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Systems of Substitutional Semantics

Published online by Cambridge University Press:  01 April 2022

Daniel Bonevac
Daniel Bonevac*
Affiliation:
Center for Cognitive Science, The University of Texas at Austin
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Abstract

I investigate substitutional interpretations of quantifiers that count existential sentences true just in case they have true instances in a parametric extension of the language. I devise a semantics meeting four criteria: (1) it accounts adequately for natural language quantification; (2) it provides an account of justification in abstract sciences; (3) it constitutes a continuous semantics for natural and formal languages; and (4) it is purely substitutional, containing no appeal to referential interpretations. The prospects for a purely substitutional theory of quantification are thus no worse than for a referential account.

Type
Research Article
Information
Philosophy of Science , Volume 51 , Issue 4 , December 1984 , pp. 631 - 656
Copyright
Copyright © Philosophy of Science Association 1984

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Footnotes

†

I am grateful to Nicholas Asher, to Allen Hazen, to Hans Kamp, and to two anonymous referees for their helpful comments on an earlier draft of this paper, and the Center for Cognitive Science of the University of Texas at Austin for its research support.

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