How To Precisify Quantifiers

Journal of Philosophical Logic 40 (1):103-111 (2011)
Download Edit this record How to cite View on PhilPapers
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.
PhilPapers/Archive ID
BAVHTP
Revision history
First archival date: 2011-02-17
Latest version: 2 (2012-10-10)
View upload history
References found in this work BETA
Four Dimensionalism.Sider, Theodore

View all 13 references / Add more references

Citations of this work BETA
Vagueness & Modality—An Ecumenical Approach.Litland, Jon Erling & Yli-Vakkuri, Juhani

Add more citations

Added to PP index
2011-02-17

Total views
363 ( #12,187 of 50,419 )

Recent downloads (6 months)
35 ( #17,452 of 50,419 )

How can I increase my downloads?

Downloads since first upload
This graph includes both downloads from PhilArchive and clicks to external links.