semantic theory of truth (STT, hereafter) was developed by Alfred Tarski in the 1930s. The theory has two separate, although interconnected, aspects. First, it is a formal mathematical theory of truth as a central concept of model theory, one of the most important branches of mathematical logic. Second, it is also a philosophical doctrine which elaborates the notion of truth investigated by philosophers since antiquity. In this respect, STT is one of the most influential ideas in contemporary analytic philosophy. This article discusses both aspects.
The STT is designed to define truth without circularity and to satisfy certain minimal conditions that must be met by any adequate theory of truth.
STT as a formal construction is explicated via set theory and the concept of satisfaction. The prevailing philosophical interpretation of STT considers it to be a version of the correspondence theory of truth that goes back to Aristotle. This theory is presented here in its modern shape, that is, as associated with first-order logic. Tarski’s original account used the elementary theory of classes (a theory similar to the simple theory of types).
One of Tarski's most important result was to show that a theory of truth for set theory cannot be given within set theory itself, and that any truth definition for a formal language L must be given in a language which is essentially stronger than L.https://www.iep.utm.edu/s-truth/
