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Platonism and Anti-Platonism in Mathematics: A Philosophical Essay on the Ontological Commitments of Mathematics
Mark Balaguer, California State University, Los Angeles

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Platonism and Anti-Platonism in Mathematics (Book)
Title: Platonism and Anti-Platonism in Mathematics
Author: Mark Balaguer
Abstract: 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.
Year: 1998
Primary URL:
Primary URL Description: Oxford Press
Publisher: Oxford University Press
Type: Single author monograph
ISBN: 0195143981