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

Philosophical Studies 156 (3):389-416 (2011)
Abstract
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
Keywords Predicate abstraction  Quantification  Modality  Existence  Singular proposition  Logical form
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References found in this work BETA
Jay David Atlas (1977). Negation, Ambiguity, and Presupposition. Linguistics and Philosophy 1 (3):321 - 336.
Richard L. Cartwright (2013). On Singular Propositions. Canadian Journal of Philosophy 27 (sup1):67-83.
Kit Fine (2005). Modality and Tense. Oxford University Press.

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