Next, Tarski requires that the languages for which truth can be defined not be “semantically closed” (1944: 348). A semantically closed language is, essentially, a language that includes its own semantics. Hence, a semantically closed language includes names for all its constitutive sentences; if the sentence ‘Snow is white’ belongs to the language, so too does the name of that sentence, ‘‘Snow is white’’. Semantically closed languages also include their own truth predicate, whose extension includes sentences of that very language. As a result, semantically closed languages enable the formation of paradoxical liar sentences, which disqualifies them from Tarski’s method. Natural languages exhibit semantic closure by way of their “universality”: “A characteristic feature of colloquial language (in contrast to various scientific languages) is its universality. It would not be in harmony with the spirit of this language if in some other language a word occurred which could not be translated into it” (1956a: 164). Hence, in his positive account, Tarski must rely on the object language/metalanguage distinction, for the truth predicate to be defined cannot belong to the language to which it applies.
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