Quantifiers in Natural Languages: Some Logical Problems

Quantifiers are by common consent among the most important ingredients in the logical structure of both formalized and natural languages. As we all know, formalized quantifiers and their generalizations have been studied extensively by logicians. In contrast, relatively little close attention has been paid to the peculiarities of the logical behavior of quantifiers in natural languages, in spite of the fact that quantifiers have figured conspicuously in some of the most important recent methodological controversies in linguistics. It is the purpose of this paper to help to change this situation by surveying some of the non-trivial logical phenomena that we find in examining natural-language quantifiers. In doing so, I am largely restricting my attention to the natural-language counterparts of logicians' existential quantifier and universal quantifier, neglecting such 'nonstandard' quantifier words as 'many' and 'most'. I shall cover in the survey a number earlier observations of mine which have already been partly published, but I shall also try to concentrate on certain new insights which serve to extend and to consolidate the old results.