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.