Abstract
Probably the best arguments for Platonism are those directed against its rival philosophies of mathematics. Frege's arguments against formalism, Godel'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.
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