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L ogic In categorical propositions of standard form, “some” is a quantifier for particular propositions and “all” or “no” are quantifiers for universal propositions. Modern predicate logic calls “some” the existential quantifier and “all” the universal quantifier. The existential quantifier is symbolized as (∀x), which reads “there is at least one x that…” or “for some x …”. The universal quantifier is symbolized as (x) or (∀x), which reads “for any x …” or “for all x …”. Quantifiers are employed in sentences with variables (x, y, …), predicates (F, G, …), relations (R, …), the identity sign (=), and the logical constants (and, or, not, if-then …). (∃x)(∃y) (if Fx and Gy, then x = y) reads “For some x and for some y, if x is F and y is G, then x is identical with y.” The individual or multiple use of the universal quantifier “all” and the existential quantifier “there exists” to bind variables in sentences has been seen as the key to the development of a powerful and flexible system of modern predicate logic. Quantifiers can occur more than once in a statement , for example “All human beings have some ancestors.” The application of the quantifier, called quantification, turns an open sentence with unbound variables into a closed sentence in which the variables are bound with quantifiers. There is debate whether quantifiers can bind items other than individual ... log in or subscribe to read full text