Definitions And Contradictions. Russell, Poincaré, And Lesniewski

Abstract

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 Le!niewski’s Ontology and
suggest that Le!niewski’s original treatment of definitions in the
foundations of mathematics is the natural solution to the problem that
divided Russell and Poincaré.