TY - CHAP

T1 - Ideal concepts, intuitions, and mathematical knowledge acquisitions in Husserl and Hilbert

AU - Okada, Mitsuhiro

PY - 2002

Y1 - 2002

N2 - 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.

AB - 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.

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UR - http://www.scopus.com/inward/citedby.url?scp=84867648159&partnerID=8YFLogxK

U2 - 10.1007/3-540-45884-0_4

DO - 10.1007/3-540-45884-0_4

M3 - Chapter

AN - SCOPUS:84867648159

SN - 3540433384

SN - 9783540433385

T3 - Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)

SP - 40

EP - 77

BT - Progress in Discovery Science

PB - Springer Verlag

ER -