Platonism and Anti-Platonism in Mathematics

Couverture
Oxford University Press, 2001 - 217 pages
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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Table des matières

The Epistemological Argument Against Platonism
21
2 Formulating the Epistemological Argument
22
3 A Taxonomy of Platonist Responses
24
Godel
25
Maddy
28
6 Knowledge Without Contact
35
A New Platonist Epistemology
48
3 Intemalist vs Extemalist Explanations
53
5 The Refutation of Realistic AntiPlatonism
104
6 Platonism and the Issue of Applicability and Indispensability
109
Denying the Existence of Indispensable Applications Toward a Nominalization of Quantum Mechanics
113
2 How Field Nominalizes
114
3 Malaments Objection
117
4 The Strategy for Nominalizing QM
120
5 The Nominalistic Status of Propensities
126
Accounting for Indispensable Applications from a Fictionalist Point of View
128

4 Defending and Motivating FBP
58
5 Consistency
69
NonUniqueness Embraced
76
2 Trying to Salvage the Numbers
77
3 Structuralism
80
4 The Solution
84
5 Two Loose Ends
90
AntiPlatonism
93
The Fregean Argument Against AntiPlatonism
95
3 In Defense of Fictionalism
98
4 NonFictionalistic Versions of AntiRealistic AntiPlatonism
100
3 A Fictionalist Account of the Applicability of Mathematics
130
4 Problems with Platonism Revisited
142
Conclusions
149
The Unsolvability of the Problem and a Kinder Gentler Positivism
151
2 The Strong Epistemic Conclusion
152
3 The Metaphysical Conclusion
158
4 My Official View
178
Notes
181
Bibliography
207
Index
213
Droits d'auteur

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Fréquemment cités

Page 7 - I have been saying the exact reverse: if the arbitrarily given axioms do not contradict one another with all their consequences, then they are true and the things defined by the axioms exist. This is for me the criterion of truth and existence.
Page 17 - I am not myself persuaded that this is right ; but even if we accept this, it does not follow that there is no fact of the matter as to which of two observationally equivalent theories, by Quine's criterion, is correct.
Page 19 - Somewhere over the rainbow Way up high There's a land that I heard of Once in a lullaby Somewhere over the rainbow Skies are blue, And the dreams that you dare to dream Really do come true...
Page 19 - Back in Kansas, Auntie Em is delivering the scolding that is the prelude to one of the cinema's immortal moments. You always get yourself into a fret about nothing ... find yourself a place where you won't get into any trouble! Some place where there isn't any trouble. Do you suppose there is such a place, Toto? There must be. Anybody who has swallowed the scriptwriters...

À propos de l'auteur (2001)

Mark Balaguer is at California State University, Los Angeles.

Informations bibliographiques