Quantifier Variance and the Demand for a Semantics

Authors
Jared Warren
Stanford University
Eli Hirsch
Brandeis University
Abstract
In the work of both Matti Eklund and John Hawthorne there is an influential semantic argument for a maximally expansive ontology that is thought to undermine even modest forms of quantifier variance. The crucial premise of the argument holds that it is impossible for an ontologically "smaller" language to give a Tarskian semantics for an ontologically "bigger" language. After explaining the Eklund-Hawthorne argument (in section I), we show this crucial premise to be mistaken (in section II) by developing a Tarskian semantics for a mereological universalist language within a mereological nihilist language (a case which we, and Eklund and Hawthorne, take as representative). After developing this semantics we step back (in section III) to discuss the philosophical motivations behind the Eklund- Hawthorne argument’s demand for a semantics. We ultimately conclude that quantifier variantists can meet any demand for a semantics that might reasonably be imposed upon them.
Keywords Quantifiers  Existence  Semantics  Mereology
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DOI 10.1111/phpr.12442
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What We Disagree About When We Disagree About Ontology.Cian Dorr - 2005 - In Mark Eli Kalderon (ed.), Fictionalism in Metaphysics. Oxford University Press. pp. 234--86.
Word and Object.Willard Van Orman Quine - 1960 - Les Etudes Philosophiques 17 (2):278-279.
Quantifier Variance and Realism.Eli Hirsch - 2002 - Philosophical Issues 12 (1):51-73.

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