How to Precisify Quantifiers
Båve, Arvid LU
(2011)
In Journal of Philosophical Logic
40(1).
p.103-111
- 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... (More) - 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. (Less)
Please use this url to cite or link to this publication:
https://lup.lub.lu.se/record/4e5374cf-9f14-4186-b130-2bea086cb306
- author
- Båve, Arvid
LU
- publishing date
- 2011-02-01
- type
- Contribution to journal
- publication status
- published
- subject
- keywords
- Quantification, Quantifiers, Unrestricted quantification, Sider, Definition, Implicit definition, Four-dimensionalism, Persistence, Endurantism, Perdurantism, Vagueness, Precisification, Mereology, Parthood, Free logic
- in
- Journal of Philosophical Logic
- volume
- 40
- issue
- 1
- pages
- 103 - 111
- publisher
- Springer
- external identifiers
-
- scopus:78751494112
- ISSN
- 0022-3611
- DOI
- 10.1007/s10992-010-9152-4
- language
- English
- LU publication?
- no
- id
- 4e5374cf-9f14-4186-b130-2bea086cb306
- date added to LUP
- 2021-11-08 10:46:36
- date last changed
- 2025-10-14 10:47:38
@article{4e5374cf-9f14-4186-b130-2bea086cb306,
abstract = {{I here argue that Ted Sider's indeterminacy argument against vagueness<br/>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.}},
author = {{Båve, Arvid}},
issn = {{0022-3611}},
keywords = {{Quantification; Quantifiers; Unrestricted quantification; Sider; Definition; Implicit definition; Four-dimensionalism; Persistence; Endurantism; Perdurantism; Vagueness; Precisification; Mereology; Parthood; Free logic}},
language = {{eng}},
month = {{02}},
number = {{1}},
pages = {{103--111}},
publisher = {{Springer}},
series = {{Journal of Philosophical Logic}},
title = {{How to Precisify Quantifiers}},
url = {{http://dx.doi.org/10.1007/s10992-010-9152-4}},
doi = {{10.1007/s10992-010-9152-4}},
volume = {{40}},
year = {{2011}},
}