Abstract

The doctrine that whatever could exist does exist leads to a proliferation of possibly concrete objects given certain principles of recombination. If, for example, there could have been a large infinite number of concrete objects, then there is at least the same number of possibly concrete objects in existence. And further cardinality considerations point to a tension between the preceding doctrine and the Cantorian conception of the absolutely infinite. This paper develops a parallel problem for a variety of possible worlds accounts of modality which eschew the commitment to a plethora of possibly concrete objects. Moreover, the difficulty is importantly different from more familiar threats of paradox exemplified by certain descendants of Russell's paradox of propositions and Kaplan's paradox