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Journal of Philosophical Logic

, Volume 45, Issue 6, pp 697–742 | Cite as

The Problem of Cross-world Predication

  • Alexander W. Kocurek
Article

Abstract

While standard first-order modal logic is quite powerful, it cannot express even very simple sentences like “I could have been taller than I actually am” or “Everyone could have been smarter than they actually are”. These are examples of cross-world predication, whereby objects in one world are related to (sometimes the same) objects in another world. Extending first-order modal logic to allow for cross-world predication in a motivated way has proven to be notoriously difficult. In this paper, I argue that the standard accounts of cross-world predication all leave something to be desired. I then propose an account of cross-world predication based on quantified hybrid logic and show how it overcomes the limitations of these previous accounts. I will conclude by discussing various philosophical consequences and applications of such an account.

Keywords

Cross-world predication Cross-world quantification Expressive power First-order modal logic Hybrid logic 

Notes

Acknowledgments

Many thanks to Johan van Benthem, Russell Buehler, Balder ten Cate, Sophie Dandelet, Melissa Fusco, Wesley Holliday, Grace Paterson, Justin Vlasits, Kai Wehmeier, and Seth Yalcin for all their helpful comments and suggestions. A version of this paper was presented at the Berkeley-Stanford Circle in Logic and Philosophy in October 2014. A version of this paper was also presented at a C-ALPHA-sponsored talk at UC Irvine in March 2015 and at the Logic Seminar at Stanford in May 2015. I am very grateful for all the helpful comments and discussion from these talks.

