Mathematics: Truth and Fiction? Review of Mark Balaguer's Platonism and Anti-Platonism in Mathematics

Philosophia Mathematica 7 (3):336-349 (1999)
Authors
Edward Zalta
Stanford University
Mark Colyvan
University of Sydney
Abstract
Mark Balaguer’s project in this book is extremely ambitious; he sets out to defend both platonism and fictionalism about mathematical entities. Moreover, Balaguer argues that at the end of the day, platonism and fictionalism are on an equal footing. Not content to leave the matter there, however, he advances the anti-metaphysical conclusion that there is no fact of the matter about the existence of mathematical objects.1 Despite the ambitious nature of this project, for the most part Balaguer does not shortchange the reader on rigor; all the main theses advanced are argued for at length and with remarkable clarity and cogency. There are, of course, gaps in the account but these should not be allowed to overshadow the sig-
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DOI 10.1093/philmat/7.3.336
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There is No Easy Road to Nominalism.M. Colyvan - 2010 - Mind 119 (474):285-306.
What is Metaphysical Equivalence?Kristie Miller - 2005 - Philosophical Papers 34 (1):45-74.
Fictionalism in Metaphysics.Frederick Kroon - 2011 - Philosophy Compass 6 (11):786-803.

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