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On The Epistemological Justification of Hilbert’s Metamathematics

Javier Legris
p. 225-238

Abstract

The aim of this paper is to examine the idea of metamathematical deduction in Hilbert’s program showing its dependence of epistemological notions, specially the notion of intuitive knowledge. It will be argued that two levels of foundations of deduction can be found in the last stages (in the 1920s) of Hilbert’s Program. The first level is related to the reduction – in a particular sense – of mathematics to formal systems, which are ‘metamathematically’ justified in terms of symbolic manipulation. The second level of foundation consists in warranting epistemologically the validity of the combinatory processes underlying the symbolic manipulation in metamathematics. In this level the justification was carried out with the aid of notions from modern epistemology, particularly the notion of intuition. Finally, some problems concerning Hilbert’s use of this notion will be shown and it will be compared with Brouwer’s

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References

Bibliographical reference

Javier Legris, On The Epistemological Justification of Hilbert’s MetamathematicsPhilosophia Scientiæ, 9-2 | 2005, 225-238.

Electronic reference

Javier Legris, On The Epistemological Justification of Hilbert’s MetamathematicsPhilosophia Scientiæ [Online], 9-2 | 2005, Online since 15 June 2011, connection on 19 April 2024. URL: http://journals.openedition.org/philosophiascientiae/540; DOI: https://doi.org/10.4000/philosophiascientiae.540

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About the author

Javier Legris

University of Buenos Aires and CONICET (Argentina)

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Copyright

The text and other elements (illustrations, imported files) are “All rights reserved”, unless otherwise stated.

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