### Topic Page: Tarski, Alfred (1902 - 1983)

**Tarski, Alfred (1901–83)**from

*Blackwell Companions to Philosophy: A Companion to Metaphysics*

Mathematician, logician, and philosopher of logic, born in Warsaw, Poland and educated there in mathematics. He studied logic with Leśniewski, Jan Lukasiewicz (1878–1956) and Tadeusz Kotarbinski (1886–1981), all of whom had studied philosophy under Kazimierz Twardowski (1866–1938), one of several prominent philosophers taught by Brentano in Vienna. Tarski's epistemo-logical and metaphysical orientation is similar to that of the materialistic empiricism, known as reism or pansomatism, which was articulated by his teacher Kotarbinski (1955) in an article translated into English by Tarski. Tarski's methodological orientation, best expressed in Tarski (1937), encompassed a combination of modern symbolic logic with a development of the traditional axiomatic (or deductive) method as treated by Pascal in the posthumous 172 8 article “L'ésprit géométrique”. In conversations Tarski revealed himself to be an atheistic humanist, strongly allied with the values implicit in modern natural science and strongly opposed to those associated with superstition and religion, which for him included not only Platonism as expounded by Frege and Gödel but also communism as practiced in the former Soviet Union. His opposition to Platonism was balanced by an equally intense opposition to the positivistic philosophy associated with the Vienna Circle (see logical positivism), the for-malistic philosophy associated with the Hilbert school, and the language-oriented philosophy associated with Wittgenstein.

Tarski's most widely recognized contribution to philosophy is his analysis of the concept of truth in syntactically precise, fully interpreted languages and his articulation of the correspondence theory of truth (see theories of truth). His longest, most comprehensive, and most widely read article on truth is the 1956 English translation “The concept of truth in formalized languages” by J.H. Woodger of the 1935 German translation by L. Blaustein of the original Polish monograph (1933). For bibliographic details, see Givant (1986). This English article, widely referred to as “The Wahrheit-sbegriff” by logicians and philosophers, is a triumph of common sense, technical virtuosity and penetrating mathematical and philosophical analysis. One of its virtues as a philosophic classic is the boldness of its presuppositions; it is valued as much for the questions that it leaves open as for those that it claims to settle. Its assumption that sentences, not propositions, are properly said to be true or false, while highly controversial at the time, has become a cornerstone of the philosophies of current writers such as Quine (see proposition, state of affairs). By clearly exemplifying the traditional philosophical and mathematical distinction between the meaning of an adjectival (or qualitative) term such as “true” and the tests (or criteria) of its applicability in individual cases, this article has become a hallmark of opposition to positivistic and idealistic philosophers (see idealism) including intuitionism (see intuitionism in logic and mathematics).

Tarski's second most widely recognized philosophical achievement is his analysis and explication of the concept of (logical) implication (or consequence) in terms of which (logical) validity of arguments is defined. An argument is valid if, and only if, its conclusion is implied by (or is a consequence of) its premise-set. Here too he exemplifies the traditional meaning-criterion distinction by emphasizing the difference between the semantic relation of logical implication and the syntactic relation of formal deducibility taken as a positive criterion for implication (Tarski, 1936). The above two analyses have been credited with the founding of model theory (or mathematical semantics), one of the main branches of modern mathematical logic.

Tarski also proposed an analysis and explication of the concept of logical notion (which is required in order to define the concept of logical constant). Evaluations of this relatively recent, posthumously published work (Tarski, 1987) are in progress but it is unlikely that it will be as widely accepted or as influential as his work on truth and on consequence. These three analyses, beside making fundamental contributions to philosophical analysis, establish a distinctive Tarskian philosophic style which itself has been highly influential. Tarski made other contributions to philosophy that may come to be regarded as of equal importance (see Corcoran, 1983, 1991; Mostowski, 1967).

Notwithstanding Tarski's lasting contributions to philosophy and the pride he took in having the philosophers Pascal, Brentano and Kotarbinski in his intellectual ancestry, he never regarded himself as a philosopher. He identified himself as a mathematician and he looked to the world of mathematicians for recognition. It is true however that he relished the acceptance of his work by mathematically informed philosophers such as Carnap, Popper, quine, and russell. Even though Tarski had deep philosophic commitments and extensive philosophic learning, he did not read current philosophical literature and he was wary, sometimes contemptuous, of professional philosophers, whose intellectual abilities and virtues he ranked far below those of mathematicians, scientists and poets. He did on occasion have discussion with philosophers but it was as if his portal had been inscribed with the supposedly Platonic injunction: let no one ignorant of mathematics enter.

As a mathematician Tarski worked in several areas other than logic, most notably abstract algebra, set theory, geometry and real analysis. In each of these areas he achieved results that will assure him a place in the history of mathematics. His contributions to philosophy, extensive as they are, constitute a small fraction of his research. He founded the interdisciplinary Group in Logic and Methodology of Sciences at the University of California at Berkeley where he was a professor of mathematics until his retirement in 1968. He continued to work productively until his death in 1983 in Berkeley, California.

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