 Abelard’s characterization of numerical sameness and difference seems to give us the tools to answer a common medieval puzzle which I will call the Problem of the Many Men. Versions of this problem can be found in a number of medieval works (see, e.g., Abelard Theologia Christiana III, § 153 (1969, 252); William of Sherwood Syncategoremata (O’Donnell ed., 60); Albert of Saxony Quaestiones in Physicam I, qq. 7–8, and his Sophismata 46, 25va-vb). The puzzle can easily be generated using a crude understanding of numerical sameness. Assume that Socrates’ body is perfectly intact: he has all his limbs, and their parts. Now consider every part of Socrates’ body except one finger. Call this whole W. W is not numerically the same as Socrates, so it appears that they must be numerically distinct. Socrates’ whole body is imbued with the soul of a man. But it also happens that W is imbued with the soul of a man. So, there are now two numerically distinct men where it initially appeared there was one. But it gets worse. Considering the body apart from one finger was only one of an indefinite number of such considerations. And by the same reasoning, these other bracketed wholes composed from Socrates’ body are also men. Hence, it is easy to generate an indefinite number of numerically distinct men where commonsense tells us that there is only one.