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Concept
Semantic theory of truth
Summary
A semantic theory of truth is a theory of truth in the philosophy of language which holds that truth is a property of sentences.
The semantic conception of truth, which is related in different ways to both the correspondence and deflationary conceptions, is due to work by Polish logician Alfred Tarski. Tarski, in "On the Concept of Truth in Formal Languages" (1935), attempted to formulate a new theory of truth in order to resolve the liar paradox. In the course of this he made several metamathematical discoveries, most notably Tarski's undefinability theorem using the same formal technique Kurt Gödel used in his incompleteness theorems. Roughly, this states that a truth-predicate satisfying Convention T for the sentences of a given language cannot be defined within that language.
To formulate linguistic theories without semantic paradoxes such as the liar paradox, it is generally necessary to distinguish the language that one is talking about (the object language) from the language that one is using to do the talking (the metalanguage). In the following, quoted text is use of the object language, while unquoted text is use of the metalanguage; a quoted sentence (such as "P") is always the metalanguage's name for a sentence, such that this name is simply the sentence P rendered in the object language. In this way, the metalanguage can be used to talk about the object language; Tarski's theory of truth (Alfred Tarski 1935) demanded that the object language be contained in the metalanguage.
Tarski's material adequacy condition, also known as Convention T, holds that any viable theory of truth must entail, for every sentence "P", a sentence of the following form (known as "form (T)"):
(1) "P" is true if, and only if, P.
For example,
(2) 'snow is white' is true if and only if snow is white.
These sentences (1 and 2, etc.) have come to be called the "T-sentences". The reason they look trivial is that the object language and the metalanguage are both English; here is an example where the object language is German and the metalanguage is English:
(3) 'Schnee ist weiß' is true if and only if snow is white.
Official source
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