Ideal concepts, intuitions, and mathematical knowledge acquisitions in Husserl and Hilbert

Mitsuhiro Okada

研究成果: Chapter

1 被引用数 (Scopus)

抄録

We analyze Husserl's and Hilbert's studies on the role of "ideal concepts" and that of the notion of "mathematical intuition" in the context of mathematical knowledge acquisitions. We note a striking similarity between Husserl's analysis in 1901 (presented at Hilbert's seminar) and Hilbert's analysis in the 1920's on the problem justifying the ideal concepts. We also analyze the similarity and difference on Husserl's standpoint and Hilbert's standpoint on mathematical objectivities and on mathematical intuitions. In the course of this analysis we compare these with Gödel's and some Hilbert scool members' standpoints. We also propose a view on mathematical knowledge acquisitions along a "dynamic" interpretation of the Husserlian philosophy of mathematics, which provides a view different from the traditional views such as realist, nominalist, constructivist, conventionalist, empiricist views.

本文言語English
ホスト出版物のタイトルProgress in Discovery Science
編集者Setsuo Arikawa, Ayumi Shinohara
ページ40-77
ページ数38
出版ステータスPublished - 2002 12月 1

出版物シリーズ

名前Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)
2281
ISSN(印刷版)0302-9743
ISSN(電子版)1611-3349

ASJC Scopus subject areas

  • 理論的コンピュータサイエンス
  • コンピュータ サイエンス(全般)

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