Philosophical Studies

, Volume 156, Issue 3, pp 389–416 | Cite as

Predicate abstraction, the limits of quantification, and the modality of existence



For various reasons several authors have enriched classical first order syntax by adding a predicate abstraction operator. “Conservatives” have done so without disturbing the syntax of the formal quantifiers but “revisionists” have argued that predicate abstraction motivates the universal quantifier’s re-classification from an expression that combines with a variable to yield a sentence from a sentence, to an expression that combines with a one-place predicate to yield a sentence. My main aim is to advance the cause of predicate abstraction while cautioning against revisionism. In so doing, however, I shall pursue a secondary aim by conveying mixed blessings to those who hold the view that in the logical sense of “existence” some existing object is such as to exist contingently. Advocates of this view must concede Williamson’s recent contention that the domain of unrestricted objectual quantification could not have been narrower than it is actually, but predicate abstraction affords them some hope of accommodating this concession.


Predicate abstraction Quantification Modality Existence Singular proposition Logical form 



I am extremely grateful to Kit Fine, Stefano Predelli, Luis Robledo, Tim Williamson, and an anonymous referee for very helpful and insightful comments on an earlier draft of this paper.


  1. Atlas, J. D. (1977). Negation, ambiguity and presupposition. Linguistics and Philosophy, 1, 321–336.CrossRefGoogle Scholar
  2. Barendregt, H. P. (1997). The impact of the lambda calculus in logic and computer science. The Bulletin of Symbolic Logic, 3, 181–214.CrossRefGoogle Scholar
  3. Bencivenga, E., & Woodruff, P. W. (1981). A new modal language with the λ operator. Studia Logica, 40, 383–389.CrossRefGoogle Scholar
  4. Cartwright, R. (1997). On singular propositions. In A. Kazmi (Ed.), Meaning and reference (pp. 67–83), Canadian Journal of Philosophy Supplementary Volume 23. Calgary: University of Calgary Press.Google Scholar
  5. Church, A. (1932). A set of postulates for the foundation of logic. Annals of Mathematics, 33, 346–366.CrossRefGoogle Scholar
  6. Fine, K. (2005). Modality and tense. Oxford: Clarendon.Google Scholar
  7. Fitting, M. (1991). Modal logic should say more than it does. In J.-L. Lassez & G. Plotkin (Eds.), Computational logic, essays in honor of Alan Robinson. Cambridge, MA: M. I. T. Press.Google Scholar
  8. Fitting, M. (1996). A modal Herbrand theorem. Fundamenta Informaticae, 28, 101–122.Google Scholar
  9. Fitting, M., & Mendleson, R. (1998). First-order modal logic. Dordrecht: Kluwer.Google Scholar
  10. Glanzberg, M. (2008). Descriptions, negation, and focus. In R. Stainton & C. Viger (Eds.), Compositionality, context and semantic values (pp. 193–220). Berlin: Springer.Google Scholar
  11. Graff Fara, D. (2006). Descriptions with adverbs of quantification. Philosophical Issues 16 (Philosophy of Language).Google Scholar
  12. Grice, H. P. (1969). Vacuous names. In D. Davidson & J. Hintikka (Eds.), Words and objections: Essays on the work of W. V. Quine. Dordrecht: Reidel.Google Scholar
  13. Hoffman, A. (2003). A puzzle about truth and singular propositions. Mind, 112, 635–651.CrossRefGoogle Scholar
  14. Horn, L.R. (1985). Metalinguistic negation and pragmatic ambiguity. Language, 61, 121–174.Google Scholar
  15. Kripke, S. (2005). Russell’s notion of scope. Mind, 114, 1005–1037.CrossRefGoogle Scholar
  16. Lambert, K., & Bencivenga, E. (1986). A free logic with simple and complex predicates. Notre Dame Journal of Formal Logic, 27, 247–256.CrossRefGoogle Scholar
  17. Ludlow, P. (2007). “Descriptions” (revised version July 26, 2007). Stanford Encyclopedia of Philosophy, available at
  18. Menzel, P. (1991). The true modal logic. Journal of Philosophical Logic, 20, 331–374.CrossRefGoogle Scholar
  19. Neale, S. (2005). A century later. Mind, 114, 809–871. doi: 10.1093/mind/fzi809.CrossRefGoogle Scholar
  20. Prior, A. N. (1971). Objects of thought. Oxford: Clarendon.CrossRefGoogle Scholar
  21. Salmon, N. (1987). Existence. In J. E. Tomberlin (Ed.), Philosophical perspectives 1: Metaphysics. Atascadero, CA: Ridgeview Press.Google Scholar
  22. Saul, J. (1997). Substitution and simple sentences. Analysis, 57, 102–108.CrossRefGoogle Scholar
  23. Stalnaker, R. (1977). Complex predicates. Monist, 60, 327–339.Google Scholar
  24. Stalnaker, R. (1995). The interaction of modality with quantification and identity. In W. Sinnott-Armstrong, et al. (Eds.), Modality, morality and belief. Cambridge: Cambridge University Press.Google Scholar
  25. Stalnaker, R. (2003). Ways a world might be. Oxford: Clarendon.Google Scholar
  26. Stephanou, Y. (2007). Serious actualism. Philosophical Review, 116, 219–250.CrossRefGoogle Scholar
  27. Thomason, R. H., & Stalnaker, R. (1968). Modality and reference. Nous, 2, 359–372.CrossRefGoogle Scholar
  28. Thomason, R. H., & Stalnaker, R. (1973). A semantic theory of adverbs. Linguistic Inquiry, 4, 195–220.Google Scholar
  29. Williamson, T. (1987). Equivocation and existence. Proceedings of the Aristotelian Society, 87, 109–127.Google Scholar
  30. Williamson, T. (1989). Being and being so. Acta Analytica, 4, 93–114.Google Scholar
  31. Williamson, T. (1999). Truthmakers and the converse Barcan formula. Dialectica, 53, 253–270.CrossRefGoogle Scholar
  32. Williamson, T. (2000). Existence and contingency. Proceedings of the Aristotelian Society, 100, 117–139.CrossRefGoogle Scholar
  33. Williamson, T. (2002). Necessary existents. In A. O’Hear (Ed.), Logic, thought and language (pp. 233–251). Cambridge: Cambridge University Press.CrossRefGoogle Scholar

Copyright information

© Springer Science+Business Media B.V. 2010

Authors and Affiliations

  1. 1.Department of PhilosophyUniversity of NottinghamNottinghamUK

Personalised recommendations