Why must Tarski’s definition of truth be stated in a richer metalanguage rather than in the object language?

Created from Britannica articles using AI. AI can make mistakes, so verify using Britannica articles.

Alfred Tarski’s definition of truth must be stated in a richer metalanguage rather than in the object language to avoid the liar paradox, which arises when a language contains its own semantic predicates.123

If a formal system were capable of defining its own concept of truth, it would be possible to construct a self-referential sentence within that system equivalent to "This sentence is not true". Such a sentence leads to a logical contradiction: if it is true, it must be false, and if it is false, it must be true. By separating the object language (the language being analyzed) from a richer metalanguage (the language used to describe the object language), Tarski ensured that the semantic term "true" is applied to the object language from a higher level, thereby preventing the system from generating these self-referential paradoxes.3124

This hierarchical approach allows for a consistent, compositional definition of truth based on the satisfaction of formulas, without the system collapsing into inconsistency.23