Finitistic Arithmetic and Classical Logic†

Author:

Ganea Mihai1

Affiliation:

1. Department of Philosophy, University of Toronto, Toronto, Ontario M5R 2M8, Canada

Abstract

Abstract It can be argued that only the equational theories of some sub-elementary function algebras are finitistic or intuitive according to a certain interpretation of Hilbert's conception of intuition. The purpose of this paper is to investigate the relation of those restricted forms of equational reasoning to classical quantifier logic in arithmetic. The conclusion reached is that Edward Nelson's ‘predicative arithmetic’ program, which makes essential use of classical quantifier logic, cannot be justified finitistically and thus requires a different philosophical foundation, possibly as a restricted form of logicism.

Publisher

Oxford University Press (OUP)

Subject

Philosophy,General Mathematics

Reference64 articles.

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2. Combinatorial principles in elementary number theory;Berarducci;Annals of Pure and Applied Logic,1991

3. Fixing Frege

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