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

Philosophical Studies 156 (3):389-416 (2011)
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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

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Philip Percival
Nottingham University

Citations of this work

Actualism, Serious Actualism, and Quantified Modal Logic.William H. Hanson - 2018 - Notre Dame Journal of Formal Logic 59 (2):233-284.

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References found in this work

Objects of thought.Arthur Norman Prior - 1971 - Oxford,: Clarendon Press. Edited by P. T. Geach & Anthony Kenny.
Modality and Tense: Philosophical Papers.Kit Fine - 2005 - Oxford, England: Oxford University Press.
Necessary existents.Timothy Williamson - 2002 - In A. O'Hear (ed.), Logic, thought, and language. Cambridge University Press. pp. 233-251.
Existence.Nathan Salmon - 1987 - Philosophical Perspectives 1:49-108.

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