Predicate abstraction, the limits of quantification, and the modality of existence
- 155 Downloads
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.
KeywordsPredicate 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.
- 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
- Fine, K. (2005). Modality and tense. Oxford: Clarendon.Google Scholar
- 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
- Fitting, M. (1996). A modal Herbrand theorem. Fundamenta Informaticae, 28, 101–122.Google Scholar
- Fitting, M., & Mendleson, R. (1998). First-order modal logic. Dordrecht: Kluwer.Google Scholar
- 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
- Graff Fara, D. (2006). Descriptions with adverbs of quantification. Philosophical Issues 16 (Philosophy of Language).Google Scholar
- 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
- Horn, L.R. (1985). Metalinguistic negation and pragmatic ambiguity. Language, 61, 121–174.Google Scholar
- Ludlow, P. (2007). “Descriptions” (revised version July 26, 2007). Stanford Encyclopedia of Philosophy, available at http://plato.stanford.edu/entries/descriptions.
- Salmon, N. (1987). Existence. In J. E. Tomberlin (Ed.), Philosophical perspectives 1: Metaphysics. Atascadero, CA: Ridgeview Press.Google Scholar
- Stalnaker, R. (1977). Complex predicates. Monist, 60, 327–339.Google Scholar
- 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
- Stalnaker, R. (2003). Ways a world might be. Oxford: Clarendon.Google Scholar
- Thomason, R. H., & Stalnaker, R. (1973). A semantic theory of adverbs. Linguistic Inquiry, 4, 195–220.Google Scholar
- Williamson, T. (1987). Equivocation and existence. Proceedings of the Aristotelian Society, 87, 109–127.Google Scholar
- Williamson, T. (1989). Being and being so. Acta Analytica, 4, 93–114.Google Scholar