How to Precisify Quantifiers
2011 (English)In: Journal of Philosophical Logic, ISSN 0022-3611, E-ISSN 1573-0433, Vol. 40, no 1, 103-111 p.Article in journal (Refereed) Published
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.
Place, publisher, year, edition, pages
2011. Vol. 40, no 1, 103-111 p.
Quantification, Quantifiers, Unrestricted quantification, Sider, Definition, Implicit definition, Four-dimensionalism, Persistence, Endurantism, Perdurantism, Vagueness, Precisification, Mereology, Parthood, Free logic
IdentifiersURN: urn:nbn:se:su:diva-67474DOI: 10.1007/s10992-010-9152-4ISI: 000286332500006OAI: oai:DiVA.org:su-67474DiVA: diva2:470662
authorCount :12011-12-292011-12-282013-01-21Bibliographically approved