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September 2005 On mathematical instrumentalism
Patrick Caldon, Aleksandar Ignjatović
J. Symbolic Logic 70(3): 778-794 (September 2005). DOI: 10.2178/jsl/1122038914

Abstract

In this paper we devise some technical tools for dealing with problems connected with the philosophical view usually called mathematical instrumentalism. These tools are interesting in their own right, independently of their philosophical consequences. For example, we show that even though the fragment of Peano's Arithmetic known as IΣ₁ is a conservative extension of the equational theory of Primitive Recursive Arithmetic (PRA), IΣ₁ has a super-exponential speed-up over PRA. On the other hand, theories studied in the Program of Reverse Mathematics that formalize powerful mathematical principles have only polynomial speed-up over IΣ₁.

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Patrick Caldon. Aleksandar Ignjatović. "On mathematical instrumentalism." J. Symbolic Logic 70 (3) 778 - 794, September 2005. https://doi.org/10.2178/jsl/1122038914

Information

Published: September 2005
First available in Project Euclid: 22 July 2005

zbMATH: 1089.03007
MathSciNet: MR2155266
Digital Object Identifier: 10.2178/jsl/1122038914

Rights: Copyright © 2005 Association for Symbolic Logic

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Vol.70 • No. 3 • September 2005
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