There Is A Problem with Substitutional Quantification

Theoria 68 (1):4-12 (2002)

Charles Sayward
University of Nebraska, Lincoln
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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Ontological Relativity and Other Essays.W. V. Quine - 1969 - Columbia University Press.

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