Alfred Tarski

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.