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The Oxford Handbook of Philosophy of Mathematics and Logic$
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Stewart Shapiro

Print publication date: 2005

Print ISBN-13: 9780195148770

Published to Oxford Scholarship Online: July 2005

DOI: 10.1093/0195148770.001.0001

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Naturalism Reconsidered

Naturalism Reconsidered

Chapter:
(p.460) Naturalism Reconsidered
Source:
The Oxford Handbook of Philosophy of Mathematics and Logic
Author(s):

Alan Weir (Contributor Webpage)

Publisher:
Oxford University Press
DOI:10.1093/0195148770.003.0014

Mathematics poses a difficult problem for methodological naturalists, those who embrace scientific method, and also for ontological naturalists who eschew non-physical entities such as Cartesian souls. Mathematics seems both essential to science but also committed to abstract non-physical entities while methodologically it seems to have no place for experiment or empirical confirmation. The chapter critically reviews a number of responses naturalists have made including logicism, Quinean radical empiricism, and Penelope Maddy’s variant thereof and suggests some further problems both for ontological and for methodological naturalists.

Keywords:   mathematics, naturalism, abstract objects, logicism, Quine, empiricism, Maddy

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