In Metaphysics A, Aristotle offers some objections to Plato’s theory of Forms to the effect that Plato’s Forms would not be explanatory in the right way, and seems to suggest that they might even make the explanatory project worse. One interesting historical puzzle is whether Aristotle can avoid these same objections to his own theory of universals. The concerns Aristotle raises are, I think, cousins of contemporary concerns about the usefulness and explanatoriness of abstract objects, some of which have recently (...) been receiving attention in the philosophy of mathematics. After discussing Aristotle’s objections and their contemporary cousins, the paper discusses some of the main available lines of response to these sorts of challenges, before concluding with an examination of whether these responses could assist Plato or Aristotle in responding to these challenges. (shrink)