Proof theoretic and semantical study of Fregean Logic

2018 Fiscal Year Final Research Report

• Project/Area Number: 16K13150
• Research Category: Grant-in-Aid for Challenging Exploratory Research
• Allocation Type: Multi-year Fund
• Research Field: Philosophy/Ethics
• Research Institution: Kyoto University
• Principal Investigator: Sato Masahiko 京都大学, 情報学研究科, 名誉教授 (20027387)
• Co-Investigator(Kenkyū-buntansha): 秋吉 亮太 早稲田大学, 高等研究所, その他(招聘研究員) (20587852)
• Project Period (FY): 2016-04-01 – 2019-03-31
• Keywords: フレーゲ論理学 / 証明論 / 無矛盾性

Outline of Final Research Achievements

In order to carry out the logicism program of reducing mathematics to logic, Frege for the first time in history organized higher-order predicate logic. Thereby, he also initiated analytic philophy and opened a way to Hilbert's formalism.
However, the logical system he created in his ``Grundgesetze der Arithmetic'' was found to be inconsistent due to the paradox pointed out by Russell. Because of this, not many attempts have been made to clarify the cause of the inconsistency of his logical system. The study aimed to find the cause by proof theoretical and semantical methods.

Free Research Field

数理論理学

Academic Significance and Societal Importance of the Research Achievements

フレーゲの論理学におけるラッセルパラドックスの原因の究明は数学的対象の存在論の哲学的分析を深化させるものであり，その学術的意義は大きい．
また，この研究により得られた論理学的成果は現実社会においても日常的に用いられている言語使用の理解にも寄与するものであり社会的にも意義のある成果である．