Quantification and ontology
Synthese 124 (1-2):1-43 (2000)
| Abstract | Quineans have taken the basic expression of ontological commitment to be an assertion of the form '' x '', assimilated to theEnglish ''there is something that is a ''. Here I take the existential quantifier to be introduced, not as an abbreviation for an expression of English, but via Tarskian semantics. I argue, contrary to the standard view, that Tarskian semantics in fact suggests a quite different picture: one in which quantification is of a substitutional type apparently first proposed by Geach. The ontological burden is borne by constant symbols, and truth is defined separately from reference. | |||||||||
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Philip Hugly & Charles Sayward (1987). Why Substitutional Quantification Does Not Express Existence. Theory and Decision 50:67-75.
Charles F. Kielkopf (1977). Quantifiers in Ontology. Studia Logica 36 (4):301-307.
Øystein Linnebo (2006). Sets, Properties, and Unrestricted Quantification. In Gabriel Uzquiano & Agustin Rayo (eds.), Absolute Generality. Oxford University Press.
Daniel Bonevac (1984). Systems of Substitutional Semantics. Philosophy of Science 51 (4):631-656.
Dale Gottlieb (1980). Ontological Economy: Substitutional Quantification and Mathematics. Oxford University Press.
Philip Hugly & Charles Sayward (1982). Indenumerability and Substitutional Quantification. Notre Dame Journal of Formal Logic 23 (4):358-366.
Berit Brogaard (2008). Inscrutability and Ontological Commitment. Philosophical Studies 141 (1):21 - 42.
Howard Peacock (2011). Two Kinds of Ontological Commitment. Philosophical Quarterly 61 (242):79-104.
Philip Hugly & Charles Sayward (1994). Quantifying Over the Reals. Synthese 101 (1):53 - 64.
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