Notre Dame Journal of Formal Logic

Worlds and Times

Ulrich Meyer

Abstract

There are many parallels between the role of possible worlds in modal logic and that of times in tense logic. But the similarities only go so far, and it is important to note where the two come apart. This paper argues that even though worlds and times play similar roles in the model theories of modal and tense logic, there is no tense analogue of the possible-worlds analysis of modal operators. An important corollary of this result is that presentism cannot be the tense analogue of actualism.

Article information

Source
Notre Dame J. Formal Logic Volume 47, Number 1 (2006), 25-37.

Dates
First available: 27 March 2006

Permanent link to this document
http://projecteuclid.org/euclid.ndjfl/1143468309

Digital Object Identifier
doi:10.1305/ndjfl/1143468309

Mathematical Reviews number (MathSciNet)
MR2211180

Zentralblatt MATH identifier
1107.03014

Subjects
Primary: 03B44: Temporal logic 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: 03C80: Logic with extra quantifiers and operators [See also 03B42, 03B44, 03B45, 03B48]

Keywords
tense logic modal logic times possible worlds actuality operator presentism actualism

Citation

Meyer, Ulrich. Worlds and Times. Notre Dame Journal of Formal Logic 47 (2006), no. 1, 25--37. doi:10.1305/ndjfl/1143468309. http://projecteuclid.org/euclid.ndjfl/1143468309.


Export citation

References

  • [1] Dummett, M. A. E., and E. J. Lemmon, "Modal logics between S4" and S5, Zeitschrift für mathematische Logik und Grundlagen der Mathematik, vol. 5 (1959), pp. 250--65.
  • [2] Evans, G., ``Does tense logic rest upon a mistake?'' pp. 343--63 in Collected Papers, The Clarendon Press, Oxford, 1985.
  • [3] Hazen, A., "The eliminability of the actuality operator in propositional modal logic", Notre Dame Journal of Formal Logic, vol. 19 (1978), pp. 617--22.
  • [4] Hazen, A., "Actuality and quantification", Notre Dame Journal of Formal Logic, vol. 31 (1990), pp. 498--508.
  • [5] Higginbotham, J., "Tense, indexicality, and consequence", pp. 197--215 in The Arguments of Time, edited by J. Butterfield, Oxford University Press, Oxford, 1999.
  • [6] Hodes, H. T., "Axioms for actuality", Journal of Philosophical Logic, vol. 13 (1984), pp. 27--34.
  • [7] Hughes, G. E., and M. J. Cresswell, A New Introduction to Modal Logic, Routledge, London, 1996.
  • [8] Kamp, H., "Formal properties of `now'", Theoria, vol. 37 (1971), pp. 227--73.
  • [9] Lewis, D., "Anselm and actuality", pp. 10--25 in Philosophical Papers, Vol. 1, Oxford University Press, Oxford, 1983.
  • [10] Lewis, D., On the Plurality of Worlds, Blackwell, Oxford, 1986.
  • [11] Meyer, U., "The presentist's dilemma", Philosophical Studies, vol. 123 (2005), pp. 213--24.
  • [12] Prior, A., ``,`Now','' Noûs, vol. 2 (1968), pp. 101--19.
  • [13] Prior, A. N., "Tense-logic and an analogue of S4", pp. 8--17 in Time and Modality, The Clarendon Press, Oxford, 1957.
  • [14] Prior, A. N., "A tense-logical analogue of S5", pp. 18--28 in Time and Modality, The Clarendon Press, Oxford, 1957.
  • [15] Prior, A. N., Time and Modality, The Clarendon Press, Oxford, 1957.
  • [16] Segerberg, K., "Two-dimensional modal logic", Journal of Philosophical Logic, vol. 2 (1973), pp. 77--96.
  • [17] Stalnaker, R. C., "Possible worlds", Noûs, vol. 10 (1976), pp. 65--75.
  • [18] van Inwagen, P., "Indexicality and actuality", Philosophical Review, vol. 89 (1980), pp. 403--26.