  Unlike concretism, then, abstractionism does not entail that  individuals are worldbound; there is no inconsistency whatever in the idea that many distinct worlds can include the existence of one and  the same individual. Indeed, typically, abstractionists are staunchly committed to transworld identity and hold that most any given  individual exists in many possible worlds and, moreover, that  contingent individuals, at least, can exemplify very different  properties from world to world. Abstractionists, therefore, have no need to appeal to counterparts to understand de re modalities  and can therefore accept the truth conditions for such modalities  given by basic possible world semantics (spelled out, of course, in  terms of their definitions AW2 and AE2). In particular,  they can take the standard possible world truth condition for, e.g.,  the right conjunct of   (16)  at face value: ‘◇(E!a ∧ ¬Ta)’ is true on the abstractionist's approach if and only if there is is a world in which Algol herself, rather than some counterpart of hers,  exists but fails to be anyone's pet. 