Alfred Tarski (1901–1983) was a Polish logician and mathematician, most famous in philosophy for his semantics of logic and development of set theory. He is considered to be one of the most important logicians of all time.

Tarski developed a system by which a semantics from a metalanguage (such as English) can be applied to an object language of symbolic logic, allowing logicians to examine not only the syntactic relationship between logical expressions, but the semantics as well.

Tarski's model theory provides the ability for notions that are symbolized by logic and mathematics to themselves be derived from the object languages of logic. His method involves creating models for logical expressions, in which certain propositions or predicate symbols are considered to be true or false on a given model or interpretation.

From this, Tarski developed the notion of logical consequence as a relation between some premises and a conclusion, stating that the conclusion is the logical consequence of its premises if and only if every model of those premises (that is, every interpretation which makes those premises true) is also a model of the conclusion (one which makes the conclusion true).

Selected Works

• Introduction to Logic and to the Methodology of Deductive Sciences (1941)
• “The Semantical Concept of Truth and the Foundations of Semantics” (1944)
• A decision method for elementary algebra and geometry (1948)
• Cardinal Algebras (1949)