Notre Dame Journal of Formal Logic

Impossible Worlds: A Modest Approach

Daniel Nolan

Abstract

Reasoning about situations we take to be impossible is useful for a variety of theoretical purposes. Furthermore, using a device of impossible worlds when reasoning about the impossible is useful in the same sorts of ways that the device of possible worlds is useful when reasoning about the possible. This paper discusses some of the uses of impossible worlds and argues that commitment to them can and should be had without great metaphysical or logical cost. The paper then provides an account of reasoning with impossible worlds, by treating such reasoning as reasoning employing counterpossible conditionals, and provides a semantics for the proposed treatment.

Article information

Source
Notre Dame J. Formal Logic Volume 38, Number 4 (1997), 535-572.

Dates
First available in Project Euclid: 10 December 2002

Permanent link to this document
http://projecteuclid.org/euclid.ndjfl/1039540769

Mathematical Reviews number (MathSciNet)
MR1648852

Digital Object Identifier
doi:10.1305/ndjfl/1039540769

Zentralblatt MATH identifier
0916.03013

Subjects
Primary: 03A05: Philosophical and critical {For philosophy of mathematics, see also 00A30}
Secondary: 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} 03B53: Paraconsistent logics

Citation

Nolan, Daniel. Impossible Worlds: A Modest Approach. Notre Dame Journal of Formal Logic 38 (1997), no. 4, 535--572. doi:10.1305/ndjfl/1039540769. http://projecteuclid.org/euclid.ndjfl/1039540769.


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References

  • [1]Anderson, A. R., Belnap, N. D., and Dunn, J. M., Entailment, vol. 2, Princeton University Press, Princeton, 1992.
  • [2] Armstrong, D. M., A Combinatorial Theory of Possibility, Cambridge University Press, Cambridge, 1989.
  • [3]Bennett, J., ``Classifying conditionals: the traditional way is right,'' Mind, vol. 104 (1995), pp. 331--54.
  • [4]Davis, W. A., ``Indicative and subjunctive conditionals,'' Philosophical Review, vol. 88 (1979), pp. 544--64.
  • [5]Edgington, D., ``Do conditionals have truth-conditions?" Critica, vol. 18, 52 (1986), pp. 3--30. Reprinted in Conditionals, edited by F. Jackson, Oxford University Press, Oxford, 1991.
  • [6]Edgington, D., ``On conditionals,'' Mind, vol. 104 (1995), pp. 235--329.
  • [7]Field, H., Realism, Mathematics and Modality, Basil Blackwell, Oxford, 1989.
  • [8]Field, H., ``The conceptual contingency of mathematical objects,'' Mind, vol. 102 (1993), pp. 285--99.
  • [9]Fraenkel, A. A., Y. Bar-Hillel, and A. Levy, Foundations of Set Theory, 2d revised edition, North-Holland, Amsterdam, 1973.
  • [10]Forbes, G., ``Physicalism, instrumentalism and the semantics of modal logic,'' Journal of Philosophical Logic, vol. 12 (1983), pp. 271--98.
  • [11]Grim, P., The Incomplete Universe: Totality, Knowledge and Truth, The MIT Press, Cambridge, 1991.
  • [12]Hinckfuss, I., ``Suppositions, presuppositions, and ontology,'' Canadian Journal of Philosophy, vol. 23 (1983), pp. 595--617.
  • [13]Jackson, F., Conditionals, Basil Blackwell, Oxford, 1987.
  • [14]Lewis, D. K., Counterfactuals, Basil Blackwell, Oxford, 1973.
  • [15]Lewis, D. K., ``Counterfactuals and comparative possibility,'' Noûs, vol. 13 (1979), pp. 455--76; reprinted in Philosophical Papers, vol. 2, Oxford University Press, Oxford, 1986.
  • [16]Lewis, D. K., ``Scorekeeping in a language game,'' Journal of Philosophical Logic, vol. 8 (1979), pp. 339--59.
  • [17]Lewis, D. K., On the Plurality of Worlds, Basil Blackwell, Oxford, 1986.
  • [18]Lewis, D. K., ``Postscript to `Counterfactual dependence and time's arrow','' pp. 52--66 in Philosophical Papers, vol. 2, Oxford University Press, Oxford, 1986.
  • [19]Lewis, D. K., ``Postscript to `Probabilities of conditionals and conditional probabilities','' in Philosophical Papers, vol. 2, Oxford University Press, Oxford, 1986.
  • [20]Merrill, G. H., ``Formalization, possible worlds and the foundations of modal logic,'' Erkenntis, vol. 12 (1978), pp. 305--27.
  • [21]Martin, E. P., and R. K. Meyer, ``Solution to the P-W problem,'' The Journal of Symbolic Logic, vol. 47 (1982), pp. 869--86.
  • [22] Priest, G., In Contradiction, Martinus Nijhoff, The Hague, 1987.
  • [23] Priest, G., ``What is a non-normal world?,'' Logique et Analyse, vol. 35 (1992), pp. 291--302.
  • [24] Priest, G., and R. Routley, ``Systems of paraconsistent logic," pp. 151--86 in Paraconsistent Logic: Essays on the Inconsistent, edited by G. Priest, R. Routley, and J. Norman, Philosophia Verlag, Munich, 1989.
  • [25]Priest, G. and R. Routley, ``The philosophical significance and inevitability of paraconsistency," pp. 483--539 in Paraconsistent Logic: Essays on the Inconsistent, edited by G. Priest, R. Routley, and J. Norman, Philosophia Verlag, Munich, 1989.
  • [26]Quine, W. V., Philosophy of Logic, Prentice Hall, Englewood Cliffs, 1970.
  • [27]Read, S., Thinking About Logic, Oxford University Press, Oxford, 1995.
  • [28]Restall, G., ``A note on naï"ve set theory in LP,'' Notre Dame Journal of Formal Logic, vol. 33 (1992), pp. 422--32.
  • [29]Rosen, G. ``Modal fictionalism,'' Mind, vol. 99 (1990), pp. 327--54.
  • [30]Routley, R., Exploring Meinong's Jungle, Australian National University, Departmental Monograph No. 3, Canberra, 1980.
  • [31]Routley, R., ``Philosophical and linguistic inroads: multiply intensional relevant logics," pp. 269--304 in Directions in Relevant Logic, edited by J. Norman and R. Sylvan, Kluwer, Dordrecht, 1989.
  • [32]Routley, R., R. Meyer, V. Plumwood, and R. Brady, Relevant Logics and Their Rivals, Ridgeview, Atascadero, 1982.
  • [33]Stalnaker, R., ``Indicative conditionals,'' Philosophia, vol. 5 (1975), pp. 269--86. %Reprinted in Harper, W.L.,
  • [34]Stalnaker, R., Inquiry, The MIT Press, Cambridge, 1984.
  • [35]van Fraassen, B., ``Probabilities of conditionals," pp. 261--308 in Foundations of Probability Theory, Statistical Inference, and Statistical Theories of Science, vol. 1, edited by W. L. Harper and C. A. Hooker, D. Reidel, Dordrecht, 1976.
  • [36]van Inwagen, P., ``Two concepts of possible worlds," Midwest Studies in Philosophy, vol. 11 (1986), pp. 185--213.