References

  1. 1.
    Aloni, M. (2005). Individual concepts in modal predicate logic. Journal of Philosophical Logic, 34(1), 1–64.CrossRefGoogle Scholar
  2. 2.
    Areces, C., Blackburn, P., & Marx, M. (2003). Repairing the interpolation theorem in quantified modal logic. Annals of Pure and Applied Logic, 124(1), 287–299.CrossRefGoogle Scholar
  3. 3.
    Blackburn, P., & Marx, M. (2002). Tableaux for quantified hybrid logic. In Automated Reasoning with Analytic Tableaux and Related Methods (pp. 38–52). Berlin: Springer.CrossRefGoogle Scholar
  4. 4.
    Blackburn, P., De Rijke, M., & Venema, Y. (2002). Modal logic.: Cambridge University Press.Google Scholar
  5. 5.
    Boolos, G. (1984). To be is to be a value of a variable (or to be some values of some variables). Journal of Philosophy, 430–449.Google Scholar
  6. 6.
    Bricker, P. (1989). Quantified modal logic and the plural de re. Midwest Studies in Philosophy, 14(1), 372–394.CrossRefGoogle Scholar
  7. 7.
    Butterfield, J., & Stirling, C. (1987). Predicate modifiers in tense logic. Logique et Analyse, 30(117), 31–50.Google Scholar
  8. 8.
    Button, T. (2012). Spotty scope and our relation to fictions. Noûs, 46(2), 243–258.CrossRefGoogle Scholar
  9. 9.
    Cantwell, J. (1995). Comparatives. Theoretical Linguistics, 21(2–3), 145–158.Google Scholar
  10. 10.
    Cresswell, M.J. (2012). Entities and indices. Vol. 41. Dordrecht: Kluwer Academic Publishers.Google Scholar
  11. 11.
    Cumming, S. (2008). Variabilism. Philosophical Review, 117(4), 525–554.CrossRefGoogle Scholar
  12. 12.
    Davies, M., & Humberstone, L. (1980). Two notions of necessity. Philosophical Studies, 38(1), 1–30.CrossRefGoogle Scholar
  13. 13.
    Fitting, M. (2013). On height and happiness, to appear in a volume honoring Rohit Parikh. http://melvinfitting.org/bookspapers/pdf/papers/HeightAndHappiness.pdf.
  14. 14.
    Fitting, M., & Mendelsohn, R.L. (1998). First-order modal logic: Kluwer Academic Publishers.Google Scholar
  15. 15.
    Forbes, G. (1989). Languages of possibility. Oxford: Blackwell.Google Scholar
  16. 16.
    Forbes, G. (1994). Comparatives in counterpart theory: another approach. Analysis, 37–42.Google Scholar
  17. 17.
    Hazen, A. (1976). Expressive completeness in modal language. Journal of Philosophical Logic, 5(1), 25–46.CrossRefGoogle Scholar
  18. 18.
    Hodes, H.T. (1984). Axioms for actuality. Journal of Philosophical Logic, 13 (1), 27–34.CrossRefGoogle Scholar
  19. 19.
    Hodes, H.T. (1984). Some theorems on the expressive limitations of modal languages. Journal of Philosophical Logic, 13(1), 13–26.CrossRefGoogle Scholar
  20. 20.
    Holliday, W.H., & Perry, J. (2014). Roles, rigidity, and quantification in epistemic logic. In Johan van Benthem on Logic and Information Dynamics (pp. 591–629): Springer.Google Scholar
  21. 21.
    King, JC (2003). Tense, modality, and semantic values. Philosophical Perspectives, 17(1), 195–246.CrossRefGoogle Scholar
  22. 22.
    Kocurek, A.W. (2015). On the expressivity of first-order modal logic with “actually”. In van der Hoek, W., Holliday, W.H., & Wang, W (Eds.) Logic, Rationality, and Interaction, 5th International Workshop, Springer (pp. 207–219).Google Scholar
  23. 23.
    Kratzer, A. (1998). More structural analogies between pronouns and tenses. In Semantics and linguistic theory (pp. 92–110).Google Scholar
  24. 24.
    Kratzer, A. (2014). Situations in natural language semantics. In Zalta, E.N (Ed.) http://plato.stanford.edu/entries/situations-semantics/: Stanford Encyclopedia of Philosophy.
  25. 25.
    Lewis, D.K. (1981). Counterfactuals and comparative possibility. Journal of Philosophical Logic, 2, 418–446.Google Scholar
  26. 26.
    Lewis, D.K. (1986). On the plurality of worlds. Oxford: Blackwell.Google Scholar
  27. 27.
    Mackay, J. (2013). Quantifying over possibilities. Philosophy in Review, 122 (4), 577–617.Google Scholar
  28. 28.
    Melia, J. (2014). Modality. Chesham: Acumen Press.Google Scholar
  29. 29.
    Menzel, C., & Zalta, E.N. (2014). The fundamental theorem of world theory. Journal of Philosophical Logic, 43(2–3), 333–363.CrossRefGoogle Scholar
  30. 30.
    Milne, P. (1992). Modal metaphysics and comparatives. Australasian Journal of Philosophy, 70(3), 248–262.CrossRefGoogle Scholar
  31. 31.
    Partee, B.H. (1973). Some structural analogies between tenses and pronouns in English. Journal of Philosophy, 601–609.Google Scholar
  32. 32.
    Pollock, J.L. (1976). Subjunctive reasoning. Dordrecht: Reidel.CrossRefGoogle Scholar
  33. 33.
    Priest, G. (2005). Towards non-being: The logic and metaphysics of intentionality. Oxford: Clarendon Press.CrossRefGoogle Scholar
  34. 34.
    Rabinowicz, W., & Segerberg, K. (1994). Actual truth, possible knowledge. Topoi, 13(2), 101–115.CrossRefGoogle Scholar
  35. 35.
    Schaffer, J. (2012). Necessitarian propositions. Synthese, 189(1), 119–162.CrossRefGoogle Scholar
  36. 36.
    Schlenker, P. (2006). Ontological symmetry in language: A brief manifesto. Mind & Language, 21(4), 504–539.CrossRefGoogle Scholar
  37. 37.
    Sider, T. (2001). Four-dimensionalism: an ontology of persistence and time: Oxford University Press.Google Scholar
  38. 38.
    von Stechow, A. (1984). Comparing semantic theories of comparison. Journal of Semantics, 3(1), 1–77.CrossRefGoogle Scholar
  39. 39.
    Stone, M. (1997). The anaphoric parallel between modality and tense. IRCS Report 97–06. PA: University of Pennsylvania.Google Scholar
  40. 40.
    Wehmeier, K.F. (2003). World travelling and mood swings. In Foundations of the Formal Sciences II (pp. 257–260). Netherlands: Springer.CrossRefGoogle Scholar
  41. 41.
    Wehmeier, K.F. (2012). Subjunctivity and cross-world predication. Philosophical Studies, 159(1), 107–122.CrossRefGoogle Scholar
  42. 42.
    Yanovich, I. (2015). Expressive power of “now” and “then” operators. Journal of Logic, Language and Information, 24(1), 65–93.CrossRefGoogle Scholar
  43. 43.
    Zalta, E.N. (1993). Twenty-five basic theorems in situation and world theory. Journal of Philosophical Logic, 22(4), 385–428.CrossRefGoogle Scholar
  44. 44.
    Zimmermann, T.E. (1989). Intensional logic and two-sorted type theory. Journal of Symbolic Logic, 54(1), 65–77.CrossRefGoogle Scholar

Copyright information

© Springer Science+Business Media Dordrecht 2016

Authors and Affiliations

  1. 1.Group in Logic and Methodology of ScienceUniversity of CaliforniaBerkeley, BerkeleyUSA

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