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On mathematical instrumentalism*

  • Patrick Caldon (a1) (a2) and Aleksandar Ignjatović (a1) (a3)
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 Peanos 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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*

This is a revised excerpt from the second author's Ph.D. Thesis submitted at the University of California at Berkeley in 1990. The author is grateful to his adviser. Professor Jack Silver, for his support, many helpful discussions and for sharing his insights, to Professor Charles Chihara for discussions and encouragements, to the referees for many most useful comments which reshaped the paper.

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The Journal of Symbolic Logic
  • ISSN: 0022-4812
  • EISSN: 1943-5886
  • URL: /core/journals/journal-of-symbolic-logic
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