Quantifier
Quantifier
Universal quantifier is the name given to the notation (x) prefixed to a logical formula A (containing the free varible x) to express that A holds for all values of x — usually, for all values of x within a certain range or domain of values, which either is implicit in the context, or is indicated by the notation through some convention. The same name is also given to variant or alternative notations employed for the same purpose. And of course the same name is given when the particular variable appearing is some other letter than x.
Similarly, existential quantifier is the name given to the notation (Ex) prefixed to a logical formula A (containing the free variable x) to express that A holds for some (i.e., at least one) value of x — usually, for some value of x within a certain range or domain. The E which forms part of the notation is often inverted, and various alternative notitions also occur.
It may also be allowed to prefix the quantifiers (x) and (Ex) to a formula (sentence) A not containing x as a free variable, (x)A and (Ex)A then having each the same meaning as A.
See logic, formal, 3. — A. C.
W. V. Quine, Elementary Logic, Boston and New York, 1941.