Quantifier

In the Philosophy of Logic, Quantifier expressions are marks of generality. They come in many syntactic categories in English, but determiners like “all”, “each”, “some”, “many”, “most”, and “few” provide some of the most common examples of quantification. In English, they combine with singular or plural nouns, sometimes qualified by adjectives or relative clauses, to form explicitly restricted quantifier phrases such as “some apples”, “every material object”, or “most planets”. These quantifier phrases may in turn combine with predicates in order to form sentences such as “some apples are delicious”, “every material object is extended”, or “most planets are visible to the naked eye”. We may conceive of determiners like “every” and “some” as binary quantifiers of the form:

Q(A,B), which may operate on two predicates, A and B, in order to form a sentence.

Binary quantifiers of this sort played an important role in what is perhaps the first formal study of quantification developed by Aristotle in the Prior Analytics. The details of Aristotle’s syllogistic logic are given in the entry on Aristotle’s Logic.