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DOI: 10.4324/9780415249126-X035-1
Version: v1,  Published online: 1998
Retrieved May 21, 2024, from

Article Summary

The quantifiers ‘some’ and ‘every’ were the object of the very first logical theory, Aristotelian syllogistic. An example of a syllogism is ‘Every Spartan is Greek, every Greek is European, therefore every Spartan is European’. In such inferences, no quantifier is governed by another one. Contrast this with ‘Everybody loves somebody’. Modern logic is often taken to have begun when Frege systematized for the first time the logic of quantifiers, including such dependent ones. In general, much of what has passed as logic over the centuries is in effect the study of quantifiers. This is especially clear with the area of logic variously known as quantification theory, lower predicate calculus or elementary logic. Some philosophers have even sought to limit the scope of logic to such a study of quantifiers. Yet the nature of quantifiers is a delicate matter which is captured incompletely by the logic initiated by Frege and Russell.

Citing this article:
Hintikka, Jaakko and Gabriel Sandu. Quantifiers, 1998, doi:10.4324/9780415249126-X035-1. Routledge Encyclopedia of Philosophy, Taylor and Francis,
Copyright © 1998-2024 Routledge.

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