Difference between revisions of "Vacuous quantification"
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'''Vacuous quantification''' obtains when a [[quantifier]] fails to bind a variable, either because the variable is not in the [[scope]] of that quantifier (cf. All(x) in (i)a), or because there is another quantifier already binding the variable (cf. All(x) in (i)b). | '''Vacuous quantification''' obtains when a [[quantifier]] fails to bind a variable, either because the variable is not in the [[scope]] of that quantifier (cf. All(x) in (i)a), or because there is another quantifier already binding the variable (cf. All(x) in (i)b). | ||
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b All(x) [ P(j) & ThereIs(x) [ Q(x) ]] | b All(x) [ P(j) & ThereIs(x) [ Q(x) ]] | ||
| − | + | == Links == | |
| − | + | *[http://www2.let.uu.nl/UiL-OTS/Lexicon/zoek.pl?lemma=Vacuous+quantification&lemmacode=102 Utrecht Lexicon of Linguistics] | |
| − | [http://www2.let.uu.nl/UiL-OTS/Lexicon/zoek.pl?lemma=Vacuous+quantification&lemmacode=102 Utrecht Lexicon of Linguistics] | ||
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| + | == References == | ||
* Partee, B.H., A. ter Meulen, and R. Wall 1990. ''Mathematical Methods in Linguistics,'' Kluwer:Dordrecht | * Partee, B.H., A. ter Meulen, and R. Wall 1990. ''Mathematical Methods in Linguistics,'' Kluwer:Dordrecht | ||
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[[Category:Semantics]] | [[Category:Semantics]] | ||
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Latest revision as of 08:51, 30 August 2014
Definition
Vacuous quantification obtains when a quantifier fails to bind a variable, either because the variable is not in the scope of that quantifier (cf. All(x) in (i)a), or because there is another quantifier already binding the variable (cf. All(x) in (i)b).
(i) a All(x) [ P(j) ] & Q(x)
b All(x) [ P(j) & ThereIs(x) [ Q(x) ]]
Links
References
- Partee, B.H., A. ter Meulen, and R. Wall 1990. Mathematical Methods in Linguistics, Kluwer:Dordrecht
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