Circularity or lacunae in Tarski's truth-schemata

Tarski avoids the liar paradox by relativizing truth and falsehood to particular languages and forbidding the predication to sentences in a language of truth or falsehood by any sentences belonging to the same language. The Tarski truth-schemata stratify an object-language and indefinitely ascending hierarchy of meta-languages in which the truth or falsehood of sentences in a language can only be asserted or denied in a higher-order meta-language. However, Tarski’s statement of the truth-schemata themselves involve general truth functions, and in particular the biconditional, defined in terms of truth conditions involving truth values standardly displayed in a truth table. Consistently with his semantic program, all such truth values should also be relativized to particular languages for Tarski. The objection thus points toward the more interesting problem of Tarski’s concept of the exact status of truth predications in a general logic of sentential connectives. Tarski’s three-part solution to the circularity objection which he anticipates is discussed and refuted in detail.
Keywords Circularity  Language, meta-language  Semantics  Tarski, Alfred  Truth
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DOI 10.1007/s10849-009-9103-z
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Hartry Field (1972). Tarski's Theory of Truth. Journal of Philosophy 64 (13):347-375.
A. Gupta (1993). A Critique of Deflationism. Philosophical Topics 21 (1):57-81.

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