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

Research output: Chapter in Book/Report/Conference proceedingChapter

1 Citation (Scopus)

Abstract

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.

Original languageEnglish
Title of host publicationLecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)
Pages40-77
Number of pages38
Volume2281
Publication statusPublished - 2002

Publication series

NameLecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)
Volume2281
ISSN (Print)03029743
ISSN (Electronic)16113349

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Knowledge Acquisition
Knowledge acquisition
Hilbert
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Concepts
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ASJC Scopus subject areas

  • Computer Science(all)
  • Theoretical Computer Science

Cite this

Okada, M. (2002). Ideal concepts, intuitions, and mathematical knowledge acquisitions in Husserl and Hilbert. In Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics) (Vol. 2281, pp. 40-77). (Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics); Vol. 2281).

Ideal concepts, intuitions, and mathematical knowledge acquisitions in Husserl and Hilbert. / Okada, Mitsuhiro.

Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics). Vol. 2281 2002. p. 40-77 (Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics); Vol. 2281).

Research output: Chapter in Book/Report/Conference proceedingChapter

Okada, M 2002, Ideal concepts, intuitions, and mathematical knowledge acquisitions in Husserl and Hilbert. in Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics). vol. 2281, Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics), vol. 2281, pp. 40-77.
Okada M. Ideal concepts, intuitions, and mathematical knowledge acquisitions in Husserl and Hilbert. In Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics). Vol. 2281. 2002. p. 40-77. (Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)).
Okada, Mitsuhiro. / Ideal concepts, intuitions, and mathematical knowledge acquisitions in Husserl and Hilbert. Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics). Vol. 2281 2002. pp. 40-77 (Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)).
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