> I don't think it's a false dilemma, because the essence of mathematical platonism isn't really that forms exist, but that these forms are how the universe really works.
Consider Euclidean geometry, which is fine, mathematically, but, it turns out, not how the universe works. If mathematical platonists were concerned about whether mathematics' forms are how the universe really works, surely they would insist on the verification of their axioms before proceeding? And then, would mathematical platonism not be just the uncontroversial parts of the physical sciences?
The author reprises the platonism / formalism issue in this article's final section, beginning with the paragraph "But there is still more to be said. Perhaps, after all some of those Big Picture questions do remain lurking in the mathematical background." He refers to Platonists as realists, but, I think, in the sense that the forms are real regardless of whether they are how the universe really works.
Consider Euclidean geometry, which is fine, mathematically, but, it turns out, not how the universe works. If mathematical platonists were concerned about whether mathematics' forms are how the universe really works, surely they would insist on the verification of their axioms before proceeding? And then, would mathematical platonism not be just the uncontroversial parts of the physical sciences?
The author reprises the platonism / formalism issue in this article's final section, beginning with the paragraph "But there is still more to be said. Perhaps, after all some of those Big Picture questions do remain lurking in the mathematical background." He refers to Platonists as realists, but, I think, in the sense that the forms are real regardless of whether they are how the universe really works.