Generalized quantifier: Difference between revisions

Revision as of 03:13, 5 January 2021

Revision as of 04:05, 5 January 2021

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:: <math>\{X \,|\, \forall x (x \text{ is a boy} \to x \in X) \}</math>

This treatment of quantifiers has been essential in achieving a [[compositionality|compositional]] [[semantics]] for sentences containing quantifiers.<ref>{{cite [[Richardbook Montague|last1=Montague, |first1=Richard]]: |author-link1=Richard Montague |date=1974, '[|url=http://www.blackwellpublishing.com/content/BPL_Images/Content_store/Sample_chapter/9780631215417/Portner.pdf |chapter=The proper treatment of quantification in English]' |title=Philosophy, Language, and Artificial Intelligence |series=Studies in Cognitive Systems |volume=2

in|editor1-last=Kulas R|editor1-first=J. Montague,|editor2-last=Fetzer Formal Philosophy, ed|editor2-first=J.H. by|editor3-last=Rankin R|editor3-first=T.L. Thomason|pages=141-162 (New|publisher=Springer, Haven).Dordrecht |doi=10.1007/978-94-009-2727-8_7}}</ref><ref name=Barwise>{{cite journal |last1=Barwise, |first1=Jon and|author-link1=Jon RobinBarwise |last2=Cooper. |first2=Robin |date=1981. |title=Generalized quantifiers and natural language |url=https://link.springer.com/article/10.1007%2FBF00350139 ''|journal=Linguistics and Philosophy'' |issue=4: |pages=159-219 |doi=10.1007/BF00350139}}</ref>

==Type theory==

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#Every boy is a boy who sleeps.

It has been proposed that ''all'' determiners{{emdash}}in every natural language{{emdash}}are conservative.<ref ([[Jon name=Barwise|Barwise]] and Cooper 1981)./> The expression ''only'' is not conservative. The following two sentences are not equivalent. But it is, in fact not common to analyze ''only'' as a [[determiner (linguistics)|determiner]]. Rather, it is standardly treated as a [[focus-sensitive]] [[adverb]].

#Only boys sleep.

#Only boys are boys who sleep.