Chapter

Mathematical Justifications are Not Infinitely Various

Neil Tennant

in Changes of Mind

Published in print June 2012 | ISBN: 9780199655755
Published online September 2012 | e-ISBN: 9780191742125 | DOI: http://dx.doi.org/10.1093/acprof:oso/9780199655755.003.0010
Mathematical Justifications are Not Infinitely Various

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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

Chapter.  2359 words. 

Subjects: Philosophy of Mathematics and Logic

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