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How did Alfred Tarski address the liar paradox?

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Marble bust of Aristotle with a beard and draped robe, showing detailed facial features and wavy hair, set against a dark background. — Truth Detail of a Roman copy (2nd century bce) of a Greek alabaster portrait bust of Aristotle (c. 325 bce); in the collection of the Museo Nazionale Romano, Rome.

Alfred Tarski addressed the liar paradox by establishing a strict distinction between an object language—the language being analyzed—and a metalanguage—the language used to describe the first.12

Tarski demonstrated that a language cannot consistently contain its own complete semantic theory, including a definition of its own truth predicate, without falling into paradox. To resolve this, he proposed that a definition of truth for a formal language must be constructed within a richer metalanguage.12

In this framework, truth is defined through "T-sentences," which specify the conditions under which a sentence is true without using semantic terms like "true" within the object language itself. For example, a T-sentence takes the form: "S" is true if and only if p, where S is a sentence in the object language and p is its translation in the metalanguage. By separating these levels of language, Tarski prevented the self-referential loops that generate the liar paradox, concluding that no language can consistently contain a complete semantic theory of its own sentences.312