In logic and mathematics, a logical value, also called a truth value, is a value indicating to what extent a proposition is true. Logic, from Classical Greek λόγος (logos), originally meaning the word, or what is spoken, (but coming to mean thought or reason) is most often said to be the study of criteria for the evaluation of arguments, although the exact definition of logic is a matter of controversy among philosophers. ... Euclid, detail from The School of Athens by Raphael. ... Proposition is a term used in logic to describe the content of assertions. ... La Vérité by the French painter Jules Joseph Lefebvre Common dictionary definitions of truth mention some form of accord with fact or reality. ...

In classical logic, the only possible truth values are true and false. However, other values are possible in other logics: fuzzy logic and other forms of multi-valued logic use more truth values than simply true and false. Classical logic identifies a class of formal logics that have been most intensively studied and most widely used. ... When someone sincerely agrees with an assertion, they might claim that it is the truth. ... FALSE is an esoteric programming language designed by Wouter van Oortmerssen in 1993, named after his favourite boolean value. ... Fuzzy logic is derived from fuzzy set theory dealing with reasoning that is approximate rather than precisely deduced from classical predicate logic. ... Multi-valued logics are logical calculi in which there are more than two possible truth values. ...

Algebraically, the set {true,false} forms a simple Boolean algebra. Other Boolean algebras may be used as sets of truth values in multi-valued logic, while intuitionistic logic generalises Boolean algebras to Heyting algebras. Wikibooks has more about Boolean logic, under the somewhat misleading title Boolean Algebra For a basic intro to sets, Boolean operations, Venn diagrams, truth tables, and Boolean applications, see Boolean logic. ... In mathematics, Heyting algebras are special partially ordered sets that constitute a generalization of Boolean algebras. ...

In topos theory, the subobject classifier of a topos takes the place of the set of truth values. Sheaves were introduced into mathematics in the 1940s and, a major theme since then has been to study a space by studying sheaves on that space. ... In category theory, a subobject classifier is a special object Ω of a category; intuitively, the subobjects of an object X correspond to the morphisms from X to Ω. Introductory example As an example, the set Ω = {0,1} is a subobject classifier in the category of sets and functions...

See also

• Logical connective
• Slingshot argument

In formal logic, logical connectives, also known as logical connectors and sometimes logical constants, serve to connect statements into more complicated compound statements. ... In philosophical logic, a slingshot argument is an argument that purports to show that all true sentences stand for the same thing (e. ...

External links

• Article on logical constants at the Stanford Encyclopedia of Philosophy

• Weblog entry "How many is two?" by Andrej Bauer discussing the relationship between truth values in intuitionistic logic and topos theory on the one hand and classical logic on the other.