In logic, a truth value, or truth-value, is a value indicating to what extent a statement 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 arguments, although the exact definition of logic is a matter of controversy amongst philosophers (see below). ... // Truth in everyday life In everyday life, people distinguish between truth and falsehood as a matter of survival. ...

In classical logic, the only possible truth values are true and false. However, other values are possible in other logics. A simple intuitionistic logic has truth values of true, false, and unknown; fuzzy logic and other forms of multi-valued logic also 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. ... Logic (from ancient Greek λόγος (logos), meaning reason) is the study of arguments. ... Intuitionistic logic, or constructivist logic, is the logic used in mathematical intuitionism and other forms of mathematical constructivism. ... This article is about the Boolean logic extension. ... 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. This article may be too technical for most readers to understand. ... 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...

References

• 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.

The Stanford Encyclopedia of Philosophy (hereafter SEP) is a free online encyclopedia of philosophy run and maintained by Stanford University. ...

See also

• Logical connective