In formal theories of truth, a truth predicate is a fundamental concept based on the sentences of a formal language as interpreted logically. That is, it formalizes the concept that is normally expressed by saying that a sentence, statement or idea "is true."

Languages which allow a truth predicate

Based on "Chomsky Definition", a language is assumed to be a

countable set In mathematics, a set is countable if either it is finite or it can be made in one to one correspondence with the set of natural numbers. Equivalently, a set is ''countable'' if there exists an injective function from it into the natural numbers ...

of sentences, each of finite length, and constructed out of a countable set of symbols. A theory of syntax is assumed to introduce symbols, and rules to construct well-formed sentences. A language is called fully interpreted if meanings are attached to its sentences so that they all are either true or false. A fully interpreted language ''L'' which does not have a truth predicate can be extended to a fully interpreted language ''Ľ'' that contains a truth predicate ''T'', i.e., the sentence ''A'' ↔ ''T''(⌈''A''⌉) is true for every sentence ''A'' of ''Ľ'', where ''T''(⌈''A''⌉) stands for "the sentence (denoted by) ''A'' is true". The main tools to prove this result are ordinary and transfinite induction, recursion methods, and

ZF set theory ZF, Z-F, or Zf may refer to: Businesses and organizations * ZF Friedrichshafen, a German supplier of automobile transmissions * Zionist Federation of Great Britain and Ireland, an organization established to campaign for a permanent homeland for t ...

(cf. and S. Heikkilä, A consistent theory of truth for languages which conform to classical logic. Nonlinear Studies (to appear)).

References

{{Ling-stub Mathematical logic Theories of truth

Languages which allow a truth predicate

See also

References