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Changes of MindAn Essay on Rational Belief Revision$
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Neil Tennant

Print publication date: 2012

Print ISBN-13: 9780199655755

Published to Oxford Scholarship Online: September 2012

DOI: 10.1093/acprof:oso/9780199655755.001.0001

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Mathematical Justifications are Not Infinitely Various

Mathematical Justifications are Not Infinitely Various

Chapter:
(p.280) Chapter 10 Mathematical Justifications are Not Infinitely Various
Source:
Changes of Mind
Author(s):

Neil Tennant

Publisher:
Oxford University Press
DOI:10.1093/acprof:oso/9780199655755.003.0010

This chapter gives a suitably texturized proof of a deep result in mathematical logic by Harvey Friedman, which was produced on request. It states that every extant mathematical theory (by virtue of satisfying a very general characterization of possible forms of axiomatic presentation) provides, for each of its theorems, at most finitely many logically distinct choices of axioms from which it can be proved. This further bolsters the philosophical argument for the theoretical adequacy of a finitary approach to the problems of belief revision.

Keywords:   theory, axiom, axiom scheme, mathematical justification, finitizability

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