Abstract
Poincare is well known for arguing against logicism that mathematical induction is known by intuition and that attempts to reduce it to pure logic were viciously circular. Much less attention has been given to another of his objections to logicism, namely that intuition is required for the application of arithmetic.
In this talk, I examine what Poincare says on this subject. I will discuss what light it might shed on his notion of intuition and how it relates to his view that applications of geometry are based on convention rather than intuition.