Philosophical Studies

, Volume 175, Issue 3, pp 809–830 | Cite as

Actuality and the a priori

Article

Abstract

We consider a natural-language sentence that cannot be formally represented in a first-order language for epistemic two-dimensional semantics. We also prove this claim in the “Appendix” section. It turns out, however, that the most natural ways to repair the expressive inadequacy of the first-order language render moot the original philosophical motivation of formalizing a priori knowability as necessity along the diagonal.

Keywords

Two-dimensional semantics Actuality A priori Expressive power 

Notes

Acknowledgements

I am deeply grateful to I-Sen Chen, Alex Kocurek, Hanti Lin, Harrison Smith-Jaoudi, Shawn Standefer, and Lloyd Humberstone for comments on different versions of this paper. Thanks also to Adam Sennet, Greg Ray, Ted Shear, G. J. Mattey, Rachel Boddy, Tyrus Fisher, Rohan French, and Greg Restall for many helpful conversations and suggestions. This paper has been presented at the Philosophy Department of the University of California, Davis; the Davis Logic, Language, Epistemology, and Mathematics Working Group; and the Logic Seminar at the University of Melbourne, Australia. I want to express my gratitude to the audiences for many insightful questions and suggestions. Finally, I am thankful to Andrew Parisi for encouraging me to write this paper, as well as to an anonymous referee for comments and advice.

