Just What Is Full-Blooded Platonism?†

Mark Balaguer's Platonism and Anti-Platonism in Mathematics presents an intriguing new brand of platonism, which he calls plenitudinous platonism, or more colourfully, full-blooded platonism. In this paper, I argue that Balaguer's attempts to characterise 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.