There Is A Problem with Substitutional Quantification

Theoria 68 (1):4-12 (2002)
Whereas arithmetical quantification is substitutional in the sense that a some-quantification is true only if some instance of it is true, it does not follow (and, in fact, is not true) that an account of the truth-conditions of the sentences of the language of arithmetic can be given by a substitutional semantics. A substitutional semantics fails in a most fundamental fashion: it fails to articulate the truth-conditions of the quantifications with which it is concerned. This is what is defended in the paper. In particular, it is defended against remarks to the contrary in a well known paper on the subject.
Keywords Quine  Kripke  substitutional quantification  arithmetic  Davidson
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DOI 10.1111/j.1755-2567.2002.tb00117.x
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Saul A. Kripke (1976). Is There a Problem About Substitutional Quantification? In Gareth Evans & John McDowell (eds.), Truth and Meaning. Oxford University Press. pp. 324-419.
Marian David (2006). A Substitutional Theory of Truth? [REVIEW] Philosophy and Phenomenological Research 72 (1):182–189.
Francesca Boccuni (2013). Plural Logicism. Erkenntnis 78 (5):1051-1067.

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