References

  1. Boolos, G. (1984). To be is to be a value of a variable (or to be some values of some variables). Journal of Philosophy, 81, 430–49.CrossRefGoogle Scholar
  2. Bricker, P. (1989). Quantified modal logic and the plural de re. Midwest Studies in Philosophy, XIV, 372–394.CrossRefGoogle Scholar
  3. Chalmers, D. (1996). The conscious mind: In search of a fundamental theory. Oxford: Oxford University Press.Google Scholar
  4. Chalmers, D. (2004). Epistemic two-dimensional semantics. Philosophical Studies, 118, 153–226.CrossRefGoogle Scholar
  5. Chalmers, D. (2011). Propositions and attitude ascriptions: A Fregean account. Nous, 45(4), 595–639.CrossRefGoogle Scholar
  6. Chalmers, D., & Jackson, F. (2001). Conceptual analysis and reductive explanation. Philosophical Review, 110, 315–361.CrossRefGoogle Scholar
  7. Chalmers, D., & Rabern, B. (2014). Two-dimensional semantics and the nesting problem. Analysis, 74(2), 210–224.CrossRefGoogle Scholar
  8. Cresswell, M. (1990). Entities and indices. Dordrecht: Kluwer Academic Publishers.CrossRefGoogle Scholar
  9. Crossley, J. N., & Humberstone, I. L. (1977). The logic of “actually”. Reports on Mathematical Logic, 8, 11–29.Google Scholar
  10. Davies, M. (2004). Reference, contingency, and the two-dimensional framework. Philosophical Studies, 118, 83–131.CrossRefGoogle Scholar
  11. Davies, M., & Humberstone, I. L. (1980). Two notions of necessity. Philosophical Studies, 38(1), 1–30.CrossRefGoogle Scholar
  12. Dorr, C. (2011). De re a priori knowledge. Mind, 120, 939–91.CrossRefGoogle Scholar
  13. Evans, G. (1979). Reference and contingency. The Monist, 62, 161–189.CrossRefGoogle Scholar
  14. Forbes, G. (1985). The metaphysics of modality. Oxford: Clarendon Press.Google Scholar
  15. Forbes, G. (1989). Languages of possibility. Oxford: Basil Blackwell.Google Scholar
  16. Fritz, P. (2013). A logic for epistemic two-dimensional semantics. Synthese, 190, 1753–1770.CrossRefGoogle Scholar
  17. Fritz, P. (2014). What is the correct logic of necessity, actuality, and apriority? The Review of Symbolic Logic, 7(3), 385–414.CrossRefGoogle Scholar
  18. Hanson, W. (2006). Actuality, necessity, and logical truth. Philosophical Studies, 130, 436–459.CrossRefGoogle Scholar
  19. Hanson, W. (2014). Logical truth in modal languages: A reply to Nelson and Zalta. Philosophical Studies, 167, 327–339.CrossRefGoogle Scholar
  20. Hazen, A. (1976). Expressive completeness in modal language. Journal of Philosophical Logic, 5, 25–46.CrossRefGoogle Scholar
  21. Hodes, H. (1984). Some theorems on the expressive limitations of modal languages. Journal of Philosophical Logic, 13, 13–26.CrossRefGoogle Scholar
  22. Holliday, W., & Perry, J. (2014). Roles, rigidity, and quantification in epistemic logic. In A. Baltag & S. Smets (Eds.), Trends in logic, outstanding contributions: Johan van Benthem on logic information dynamics (pp. 591–629). Berlin: Springer.Google Scholar
  23. Humberstone, L. (1982). Scope and subjunctivity. Philosophia, 12(1–2), 99–126.CrossRefGoogle Scholar
  24. Humberstone, L. (2004). Two-dimensional adventures. Philosophical Studies, 118, 17–65.CrossRefGoogle Scholar
  25. Jackson, F. (1998). From metaphysics to ethics: A defence of conceptual analysis. Oxford: Oxford University Press.Google Scholar
  26. Kamp, J. A. W. (1971). Formal properties of “now”. Theoria, 37, 227–273.CrossRefGoogle Scholar
  27. Kaplan, D. (1989). Demonstratives. In J. Almog, J. Perry & H. Wettstein (Eds.), Themes from Kaplan (pp. 481–563). Oxford: Oxford University Press.Google Scholar
  28. Kocurek, A. W. (2016). On the expressive power of first-order modal logic with two-dimensional operators. Synthese. doi: 10.1007/s11229-016-1172-3.Google Scholar
  29. Kripke, S. (1963). Semantical considerations on modal logic. Acta Philosophica Fennica, 16, 83–94.Google Scholar
  30. Kripke, S. (1980). Naming and necessity. Cambridge, MA: Harvard University Press.Google Scholar
  31. Lampert, F. (manuscript). Actuality, tableaux, and two-dimensional modal logic.Google Scholar
  32. Lewis, D. (1970). How to define theoretical terms. Journal of Philosophy, 67, 427–446.CrossRefGoogle Scholar
  33. Linnebo, Ø. (2016). Plurals and modals. Canadian Journal of Philosophy, 46(4–5), 654–676.CrossRefGoogle Scholar
  34. Meyer, U. (2013). Counterpart theory and the actuality operator. Mind, 122(485), 27–42.CrossRefGoogle Scholar
  35. Montague, R. (1968). Pragmatics. In R. Klibansky (Ed.), Contemporary philosophy: A survey (pp. 102–122). Florence: La Nuova Italia Editrice. (Reprinted in R. H. Thomason (Ed.), Formal philosophy: Selected papers of Richard Montague. New Haven, CT: Yale University Press, 1974, pp. 95–118).Google Scholar
  36. Nelson, M., & Zalta, E. (2012). A defence of contingent logical truths. Philosophical Studies, 157, 153–162.CrossRefGoogle Scholar
  37. Restall, G. (2012). A cut-free sequent system for two-dimensional modal logic, and why it matters. Annals of Pure and Applied Logic, 163, 1611–1623.CrossRefGoogle Scholar
  38. Soames, S. (2005). Reference and description: The case against two-dimensionalism. Princeton: Princeton University Press.Google Scholar
  39. Stalnaker, R. (1978). Assertion. In P. Cole (Ed.), Syntax and Semantics: Pragmatics (Vol. 9, pp. 315–339). New York: Academic Press.Google Scholar
  40. Urquhart, A. (2015). First degree formulas in quantified S5. Australasian Journal of Logic, 12(5), 204–210.Google Scholar
  41. Uzquiano, G. (2011). Plural quantification and modality. Proceedings of the Aristotelian Society, 111(2), 219–250.CrossRefGoogle Scholar
  42. van Benthem, J. (2010). Frame correspondences in modal predicate logic. In Proofs, categories and computations: Essays in honor of Grigori Mints (pp. 1–14). London: College Publications.Google Scholar
  43. Vlach, F. (1973). ‘Now’ and ‘Then’: A formal study in the logic of tense anaphora. Ph.D. thesis, UCLA, Los Angeles.Google Scholar
  44. Wehmeier, K. (2001). World travelling and mood swings. In B. Löwe, T. Räsch, & W. Malkzorn (Eds.), Foundations of the formal sciences II. Trends in Logic (pp. 257–260). Dordrecht: Kluwer.Google Scholar
  45. Wehmeier, K. (2004). In the mood. Journal of Philosophical Logic, 33, 607–630.CrossRefGoogle Scholar
  46. Wehmeier, K. (2005). Modality, mood, and descriptions. In R. Kahle (Ed.), Intensionality: An interdisciplinary discussion (pp. 187–216)., Lecture notes in logic Wellesley: AK Peters.Google Scholar
  47. Williamson, T. (2003). Everything. Philosophical Perspectives, 17, 415–65.CrossRefGoogle Scholar
  48. Williamson, T. (2010). Necessitism, contingentism, and plural quantification. Mind, 119(475), 657–748.CrossRefGoogle Scholar
  49. Williamson, T. (2013). Modal logic as metaphysics. Oxford: Oxford University Press.CrossRefGoogle Scholar
  50. Zalta, E. (1988). Logical and analytic truths that are not necessary. Journal of Philosophy, 85, 57–74.CrossRefGoogle Scholar

Copyright information

© Springer Science+Business Media Dordrecht 2017

Authors and Affiliations

  1. 1.Department of PhilosophyUniversity of CaliforniaDavisUSA

Personalised recommendations