THEORY OF DEFINABILITY

TARSKI, ALFRED.

Z badan metodologicznych nad definjowalnoscia terminow [Polish, i.e.: Some Methodological Investigations on the Definability of Concepts]. Odbitka z XXXVII Rocznika przegladn filozoficznego.

Warszawa [Warsaw], 1934.

8vo. Orig. printed brown wrappers. Near mint condition. 25 pp (pp. 438-60 in Przeglad Filozoficzny, vol. 37).

Exceedingly scarce first edition, off-print with own pagination also, of this very important article by one of the four greatest logicians ever, the Polish-American Alfred Tarski.

Tarski's theory of definability, which he presents in this article, belongs to one of his main contributions to logic. Tarski here distinguishes between groups of concepts within the methodology of the deductive sciences: 1) concepts such as "axiom", "theorem", "rule of inference", "proof", and 2) "primitive (undefined) concept" (or "primitive term"), "definable concept", "rule of definition", "definition". "A far-reaching parallelism can be established between the concepts of the two groups: The primitive concepts correspond to the axioms, the defined concepts to the derivable sentences, the process and rules of definition to the process and rules of proof." (English translation of the article, 1956, p. 296).

Until this article was written, nothing on the subject of methodology of deductive sciences had primarily dealt with the concepts of the first group, but, as Tarski himself states, "in considering the second group of concepts many interesting and important problems force themselves upon us, some of which are quite analogous to those which arise in connection with the first group." (Introduction, English translation, 1956, p. 296). Two problems are discussed within this domain: the problem of the definability and the mutual independence of concepts, as well as the problem of the completeness of concepts of an arbitrary deductive theory.

Tarski (1901-1983) has contributed seminally to the fields of mathematics and logic in a number of ways, and together with Frege, Russell and Gödel, he now ranks as the most important contributor to the field of logic. He is thus considered one of the four greatest logicians of all times.

Order-nr.: 35551