Just What Is Full-Blooded Platonism?†

Abstract

Mark Balaguer's Platonism and Anti-Platonism in Mathematics presents an intriguing new brand of Platonism, which he calls plenitudinous Platonism, or more colorfully, full-blooded Platonism. In this paper, I argue that Balaguer's attempts to characterize full-blooded Platonism fail. They are either too strong, with untoward consequences we all reject, or too weak, not providing a distinctive brand of Platonism strong enough to do the work Balaguer requires of it.