Ideal concepts, intuitions, and mathematical knowledge acquisitions in Husserl and Hilbert
pp. 40-77
in: Setsuo Arikawa, Ayumi Shinohara (eds), Progress in discovery science, Berlin, Springer, 2002Abstract
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.
