In “The Semantic Conception of Truth and the Foundations of Semantics” Tarski seeks a clear and formalized
definition of
‘true’. He points out that the notion of truth in ordinary language is ambiguous and its
definition must be more clearly explicated if its true meaning is to be understood. The notion of truth has to do with a sentence’s correspondence to reality. However, this notion is vague. He goes on to say that a definition of truth must accord with equivalences of the following sort: The sentence ‘Snow is White’ is true if and only if, snow is white. He generalizes this form, as X is true, if and only if, p, where p is the sentence and X is the name of the sentence.
He then says that statements of this form are known to generate paradoxes but this is only because these paradoxes are stated in semantically closed languages. He uses the example of, “The sentence printed on this paper is not true” This sentence generates the following paradox: ‘S’ is true if, and only if, ‘S’ is not true. He concludes that this paradox is generated because it is stated in a semantically closed language. A semantically closed language not only includes
sentences but also names of sentences. Natural languages are semantically closed and if we are to avoid paradoxes we must divide them into an object- languages and a meta-language. Generally when we speak we refer to things in the world. The subjects and objects of our sentences are not sentences themselves. However, Tarski maintains that on the occasions that one uses the names of sentences as the object or subject together with words such as 'true' or 'false' we are using a meta-language. However, meta-languages and object languages are relative. There could possibly be a meta-langugae of the meta-language in which case the original meta language would become an object language. Basically the paradoxes are generated when one confusedly uses the meta-language and object language as if they were the same language.
The definition of truth can be defined in a meta-language. Tarski begins by defining satisfaction in order to use this in his definition of truth. To define satisfaction in a formal language one takes all simple sentential functions and indicates which objects will satisfy them. If this is given one can derive which objects satisfy the compound sentential functions. He points out that sentences are just sentential functions with no free variables. He finally comes to the conclusion that a sentence is true if it is satisfied by all variables and false otherwise.