Platonism and Anti-Platonism in Mathematics

Overview

In this highly absorbing work, Balaguer demonstrates that no good arguments exist either for or against mathematical platonism-for example, the view that abstract mathematical objects do exist and that mathematical theories are descriptions of such objects. Balaguer does this by establishing that both platonism and anti-platonism are justifiable views. Introducing a form of platonism, called "full-blooded platonism," that solves all problems traditionally associated with the view, he proceeds to defend ...

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Platonism and Anti-Platonism in Mathematics

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Overview

In this highly absorbing work, Balaguer demonstrates that no good arguments exist either for or against mathematical platonism-for example, the view that abstract mathematical objects do exist and that mathematical theories are descriptions of such objects. Balaguer does this by establishing that both platonism and anti-platonism are justifiable views. Introducing a form of platonism, called "full-blooded platonism," that solves all problems traditionally associated with the view, he proceeds to defend anti-platonism (in particular, mathematical fictionalism) against various attacks-most notably the Quine-Putnam indispensability attack. He concludes by arguing that it is not simply that we do not currently have any good arguments for or against platonism but that we could never have such an argument. This lucid and accessible book breaks new ground in its area of engagement and makes vital reading for both specialists and all those intrigued by the philosophy of mathematics, or metaphysics in general.

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Product Details

  • ISBN-13: 9780195143980
  • Publisher: Oxford University Press, USA
  • Publication date: 7/28/2001
  • Edition description: REPRINT
  • Pages: 240
  • Sales rank: 1,046,900
  • Product dimensions: 8.90 (w) x 5.70 (h) x 0.80 (d)

Table of Contents

1 Introduction 3
1 Platonism 19
2 The Epistemological Argument Against Platonism 21
3 A New Platonist Epistemology 48
4 Non-Uniqueness Embraced 76
2 Anti-Platonism 93
5 The Fregean Argument Against Anti-Platonism 95
6 Denying the Existence of Indispensable Applications: Toward a Nominalization of Quantum Mechanics 113
7 Accounting for Indispensable Applications from a Fictionalist Point of View 128
3 Conclusions 149
8 The Unsolvability of the Problem and a Kinder, Gentler Positivism 151
Notes 181
Bibliography 207
Index 213
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