Truth predicate

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 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 (cf.[1] and [2]).

See also

References
  1. S. Heikkilä, A mathematically derived theory of truth and its properties. Nonlinear Studies, 25, 1, 173--189, 2018
  2. S. Heikkilä, A consistent theory of truth for languages which conform to classical logic. Nonlinear Studies (to appear)


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