On what Hilbert aimed at in the foundations


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 axiomatization



External links

  • This entry has no external links. Add one.
Setup an account with your affiliations in order to access resources via your University's proxy server

Through your library

  • Only published works are available at libraries.

Similar books and articles

Aspekte der frege–hilbert-korrespondenz.Kai F. Wehmeier - 1997 - History and Philosophy of Logic 18 (4):201-209.
On The Infinite / Sur L’infini.Marcel Bodea - 2001 - Studia Philosophica 1.
Mathematical Intuition and Hilbert’s “Minimal” Philosophy.Vitali Tselishchev - 2018 - Proceedings of the XXIII World Congress of Philosophy 56:53-57.
Hilbert, completeness and geometry.Giorgio Venturi - 2011 - Rivista Italiana di Filosofia Analitica Junior 2 (2):80-102.
The Ways of Hilbert's Axiomatics: Structural and Formal.Wilfried Sieg - 2014 - Perspectives on Science 22 (1):133-157.


Added to PP

149 (#86,004)

6 months
38 (#34,815)

Historical graph of downloads
How can I increase my downloads?

Author's Profile

Citations of this work

No citations found.

Add more citations

References found in this work

Logic in the twenties: The nature of the quantifier.Warren D. Goldfarb - 1979 - Journal of Symbolic Logic 44 (3):351-368.
Second-order logic and foundations of mathematics.Jouko Väänänen - 2001 - Bulletin of Symbolic Logic 7 (4):504-520.
Hilbert's Programs: 1917–1922.Wilfried Sieg - 1999 - Bulletin of Symbolic Logic 5 (1):1-44.
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.

View all 11 references / Add more references