Notre Dame Journal of Formal Logic

A Classically-Based Theory of Impossible Worlds

Edward N. Zalta

Abstract

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.

Article information

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

Dates
First available in Project Euclid: 10 December 2002

Permanent link to this document
https://projecteuclid.org/euclid.ndjfl/1039540774

Digital Object Identifier
doi:10.1305/ndjfl/1039540774

Mathematical Reviews number (MathSciNet)
MR1648857

Zentralblatt MATH identifier
0914.03001

Subjects
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

Citation

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. https://projecteuclid.org/euclid.ndjfl/1039540774.


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References

  • [1] Cresswell, M., ``The interpretation of some Lewis systems of modal logic,'' Australasian Journal of Philosophy, vol. 45 (1967), pp. 198--206.
  • [2] Cresswell, M., ``Intensional logics and logical truth,'' Journal of Philosophical Logic, vol. 1 (1972), pp. 2--15.
  • [3] Kripke, S., ``Semantic analysis of modal logic II: Non-normal modal propositional calculi,'' pp. 206--20 in The Theory of Models, edited by J. Addison et al., North-Holland, Amsterdam, 1965.
  • [4] Linsky, B., and E. Zalta, ``Naturalized Platonism vs. platonized naturalism,'' The Journal of Philosophy, vol. 92, (1995), pp. 525--55.
  • [5] Mares, E., ``Who's afraid of impossible worlds?,'' Notre Dame Journal of Formal Logic, vol. 38 (1997), pp. 516--26.
  • [6] Morgan, C., ``Systems of modal logic for impossible worlds,'' Inquiry, vol. 16 (1973), pp. 280--9.
  • [7] Paśniczek, J., ``Non-standard possible worlds, generalised quantifiers, and modal logic,'' pp. 187--98 in Philosophical Logic in Poland, edited by J. Wolenski, Kluwer, Dordrecht, 1994.
  • [8] Perszyk, K., ``Against extended modal realism,'' Journal of Philosophical Logic, vol. 22 (1993), pp. 205--14.
  • [9] Priest, G., ``What is a non-normal world?,'' Logique et Analyse, vol. 35 (1992), pp. 291--302.
  • [10] Priest, G., In Contradiction, Martinus Nijhoff, The Hague, 1987.
  • [11] Priest, G., and R. Sylvan, ``Simplified semantics for basic relevant logics,'' Journal of Philosophical Logic, vol. 21 (1992), pp. 217--32.
  • [12] Rantala, V., ``Impossible world semantics and logical omniscience,'' Acta Philosophica Fennica, vol. 35 (1982), pp. 106--15.
  • [13] Rescher, N., and R. Brandom, The Logic of Inconsistency: A Study in Non-Standard Possible World Semantics and Ontology, Basil Blackwell, Oxford, 1980.
  • [14] Restall, G., ``Ways things can't be,'' Notre Dame Journal of Formal Logic, vol. 38 (1997), pp. 583--96.
  • [15] Routley, R., Exploring Meinong's Jungle and Beyond, Departmental Monograph #3, Philosophy Department, Research School of Social Sciences, Australian National University, Canberra, 1980.
  • [16] Yagisawa, T., ``Beyond possible worlds,'' Philosophical Studies, vol. 53 (1988), pp. 175--204.
  • [17] Zalta, E., ``The modal object calculus and its interpretation,'' pp. 249--79 in Advances in Intensional Logic, edited by M. de Rijke, Kluwer, Dordrecht, 1997.
  • [18] Zalta, E., ``Twenty-five basic theorems in situation and world theory,'' Journal of Philosophical Logic, vol. 22 (1993), pp. 385--428.
  • [19] Zalta, E., Intensional Logic and the Metaphysics of Intentionality, Bradford Books, The MIT Press, Cambridge, 1988.
  • [20] Zalta, E., ``A comparison of two intensional logics,'' Linguistics and Philosophy, vol. 11 (1988), pp. 59--89.
  • [21] Zalta, E., Abstract Objects: An Introduction to Axiomatic Metaphysics, D. Reidel, Dordrecht, 1983.
  • [22] Zalta, E., ``Meinongian type theory and its applications,'' Studia Logica, vol. 41 (1982), pp. 297--307.