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Why did Alfred Tarski require a richer metalanguage to define truth for a formal language?

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logic: universal affirmative — Modern logic Representations of the universal affirmative, “All A's are B's” in modern logic.

Alfred Tarski required a richer metalanguage to define truth for a formal object language primarily to avoid the liar paradox and similar self-referential contradictions.12

In the early 20th century, logicians sought to define truth for formal systems while avoiding paradoxes where a sentence asserts its own falsehood (e.g., "This sentence is false"). Tarski demonstrated that if a language were allowed to contain its own semantic terms—specifically the predicate "true"—it would inevitably lead to such paradoxes.12

To resolve this, Tarski established that a definition of truth must be constructed in a metalanguage that is distinct from and richer than the object language being analyzed. By using a metalanguage, Tarski could assign truth conditions to sentences in the object language without the object language needing to contain the term "true" itself. This approach ensures that the definition of truth remains consistent and free from the logical instability caused by unrestricted self-reference.12