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2014 Peter van Inwagen, Substitutional Quantification, and Ontological Commitment
William Craig
Notre Dame J. Formal Logic 55(4): 553-561 (2014). DOI: 10.1215/00294527-2798736


Peter van Inwagen has long claimed that he doesn’t understand substitutional quantification and that the notion is, in fact, meaningless. Van Inwagen identifies the source of his bewilderment as an inability to understand the proposition expressed by a simple sentence like “(Σx) (x is a dog),” where “Σ” is the existential quantifier understood substitutionally. I should think that the proposition expressed by this sentence is the same as that expressed by “(x) (x is a dog).” So what’s the problem? The problem, I suggest, is that van Inwagen takes traditional existential quantification to be ontologically committing and substitutional quantification to be ontologically noncommitting, which requires that the two quantifiers have different meanings—but no different meaning for the substitutional quantifier is forthcoming. What van Inwagen fails to appreciate is that substitutional quantification is directed at a criterion of ontological commitment, namely, W. V. O. Quine’s, which is quite different from van Inwagen’s criterion. Substitutional quantification successfully avoids the commitments Quine’s criterion would engender but has the same commitments as existential quantification given van Inwagen’s criterion. The question, then, is whether the existential quantifier is ontologically committing, as van Inwagen believes. The answer to that question will depend on whether the ordinary language “there is/are,” which is codified by the existential quantifier, is ontologically committing. There are good reasons to doubt that it is.


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William Craig. "Peter van Inwagen, Substitutional Quantification, and Ontological Commitment." Notre Dame J. Formal Logic 55 (4) 553 - 561, 2014.


Published: 2014
First available in Project Euclid: 7 November 2014

zbMATH: 1335.03003
MathSciNet: MR3276411
Digital Object Identifier: 10.1215/00294527-2798736

Primary: 03-XX

Rights: Copyright © 2014 University of Notre Dame


Vol.55 • No. 4 • 2014
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