In his 1933 article on « The Concept of Truth in formalized Languages », Alfred Tarski set out two fundamental logical results: on the one hand, a definition of what he calls the semantical conception of truth and, on the other hand, the demonstration of the indefinability of all truth predicate for a language in this same language. This last result which is one of the limitations of the formal systems has recently been called into question by Jaakko Hintikka in his provocative book: The Principles of Mathematics Revisited.
In this fifteenth volume of the Cahiers du Centre de logique, Sébastien Richard introduces those results from the point of view of the philosophical concepts and of the logical machinery used by Tarski in his definition and his theorem about truth.

This presentation also describes the numerous critics that have been raised against the semantical conception of truth. Finally, the author tries to show how Jaakko Hintikka, in developing an original semantic theory based on semantic games and integrating a notion of quantificational independence in logic, claims to go beyond Tarski’s negative result and defines the truth for a language in this same language.

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