Definitions And Contradictions. Russell, Poincaré, And Lesniewski

This paper is composed of two independent parts. The first is concerned with Russell’s early philosophy of mathematics and his quarrel with Poincaré about the nature of their opposition. I argue that the main divergence between the two philosophers was about the nature of definitions. In the second part, I briefly present Lesniewski’s Ontology and suggest that Lesniewski’s original treatment of definitions in the foundations of mathematics is the natural solution to the problem that divided Russell and Poincaré.