Cantor and Continuity

Abstract

Georg Cantor (1845-1919) made seminal contributions to the mathematical conceptualization of continuity and continua that would become basic for the development of topology and measure theory in mathematics. His articulations in this direction were part and parcel of his development of set theory out of mathematical analysis and, on a larger canvas, very much part of the rigorization of mathematics in the latter 19th Century. We consider Cantor’s work on the formulation of the real numbers; uncountability and dimension; and continua as formulated in terms of perfect and connected sets as seen in this light. The thematic emphasis will be on the drive of mathematical necessity for the mathematization of metaphysicially based concepts.