The individuation of mathematical objects

Against mathematical platonism, it is sometimes objected that mathematical objects are mysterious. One possible elaboration of this objection is that the individuation of mathematical objects cannot be adequately explained. This suggests that facts about the numerical identity and distinctness of mathematical objects require an explanation, but that their supposed nature precludes us from providing one. In this paper, we evaluate this nominalist objection by exploring three ways in which mathematical objects may be individuated: by the intrinsic properties they possess, by the relations they stand in, and by their underlying ‘substance’. We argue that only the third mode of individuation raises metaphysical problems that could substantiate the claim that mathematical objects are somehow mysterious. Since the platonist is under no obligation to accept this thesis over the alternatives, we conclude that, at least as far as individuation is concerned, the nominalist objection has no bite.