Alfred Tarski

by

Mario Gómez-Torrente

• LAST REVIEWED: 22 August 2023
• LAST MODIFIED: 22 August 2023
• DOI: 10.1093/obo/9780195396577-0186

Introduction

Alfred Tarski (b. 1901–d. 1983) was a Polish–American mathematician, widely regarded as one of the greatest logicians of all time. Tarski’s work has been influential in philosophy, especially through his theories of three concepts of traditional philosophical and, specifically, logical interest: the concepts of truth, of logical consequence, and of a logical constant. These theories amount to methods for the mathematical characterization of those concepts relative to particular formalized languages. However, he wrote very little on strictly philosophical matters, including issues concerning the philosophical (as opposed to mathematical) aspects of those three theories. The literature bearing on Tarski’s work on philosophical issues, therefore, consists for the most part of discussions of the abstract nature of those theories, and it does not make special efforts to elucidate Tarski’s actual philosophical views on them. Philosophical discussions of Tarski’s theory of truth have considered issues such as whether the theory is compatible with physicalism, whether it is in some sense an analysis of the concept of truth, whether it can be the basis for a theory of linguistic meaning, whether it provides an adequate solution to the liar paradox, and others. Philosophical discussions of his theory of logical consequence have dealt with issues such as whether it is in some sense an analysis of the concept and whether it is extensionally adequate. Philosophical discussions of the theory of logical constants have dealt especially with the question of whether it provides a plausible view of the extent and nature of logic. Nevertheless, interest in Tarski’s actual philosophical views on his theories has steadily grown over the years, and there is currently a considerable literature on these and other historical and exegetical aspects of Tarski’s work, including especially issues concerning truth and logical consequence. There is now also a rich literature that explores Tarski’s philosophical background and his general philosophical views. Finally, Tarski’s more strictly mathematical work, though largely unfamiliar to philosophers, is of enormous importance for mathematical logicians, and it is also of great interest to philosophically oriented historians of logic. This mathematical work includes work spanning set theory, model theory, algebra and geometry, and features results and developments such as the Banach-Tarski paradox, the theorem on the indefinability of truth, the completeness and decidability of elementary algebra and geometry, and the creation and mathematical study of the notions of cardinal, ordinal, relation, and cylindric algebras.

Texts by Tarski

Tarski 1983a is a collection of translations of papers by Tarski from the 1920s and 1930s, including Tarski 1983b, Tarski 1983c, and other papers on semantics. Tarski presented his mathematical theory of truth in Tarski 1983b, and he gave an exposition and defense of it, aimed at the philosophical public, in Tarski 1944. Tarski 1983c and Tarski 2002 contain Tarski’s presentation of the theory of logical consequence. Tarski 1986a develops a characterization of the concept of a logical notion, used in Tarski and Givant 1987 in the characterization of the concept of a logical constant. Tarski 1994 is a logic manual where a number of Tarskian ideas on logic are presented in an accessible form. Tarski 1986b contains reprints of all of Tarski’s papers published until 1986.

• Tarski, A. “The Semantic Conception of Truth and the Foundations of Semantics.” Philosophy and Phenomenological Research 4 (1944): 341–376.

  DOI: 10.2307/2102968

  An exposition of Tarski’s theory of truth, written for philosophers. Tarski defends his theory against philosophical criticisms, arguing that it is metaphysically and epistemologically neutral.

• Tarski, Alfred. Logic, Semantics, Metamathematics. 2d ed. Indianapolis, IN: Hackett, 1983a.

  A widely used collection edited by John Corcoran, containing translations by J. H. Woodger of some of the most important papers by Tarski from the 1920s and 1930s, including translations of the German versions of his papers on truth and logical consequence.

• Tarski, Alfred. “The Concept of Truth in Formalized Languages.” In Logic, Semantics, Metamathematics. 2d ed. By A. Tarski. Edited by J. Corcoran, 152–278. Indianapolis, IN: Hackett, 1983b.

  Tarski’s classic monograph gives his method for constructing a defined predicate of truth for any classical formalized language. A translation of the 1935 German version, which contains an important postscript not included in the 1933 Polish original. (Original title of the 1935 German version: “Der Wahrheitsbegriff in den formalisierten Sprachen.” Original title of the 1933 Polish version: “Pojęcie prawdy w językach nauk dedukcyjnych”).

• Tarski, Alfred. “On the Concept of Logical Consequence.” In Logic, Semantics, Metamathematics. 2d ed. By Alfred Tarski. Edited by J. Corcoran, 409–420. Indianapolis, IN: Hackett, 1983c.

  Tarski’s presentation of his theory of logical consequence as universal truth-preservation over interpretations of the non-logical constants. A widely used translation of the 1936 German version. (Original title of the 1936 German version: “Über den Begriff der logischen Folgerung.”)

• Tarski, Alfred. “What Are Logical Notions?” History and Philosophy of Logic 7.2 (1986a): 143–154.

  DOI: 10.1080/01445348608837096

  A mathematical characterization of the concept of a logical notion as one invariant under permutations. The text of a 1966 lecture by Tarski, edited by John Corcoran.

• Tarski, Alfred. Collected Papers. 4 vols. Basel, Switzerland: Birkhäuser, 1986b.

  A collection of reprints of all of Tarski’s papers published until 1986, edited by Steven Givant and R. McKenzie.

• Tarski, Alfred, and Steven Givant. A Formalization of Set Theory without Variables. Providence, RI: American Mathematical Society, 1987.

  DOI: 10.1090/coll/041

  A mathematical study of algebraic formalizations of set theory, containing also Tarski’s theory of the concept of a logical constant as a symbol denoting a notion invariant under permutations in all universes, based on his proposal in Tarski 1986a.

• Tarski, Alfred. Introduction to Logic and to the Methodology of Deductive Science. New York: Oxford University Press, 1994.

  Tarski’s logic manual, where a number of Tarski’s ideas on logic are presented in an accessible way. These include (though not with these names) the notions of truth in an interpretation and of consequence as truth preservation over interpretations. The text evolved over the years from an original Polish version of 1936. This is the fourth edition, edited by Jan Tarski. (Original title of the 1936 Polish version: O logice matematycznej i metodzie dedukcyjnej. Original title of the 1937 German version: Einführung in die mathematische Logik und in die Methodologie der Mathematik.)

• Tarski, Alfred. “On the Concept of Following Logically.” History and Philosophy of Logic 23.3 (2002): 155–196.

  DOI: 10.1080/0144534021000036683

  A translation by Magda Stroińska and David Hitchcock of the 1936 Polish version of Tarski’s presentation of his theory of logical consequence. (Original title of the 1936 Polish version: “O pojęciu wynikania logicznego.”)