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Logic Journal of IGPL Advance Access published online on September 24, 2007
Logic Journal of IGPL, doi:10.1093/jigpal/jzm042
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© The Author, 2007. Published by Oxford University Press. All rights reserved. For Permissions, please email: journals.permissions@oxfordjournals.org

Why and How Platonism?

Guillermo E. Rosado Haddock

Department of Philosophy, University of Puerto Rico at Río Piedras. E-mail: grosado{at}uprrp.edu


  Abstract

Probably the best arguments for Platonism are those directed against its rival philosophies of mathematics. Frege's arguments against formalism, Gödel's arguments against constructivism and those against the so-called syntactic view of mathematics, and an argument of Hodges against Putnam are expounded, as well as some arguments of the author. A more general criticism of Quine's views follows. The paper ends with some thoughts on mathematics as a sort of Platonism of structures, as conceived by Husserl and essentially endorsed by the author.

Key Words: Platonism • Mathematics • Logic • Gottlob Frege • Kurt Gödel • Hilary Putnam • W. V. O. Quine • Edmund Husserl


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