Naturalism in Mathematics

Naturalism in Mathematics

3.92 (14 ratings by Goodreads)
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Description

Our much-valued mathematical knowledge rests on two supports: the logic of proof and the axioms from which those proofs begin. Naturalism in Mathematics investigates the status of the latter, the fundamental assumptions of mathematics. These were once held to be self-evident, but progress in work on the foundations of mathematics, especially in set theory, has rendered that comforting notion obsolete. Given that candidates for axiomatic status cannot be proved, what sorts of considerations can be offered for or against them? That is the central question addressed in this book. One answer is that mathematics aims to describe an objective world of mathematical objects, and that axiom candidates should be judged by their truth or falsity in that world. This promising view-realism-is assessed and finally rejected in favour of another- naturalism-which attends less to metaphysical considerations of objective truth and falsity, and more to practical considerations drawn from within mathematics itself. Penelope Maddy defines this naturalism, explains the motivation for it, and shows how it can be helpfully applied in the assessment of candidates for axiomatic status in set theory. Maddy's clear, original treatment of this fundamental issue is informed by current work in both philosophy and mathematics, and will be accessible and enlightening to readers from both disciplines.show more

Product details

  • Paperback | 266 pages
  • 134.62 x 210.82 x 17.78mm | 408.23g
  • Oxford University Press
  • Clarendon Press
  • Oxford, United Kingdom
  • English
  • Revised ed.
  • 0198250754
  • 9780198250753
  • 1,111,025

Review quote

'This book represents the culmination of Penelope Maddy's recent work in the philosophy of mathematics. . . . The book is beautifully written, tightly argued and makes compelling reading. I believe the position Maddy introduces and defends - set theoretic naturalism - is a significant and original addition to the philosophy of mathematics landscape, and one that will certainly attract a great deal of attention. . . . In sum, this is a very important book covering some fascinating terrain on the border between philosophy and mathematics. * Mind * An excellent book ... The philosopher's task is not to provide external criticism, but rather to clarify debates in this so-called mathematical community. And Ms Maddy makes some fascinating (and very technical) steps in this direction. * The Economist Review *show more

About Penelope Maddy

Penelope Maddy is Professor of Philosophy at the University of California, Irvine.show more

Table of contents

PART I: THE PROBLEM; PART II: REALISM; PART III: NATURALISMshow more

Rating details

14 ratings
3.92 out of 5 stars
5 36% (5)
4 36% (5)
3 14% (2)
2 14% (2)
1 0% (0)
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