In this paper, the author derives a metaphysical theory of impossible worlds from an axiomatic theory of abstract objects. The underlying logic of the theory is classical. Impossible worlds are not taken to be primitive entities but are instead characterized intrinsically using a definition that identifies them with, and reduces them to, abstract objects. The definition is shown to be a good one–the proper theorems derivable from the definition assert that impossible worlds have the important characteristics that philosophers suppose them to have. None of these consequences, however, imply that any contradiction is true (though contradictions can be "true at" impossible worlds). This classically-based conception of impossible worlds provides a subject matter for paraconsistent logic and demonstrates that there need be no conflict between the laws of paraconsistent logic and the laws of classical logic, for they govern different kinds of worlds. It is argued that the resulting theory constitutes a theory of genuine (as opposed to ersatz) impossible worlds. However, impossible worlds are not needed to distinguish necessarily equivalent propositions or for the treatment of the propositional attitudes, since the underlying theory of propositions already has that capacity.
"A Classically-Based Theory of Impossible Worlds." Notre Dame J. Formal Logic 38 (4) 640 - 660, Fall 1997. https://doi.org/10.1305/ndjfl/1039540774