On what Hilbert aimed at in the foundations
Abstract
Hilbert's axiomatic approach was an optimistic take over on the side of the logical foundations. It was also a response to various restrictive views of mathematics supposedly bounded by the reaches of epistemic elements in mathematics. A complete axiomatization should be able to exclude epistemic or ontic elements from mathematical theorizing, according to Hilbert. This exclusion is not necessarily a logicism in similar form to Frege's or Dedekind's projects. That is, intuition can still have a role in mathematical reasoning. Nevertheless, this role is to be given a structural orientation with the help of explications of the underlying logic of axiomatizationAuthor's Profile
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References found in this work
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Second-order logic and foundations of mathematics.Jouko Väänänen - 2001 - Bulletin of Symbolic Logic 7 (4):504-520.
Consciousness, Philosophy, and Mathematics.L. E. J. Brouwer - 1949 - Proceedings of the Tenth International Congress of Philosophy 2:1235-1249.
Consciousness, Philosophy and Mathematics.L. E. J. Brouwer - 1949 - In E. W. Beth, H. J. Pos & H. J. A. Hollak (eds.), Library of the Tenth International Congress in Philosophy, August 1948. North-Holland. pp. 1235--1249.
