History of the foundations of mathematics via sociological and inforrmatiics methods

2018 Fiscal Year Final Research Report

• Project/Area Number: 16K12799
• Research Category: Grant-in-Aid for Challenging Exploratory Research
• Allocation Type: Multi-year Fund
• Research Field: Sociology/History of science and technology
• Research Institution: Kyoto University
• Principal Investigator: Hayashi Susumu 京都大学, 文学研究科, 教授 (40156443)
• Project Period (FY): 2016-04-01 – 2019-03-31
• Keywords: 数学基礎論史 / 数理論理学史 / social graph

Outline of Final Research Achievements

Some unknown aspects of the development of mathematical logic and the foundations of mathematics from 19th century to early 20th century were elucidated. For example, the "Logik" (logic) of the booklet "Was sind und sollen die Zahlen? (1888)" by Richard Dedekind was the traditional logic plus maps (Abbiludng) for the author Richard Dedekind. This had been pointed out by several authors, but a new evidence was pointed out by relating Dedekind's logic with Schroeder's logic that Dedekind mentioned in the second edition of the booklet. Schroeder had explicitly and intentionally excluded the usage of "belong to" relation and the traditional way to make use of "copula". By Dedekind's mentions of Schroeder's works in the second edition of the booklet, we can understand that Dedekind's "reversed epsilon" was also a version of "copula". Another point elucidated was the role of British mathematician Venn known as the inventor of Venn diagram. Venn invented it to simplify the traditional logic.

Free Research Field

数学史

Academic Significance and Societal Importance of the Research Achievements

現在の数学の基礎付けが、どの様な歴史的プロセスを経て生まれたかを明らかにすることにより、文系の非専門家からも関心を集めることが多い、「数学基礎論」の真の姿を明らかにし、一般向け書籍だけでなく、専門書にも散見されることがある、数学の基礎についての誤解を明らかにできる。
また、本研究プロジェクトは、本来、何らかの理由で史料が失われている場合に、それを迂回して関連する他分野の史料を通して「失われた史料」を「補完」できることを実例で示すことを目的としていたが、これは今回の史料においては達成できなかったものの、将来的には歴史学に大きな貢献をなし得る方法論であることが確認できたことは、大きな成果だろう。