Alfred Tarski

Works

• 1933The Concept of Truth in Formalized Languages

  A definition of truth for formal languages, given in a richer metalanguage – and the proof that no such language can define its own truth.

• 1944The Semantic Conception of Truth

  An accessible statement of his theory: “snow is white” is true if and only if snow is white – a precise form of Aristotle’s classical conception.

Position

Tarski’s monograph on truth (Polish 1933, German 1935) asked how the word “true” can be used without falling into paradoxes such as the liar. His answer distinguishes an object language from the metalanguage in which we talk about it. A definition of truth for the object language is adequate if it entails, for every sentence, an instance of “Convention T”: “snow is white” is true if and only if snow is white. For formal languages he gave such a definition, built up through the notion of satisfaction, and proved that no sufficiently rich language can define its own truth predicate. The Semantic Conception of Truth (1944) presented this as a precise form of Aristotle’s classical conception. In 1936 he defined logical consequence: a conclusion follows if every interpretation that makes the premises true makes it true. These definitions founded model theory, which he developed at Berkeley, along with decision procedures for elementary algebra and geometry. Carnap’s turn from syntax to semantics followed his meetings with Tarski, Popper credited him with rehabilitating the correspondence theory of truth, and Davidson built a theory of meaning on Convention T. Kripke’s theory of truth of 1975 was designed to avoid Tarski’s hierarchy of languages.

Life & context

Alfred Tarski was born Alfred Tajtelbaum in Warsaw in 1901 into an assimilated Jewish family. In 1923 he and his brother changed their name to Tarski, and he became a Roman Catholic. He took his doctorate under Stanisław Leśniewski in 1924, the year of the Banach–Tarski paradox, and belonged to the Lwów–Warsaw school of logic. He never obtained a chair in Poland – antisemitism is thought to have played a part – and taught for years at a Warsaw secondary school alongside his university lectures. In August 1939 he travelled to a congress for the Unity of Science at Harvard and was cut off by the outbreak of war. His wife and children survived in Poland and joined him in 1946; his parents and his brother did not survive the war. From 1942 he taught at Berkeley, where he built a leading centre of logic. He died in Berkeley in 1983.

Further main works

• On the Concept of Logical Consequence (1936)
• Introduction to Logic and to the Methodology of Deductive Sciences (1936)
• A Decision Method for Elementary Algebra and Geometry (1948)
• Logic, Semantics, Metamathematics (collected papers, 1956)