Reconsideration of the relationship between formalism and intuitionism via proof-theoretical method

• Project/Area Number: 22820054
• Research Category: Grant-in-Aid for Research Activity Start-up
• Allocation Type: Single-year Grants
• Research Field: Philosophy/Ethics
• Research Institution: Keio University
• Principal Investigator: AKIYOSHI Ryota 慶應義塾大学, 文学研究科, 助教 (20587852)
• Project Period (FY): 2010 – 2011
• Project Status: Completed (Fiscal Year 2011)
• Budget Amount: ¥2,340,000 (Direct Cost: ¥1,800,000、Indirect Cost: ¥540,000); Fiscal Year 2011: ¥1,170,000 (Direct Cost: ¥900,000、Indirect Cost: ¥270,000); Fiscal Year 2010: ¥1,170,000 (Direct Cost: ¥900,000、Indirect Cost: ¥270,000)
• Keywords: 哲学 / 倫理学 / 数学基礎論

Research Abstract

We investigated the relationship between formalism and intuitionism from the view points of mathematical logic and philosophy. In the joint mathematical work with G. Mints(Stanford University), the complete cut-elimination theorem for Omega-rule, which had been an open problem, is proved. In the philosophical work, we analysed the history of proof theory from the viewpoint of "analysis of impredicativity" and presented some issues to be addressed.

Research Products

• [Journal Article] 非可述性の分析としての証明論 (2012)
  • Author(s): 秋吉亮太
  • Journal Title: 科学基礎論研究 Volume: 第39巻 Pages: 43-57
  • Peer Reviewed
• [Journal Article] An Extension of the Iterated Omega-Rule (2011)
  • Author(s): Ryota Akiyoshi
  • Journal Title: CARLS Series of Advanced Study of Logic and Sensibility Volume: Vol.5 Pages: 221-230
• [Journal Article] Analysis and Extension of Omega-Rule (2011)
  • Author(s): Ryota Akiyoshi and Grigori Mints
  • Journal Title: arXiv
  • URL: http://arxiv.org/abs/0904.4742
• [Journal Article] An Ordinal-Free Proof of the Cut-elimination Theorem for Pi^1_1-CA withω-rule (2011)
  • Author(s): Ryota Akiyoshi and Grigori Mints
  • Journal Title: The Bulletin of Symbolic Logic Volume: Volume16 Pages: 293-293
• [Journal Article] An Extension of the Iterated Omega-Rule (2011)
  • Author(s): Ryota Akiyoshi
  • Journal Title: CARLS Series of Advance Study of Logic and Sensibility Volume: 5 Pages: 221-230
• [Journal Article] Analysis and Extension of Omega-Rule (2011)
  • Author(s): Ryota Akiyoshi, Grigori Mints
  • Journal Title: arXiv(オンラインジャーナル)
• [Journal Article] Gentzen's First Consistency Proof Revisited (2010)
  • Author(s): Ryota Akiyoshi
  • Journal Title: CARLS Series of Advanced Study of Logic and Sensibility Volume: Vol.4 Pages: 315-324
• [Journal Article] An Ordinal-Free Proof of the Cutelimination Theorem for II^1_1-CA withω-rule (2010)
  • Author(s): Ryota Akiyoshi, Grigori Mints
  • Journal Title: Bulletin Symbolic Logic Volume: 16 Pages: 293-293
  • Peer Reviewed
• [Journal Article] Complete Cut-Elimination Theorem forΩ-Rule
  • Author(s): Ryota Akiyoshi and Grigori Mints
  • Journal Title: The Bulletin of Symbolic Logic
• [Presentation] Complete Cut-Elimination Theorem for Ω-Rule (2011)
  • Author(s): R.Akiyoshi, G.Mints
  • Organizer: Logic Colloquium 2011
  • Place of Presentation: University of Barcelona
  • Year and Date: 2011-07-11
• [Presentation] 非可述性の分析としての証明論 (2011)
  • Author(s): 秋吉亮太
  • Organizer: 2011年度科学基礎論学会ワークショップ「あたらしい数理論理学の揺籃～証明論的な順序数と集合論的順序数」における提題者
  • Place of Presentation: 愛媛大学(招待講演)
  • Year and Date: 2011-06-05
• [Presentation] Complete Cut-Elimination Theorem forΩ-Rule (2011)
  • Author(s): Ryota Akiyoshi and Grigori Mints
  • Organizer: Logic Colloquium 2011
  • Place of Presentation: University of Barcelona
• [Presentation] Ω規則の拡張について (2011)
  • Author(s): 秋吉亮太
  • Organizer: 第四十四回日本科学哲学会
  • Place of Presentation: 日本大学
• [Presentation] 非可述性の分析としての証明論 (2011)
  • Author(s): 秋吉亮太
  • Organizer: 2011年度科学基礎論学会
  • Place of Presentation: 愛媛大学
• [Presentation] Finite Notations for Omega_mu+1-rule (2010)
  • Author(s): Ryota Akiyoshi
  • Organizer: Logic Colloquium 2010
  • Place of Presentation: パリ第七大学
  • Year and Date: 2010-07-27
• [Presentation] Introduction to Proof Theory for Impredicative Systems (2010)
  • Author(s): 秋吉亮太
  • Organizer: Logic Seminar
  • Place of Presentation: 東北大学
  • Year and Date: 2010-06-04
• [Presentation] Finite Notations forΩ_μ+1-rule (2010)
  • Author(s): Ryota Akiyoshi
  • Organizer: Logic Colloquium 2010
  • Place of Presentation: Paris Dederot University
• [Presentation] ゲンツェンの無矛盾性証明再訪 (2010)
  • Author(s): 秋吉亮太
  • Organizer: 論理学と数学の哲学の研究会
  • Place of Presentation: 大阪大学