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

Philosophia Mathematica 7 (3):336-349 (1999)
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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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Author Profiles

Edward Zalta
Stanford University
Mark Colyvan
University of Sydney

Citations of this work

There is No Easy Road to Nominalism.M. Colyvan - 2010 - Mind 119 (474):285-306.
Abstract Objects.Gideon Rosen - 2008 - Stanford Encyclopedia of Philosophy.
Fictionalism in Metaphysics.Frederick Kroon - 2011 - Philosophy Compass 6 (11):786-803.
Mathematical and Moral Disagreement.Silvia Jonas - 2020 - Philosophical Quarterly 70 (279):302-327.

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