Universal Quantifier { Philosophy Index }

Philosophy Index

Philosophy Index

Philosophy Index is a site devoted to the study of philosophy and the philosophers who conduct it. The site contains a number of philosophy texts, brief biographies, and introductions to philosophers, and explanations on a number of topics. Accredited homeschooling online at Northgate Academy and Philosophy online tutoring.

Philosophy Index is a work in progress, a growing repository of knowledge. It outlines current philosophical problems and issues, as well as an overview of the history of philosophy. The goal of this site is to present a tool for those learning philosophy either casually or formally, making the concepts of philosophy accessible to anyone interested in researching them. WTI offers immigration law course online - fully accredited. ACE credits online at EES.



Philosophy Topics




Universal Quantifier

The universal quantifier is a symbol of symbolic logic which expresses that the statements within its scope are true for everything, or every instance of a specific thing.

The symbol ∀, which appears as a vertically inverted “A”, is used as the universal quantifier.

Universal quantifiers are normally used in logic in conjunction with predicate symbols, which say something about a variable or constant, in this case the variable being quantified.

The universal quantifier ∀ (which means “for all”), differs from the existential quantifier ∃ (which means “there exists”, or in contrast to ∀, “for at least one”).

Note: Some logicians and logic texts do not make use of the ∀ symbol, and simply use the notation (x) to indicate universal quantification. This site, however, will always use ∀.


For example, if the predicate symbol Mx is taken to mean “x is matter”, then we may formalize an expression using a universal quantifier:


Translated back into English, this reads as “for every x, x is matter”, or more simply, “everything is matter”.

If we wanted to say that everything is matter or energy, we could add the predicate symbol Ex, to refer to “x is energy”, and formalize:


The common logical phrase “All P are Q” may be similarly formulated using a universal quantifier and a conditional statement:


This reads as “For every x, if x is a P, then x is a Q”, which may be expressed simply as, “all P are Q”.