Abstract
This paper aims to elucidate what intuition is regarded to be in Jean Cavaillès’ philosophy of mathematics, by investigating his study of the emergence of Cantorian set theory. Cavaillès construes the emergence to consist in three steps: first, Georg Cantor invented point-set derivation to solve a problem for analysis; second, he also showed that point-set derivation can produce infinitely ascending derived sets without arriving at any continuum; third, by replacing point-set derivation with two generating principles and a restricting principle, Cantor established the existence of transfinite ordinal numbers. Cavaillès finds a central role of mathematical intuition in the emergence of set theory thus construed.
