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