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Studies on the interaction between analysis and algebra through "Philosophy of Concepts": in the cases of noncommutative geometry and algebraic geometry

Research Project

Project/Area Number 23520033
Research Category

Grant-in-Aid for Scientific Research (C)

Allocation TypeMulti-year Fund
Section一般
Research Field Philosophy/Ethics
Research InstitutionSeisen University. (2013)
Sendai Shirayuri Women's College (2011-2012)

Principal Investigator

HARADA Masaki  清泉女子大学, 付置研究所, 准教授 (90453357)

Project Period (FY) 2011 – 2013
Project Status Completed (Fiscal Year 2013)
Budget Amount *help
¥2,340,000 (Direct Cost: ¥1,800,000、Indirect Cost: ¥540,000)
Fiscal Year 2013: ¥780,000 (Direct Cost: ¥600,000、Indirect Cost: ¥180,000)
Fiscal Year 2012: ¥780,000 (Direct Cost: ¥600,000、Indirect Cost: ¥180,000)
Fiscal Year 2011: ¥780,000 (Direct Cost: ¥600,000、Indirect Cost: ¥180,000)
Keywordsエピステモロジー / 概念の哲学 / ヴュイユマン / グランジェ / 作用素代数 / 非可換幾何学 / 代数幾何学 / ガロア理論
Research Abstract

This research puts into practice for modern mathematics "Philosophy of Concepts" developed by such French philosophers, as J. Vuillemin and G.-G. Granger. Using the method of Vuillemin's "Philosophy of Algebra" (1962), which philosophically analyzes the birth of Glois group and its extension to many domains of mathematics, I apply this method for studying the birth and generation of the concepts in noncommutative geometry introduced by A. Connes, as well as of those in algebraic geometry developed by A. Grothendieck. New geometrical objects are born through rich interactions between analytical and algebraic operations in these geometries. There, the concepts such as group, sheaf and (co)homology play important roles for clarifying and relating the structures of objects in many mathematical domains.

Report

(4 results)
  • 2013 Annual Research Report   Final Research Report ( PDF )
  • 2012 Research-status Report
  • 2011 Research-status Report
  • Research Products

    (11 results)

All 2014 2013 2012 2011 Other

All Journal Article (3 results) (of which Peer Reviewed: 1 results) Presentation (6 results) (of which Invited: 3 results) Book (2 results)

  • [Journal Article] Etude Phenomenologique, epistemologique et hermeneutique de la geometrie non commutative2012

    • Author(s)
      Masaki Harada
    • Journal Title

      Revue Philosophique de Louvain

      Volume: 110(2) Pages: 293-324

    • Related Report
      2013 Final Research Report
  • [Journal Article] Etude phenomenologique, epistemologique et hermeneutique de la geometrie non commutative2012

    • Author(s)
      Masaki HARADA
    • Journal Title

      Revue philosophique de Louvain

      Volume: 110 (2) Pages: 297-328

    • Related Report
      2011 Research-status Report
    • Peer Reviewed
  • [Journal Article] 数学と哲学における操作、対象、経験:フッサールのノエシス-ノエマ相関とグランジェの操作-対象双対2011

    • Author(s)
      原田雅樹
    • Journal Title

      VOL(特集:エピステモロジー、以文社)

      Pages: 546-557

    • Related Report
      2013 Final Research Report
  • [Presentation] ヴュイユマンの『代数学の哲学』は代数的様式によって証明されたエチカであるか?2014

    • Author(s)
      原田雅樹
    • Organizer
      科研「フランス・エピステモロジーの伏流としてのスピノザ」、第2回研究会
    • Place of Presentation
      大阪大学豊中キャンパス
    • Year and Date
      2014-03-08
    • Related Report
      2013 Final Research Report
    • Invited
  • [Presentation] ジュール・ヴュイユマンの『代数の哲学』―ガロア理論から作用・操作の存在論、構造分析の方法論へ2012

    • Author(s)
      原田雅樹
    • Organizer
      第7回科学基礎論春のセミナー
    • Place of Presentation
      名古屋大学
    • Year and Date
      2012-03-05
    • Related Report
      2013 Final Research Report
    • Invited
  • [Presentation] ジュール・ヴュイユマンの『代数学の哲学』-ガロア理論から作用・操作の存在論、構造分析の方法論へ-2012

    • Author(s)
      原田雅樹
    • Organizer
      第7回科学基礎論春のセミナー(招待講演)
    • Place of Presentation
      名古屋大学
    • Related Report
      2011 Research-status Report
  • [Presentation] Kant, Fichte and Algebraic Operations: Philosophy of Algebra according to Jules Vuillemin2011

    • Author(s)
      Masaki Harada
    • Organizer
      14th Congress of logic, methodology and philosophy of science
    • Place of Presentation
      Nance, France
    • Related Report
      2013 Final Research Report
  • [Presentation] Kant, Fichte and Algebraic Operations: Philosophy of Algebra according to Jules Vuillemin2011

    • Author(s)
      原田雅樹 HARADA, Masaki
    • Organizer
      14th Congress of Logic, methodology and Philosophy of Science
    • Place of Presentation
      Nancy, France
    • Related Report
      2011 Research-status Report
  • [Presentation] ヴュイユマンの『代数学の哲学』は代数的様式によって証明されたエチカであるか?

    • Author(s)
      原田雅樹
    • Organizer
      科研「フランス・エピステモロジーの伏流としてのスピノザ」第2回研究会
    • Place of Presentation
      大阪大学豊中キャンパス
    • Related Report
      2013 Annual Research Report
    • Invited
  • [Book] ヴュイユマンにおける〈代数学の哲学〉-ガロア理論から操作・作用の存在論、構造分析の方法論へ『エピステモロジー-20世紀のフランス科学思想史』2013

    • Author(s)
      原田雅樹
    • Publisher
      慶應義塾大学出版会
    • Related Report
      2013 Final Research Report
  • [Book] 「ヴュイユマンにおける〈代数学の哲学〉―ガロア理論から操作・作用の存在論、構造分析の方法論へ」、『エピステモロジー―20世紀のフランス科学思想史』所収2013

    • Author(s)
      原田雅樹 (金森修 編集)
    • Publisher
      慶應大学出版会
    • Related Report
      2012 Research-status Report

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Published: 2011-08-05   Modified: 2019-07-29  

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