Metamathematics, the foundations of mathematics and the semantic conception of truth

pp. 162-184

in: Jan Woleński, Logic and philosophy in the Lvov—Warsaw school, Berlin, Springer, 1989

Abstract

The first serious work on metamathematics in Poland was written outside the Warsaw School, although within the Lvov—Warsaw School. It was Ajdukiewicz's work (1921) on the methodology of the deductive sciences. He analysed three problems: the concept of proof in the logical sense of the term, the consistency of axioms, and the concept of existence in the deductive sciences. In his book Ajdukiewicz basically reported on Hilbert's views, but two of his results seem original: the definition of logical consequence (a sentence B follows logically from a sentence A if and only if the implication A → B is a logical theorem) and the relativization of the concept of existence to a given formal system. This last idea suggested the relativization of other metalogical and metamathematical concepts to fixed formal systems.