Notre Dame Journal of Formal Logic

A Classically-Based Theory of Impossible Worlds

Edward N. Zalta


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.

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Notre Dame J. Formal Logic, Volume 38, Number 4 (1997), 640-660.

First available in Project Euclid: 10 December 2002

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Zentralblatt MATH identifier

Primary: 03B45: Modal logic (including the logic of norms) {For knowledge and belief, see 03B42; for temporal logic, see 03B44; for provability logic, see also 03F45}
Secondary: 03A05: Philosophical and critical {For philosophy of mathematics, see also 00A30} 03B53: Paraconsistent logics


Zalta, Edward N. A Classically-Based Theory of Impossible Worlds. Notre Dame J. Formal Logic 38 (1997), no. 4, 640--660. doi:10.1305/ndjfl/1039540774.

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