How To Precisify Quantifiers

Journal of Philosophical Logic 40 (1):103-111 (2011)
Abstract
I here argue that Ted Sider's indeterminacy argument against vagueness in quantifiers fails. Sider claims that vagueness entails precisifications, but holds that precisifications of quantifiers cannot be coherently described: they will either deliver the wrong logical form to quantified sentences, or involve a presupposition that contradicts the claim that the quantifier is vague. Assuming (as does Sider) that the “connectedness” of objects can be precisely defined, I present a counter-example to Sider's contention, consisting of a partial, implicit definition of the existential quantifier that in effect sets a given degree of connectedness among the putative parts of an object as a condition upon there being something (in the sense in question) with those parts. I then argue that such an implicit definition, taken together with an “auxiliary logic” (e.g., introduction and elimination rules), proves to function as a precisification in just the same way as paradigmatic precisifications of, e.g., “red”. I also argue that with a quantifier that is stipulated as maximally tolerant as to what mereological sums there are, precisifications can be given in the form of truth-conditions of quantified sentences, rather than by implicit definition.
Keywords Quantification  vagueness  Sider  precisification  mereology  Lewis
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DOI 10.1007/s10992-010-9152-4
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References found in this work BETA
Quantifier Variance and Realism.Eli Hirsch - 2002 - Philosophical Issues 12 (1):51-73.
Against Vague Existence.Theodore Sider - 2003 - Philosophical Studies 114 (1-2):135 - 146.
Sider on Existence.David Liebesman & Matti Eklund - 2007 - Noûs 41 (3):519–528.

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