The doctrine of the Trinity maintains that there are exactly three divine Persons (Father, Son, and Holy Spirit) but only one God. The philosophical problem raised by this doctrine is well known. On the one hand, the doctrine seems clearly to imply that the divine Persons are numerically distinct. How else could they be ’three’ rather than one? On the other hand, it seems to imply that Father, Son, and Holy Spirit are identical. If each Person is divine, how else (...) could there be exactly ’one’ God? But the divine Persons can’t be both distinct and identical. Thus, the doctrine appears to be incoherent. Some try to solve this problem by appeal to the view that identity is sortal-relative. In this paper, I argue that this strategy is unsuccessful as a stand-alone solution to the problem of the Trinity. (shrink)