Notes on types, set and logicism, 1930-1950

Abstract

The present paper is a contribution to the history of logic and its philosophy toward the mid-20th century. It examines the interplay between logic, type theory and set theory during the 1930s and 40s before the reign of first-order logic, and the closely connected issue of the fate of logicism. After a brief presentation of the emergence of logicism, set theory, and type theory (with particular attention to Carnap and Tarski), Quine’s work is our central concern, since he was seemingly the most outstanding logicist around 1940, though he would shortly abandon that view point and promote first order logic as all of logic. Quine’s class-theoretic systems NF and ML, and his farewell to logicism, are examined. The last section attempts to summarize de motives why set theory was preferred to order systems, and first order logic won its position as the paradigm logic system after the great War.