤 邦武: "言語と自由" 現代哲学の昌険(13) 制度と自由 (岩波書店). 333-398 (1991)

    • Related Report
      1991 Annual Research Report
  • [Publications] Hideyuki Nakashima & Syun Tutiya: "Inferring in a Situation about Situations" Situation Theory and Its Applicaions,vol.2,ed.by J.Barwise,J.M.Gawron,G.Plotkin and Syun Tutiya (Center for the Study of Lnmguage and Information). 215-227 (1991)

    • Related Report
      1991 Annual Research Report
  • [Publications] Hiroyuki Suzuki & Syun Tutiya: "A Strictly Incremental Approach to Japanese Grammar" Situation Theory and Its Applicaons,vol.2,ed.by J.Barwise,J.M.Gawron,G.Plotkin and Syun Tutiya(Center for the Study of Language and Information). 517-532 (1991)

    • Related Report
      1991 Annual Research Report

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Published: 1991-04-01   Modified: 2016-04-21  

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