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universal quantifier


Subject Philosophy

DOI: 10.1111/b.9781405106795.2004.x


Extract

L ogic Frege suggests that the universal categorical statements of traditional logic, that is, “All s are p,” and “All s are not p,” can be read respectively as “For all x, if x is s, then x is p,” and “For all x, if x is s, then x is not p.” The former can be symbolized as “(x) (sx → px), and the latter as “(x) (sx → ∼px).” (x) is called the “universal quantifier” and means that “For all x …” or “For every x …” The universal quantifier and the existential quantifier (There exists an x …) have been crucial in the development of modern predicate logic and the philosophy dependent upon it. The universal quantifier is also symbolized as “forall;(x).” “The universal quantifier (x) may be read ‘each object x is such that …’.” Quine, Theories and Things ... log in or subscribe to read full text

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