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Applying Pure Mathematics

Published online by Cambridge University Press:  01 April 2022

Anthony Peressini
Anthony Peressini*
Affiliation:
Marquette University
*
†Department of Philosophy, Marquette University, Milwaukee, WI 53201–1881; e-mail: peressinia@marquette.edu
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Abstract

Much of the current thought concerning mathematical ontology and epistemology follows Quine and Putnam in looking to the indispensable application of mathematics in science. A standard assumption of the indispensability approach is some version of confirmational holism, i.e., that only “sufficiently large” sets of beliefs “face the tribunal of experience.” In this paper I develop and defend a distinction between a pure mathematical theory and a mathematized scientific theory in which it is applied. This distinction allows for the possibility that pure mathematical theories are systematically insulated from such confirmation in virtue of their being distinct from the “sufficiently large” blocks of scientific theory that are empirically confirmed.

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Footnotes

‡

I thank Mike Byrd, Malcolm Forster, Penelope Maddy, Michael Resnik, Elliott Sober, and Mark Steiner for comments and discussion.

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