Platonism and Anti-Platonism in Mathematics

Platonism and anti-platonism in mathematics is an impressive work. Balaguer presents forceful arguments for the viability of both FBP and fictionalism, and against the feasibility of any substantially different Platonist or anti-Platonist position. ... an admirable achievement. * The Bulletin of Symbolic Logic *
Brings several interesting new ideas to the philosophy of mathematics. The most important is a new position concerning the existence of mathematical objects--his Full-Blooded Platonism. This is the novel and radical claim that any mathematical object that can consistently exist does exist. Balaguer has done an excellent job of expounding and defending this idea. I find his philosophical style unique in its honesty and boldness; for he manages to make his initially provocative claims quite plausible without having to weaken or qualify them. This is an important work from which not only philosophers of mathematics but also epistemologists and metaphysicians will profit. * Michael D. Resnik, University of North Carolina, Chapel Hill *
In the end the author, quite as much as Goodman and Quine, though in a different way, rejects scientific standards and classical mathematics, and remains true to the spirit, if not the letter, of nominalism...In addition to his ultimate and intermediary conclusions, the author reaches conclusions on many lesser controversial questions, and offers a number of insights on the way. * John P. Burgess, Princeton University, The Philosophical Review *
Platonism and anti-platonism in mathematics is an impressive work. Balaguer presents forceful arguments for the viability of both FBP and fictionalism, and against the feasibility of any substantially different Platonist or anti-Platonist position. ... an admirable achievement. * The Bulletin of Symbolic Logic *