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."
YouTube Encyclopedic
-
1/3Views:10 40311 1363 895
-
Alfred Tarski's Convention T (Theories of Truth)
-
The Indefinability of Truth (Tarski's Theorem)
-
Saul Kripke's Theory of Truth (Semantic Type-Free)
Transcription
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
| General | |||||||||
|---|---|---|---|---|---|---|---|---|---|
| Theorems (list) & paradoxes | |||||||||
| Logics |
| ||||||||
| Set theory |
| ||||||||
| Formal systems (list), language & syntax |
| ||||||||
| Proof theory | |||||||||
| Model theory | |||||||||
| Computability theory | |||||||||
| Related | |||||||||
 | This logic-related article is a stub. You can help Wikipedia by expanding it. |
 | This linguistics article is a stub. You can help Wikipedia by expanding it. |
This page was last edited on 2 June 2023, at 03:03