Recombination and ParadoxSkip other details (including permanent urls, DOI, citation information)
This work is licensed under a Creative Commons Attribution-NonCommercial-NoDerivatives 3.0 License. Please contact email@example.com to use this work in a way not covered by the license. :
For more information, read Michigan Publishing's access and usage policy.
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.