Imagine, one next to the other, two otherwise identical objects. The problem of universals concerns what it is in virtue of which the two objects are identical. The problem of individuation, on the other hand, concerns what it is in virtue of which the two objects are distinct. Although these correlative problems of qualitative sameness and numerical difference generally received reduced attention in the early modern period, they were not entirely eclipsed and were never without the structural importance they had in previous periods. The position that philosophers of any period take on these problems, even just implicitly, determines much of the rest of what else they say. Descartes is no exception, though how that is so can be only suggested here. More problematically, the question of just what Descartes’ position itself is has generated a great deal of disagreement, especially over whether he is a pluralist, recognizing the individuation of many corporeal substances, or a monist, recognizing just one. (The references at the end provide an entrée to the literature; also see substance)

Just by the contrapositive of Leibniz's principle of the identity of indiscernibles, qualitative difference is sufficient for numerical difference: (qualitative) discernibility entails (numerical) difference. So, the property-dualist Descartes has no problem individuating minds with respect to bodies and conversely. The problem lies with individuating minds against each other, and with individuating bodies against each other (and all of them against God, though that problem will be addressed here only very obliquely).

Like “substance,” the term “body” is for Descartes ambiguous – in fact, multiply so (AT IV 166, CSMK 242). The different senses of body might be thought of as picking out things existing on different levels (and the different levels themselves might be thought of in different ways; see Sowaal 2004). A focal text with respect to the individuation of body is the Synopsis of the Meditations, where Descartes distinguishes three levels of body, apparently with three different principles of individuation (AT VII 14, CSM II 10). First, there is body “taken in the general sense” (corpus in genere sumptum). Descartes does not mean a nonspecific body in the sense of a body taken at random. Rather, he means body as a kind. He says of body in this sense that it is a substance, the one substance that is the entire physical world (Nelson and Smith, 2010). It might be thought of as the thing that God creates when he makes geometry true by giving it an object (space or body). Like all substances, in any case, body in this sense is incorruptible and would cease to exist only if God withdrew his concurrence with its existence (a sort of passive annihilation of it) (see concurrence versus conservation, divine). Such exalted status is what one would expect of a kind.