Ground and Cardinality: The Two Dimensions of Identity Puzzles

Abstract Identity puzzles like the Ship of Theseus turn on two questions, not one. The first is a question of ground: in virtue of what does an object remain the same—the persistence of its matter, or the persistence of its form? The second is a question of cardinality: how many bearers is the situation allowed—one name with one referent, one region with one object, or more? This paper argues that the two questions are independent—neither answer forces the other—and that the tradition has silently treated them as one, welding a choice of ground to a matching cardinality without noticing the second choice was a choice. I defend the independence directly (all four combinations of {matter, form} × {one bearer, many} are coherent, occupied, and rationally adoptable—not ruled out by the puzzle itself, which is the modest status the argument needs) and then show it doing work: it explains why the canonical versions of the puzzle are differently structured rather than the same problem at…