For a long time, the word ‘quantifier’ in linguistics and philosophy simply stood for the universal and existential quantifiers of standard predicate logic. In fact, this use is still prevalent in elementary textbooks. It seems fair to say that the dominance of predicate logic in these fields has obscured the fact that the quantifier expressions form a syntactic category, with characteristic interpretations, and with many more members than ∀ and ∃.
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Westerstaåhl, D. (2007). Quantifiers in Formal and Natural Languages. In: Gabbay, D., Guenthner, F. (eds) Handbook of Philosophical Logic. Handbook of Philosophical Logic, vol 14. Springer, Dordrecht. https://doi.org/10.1007/978-1-4020-6324-4_4
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