CANTOR AND THE BURALI-FORTI PARADOX Introduction

In studying the early history of mathematical logic and set theory one typically reads that Georg Cantor discovered the so-called Burali-Forti (BF) paradox sometime in 1895, and that he offered his solution to it in his famous 1899 letter to Dedekind.! This account, however, leaves it something of a mystery why Cantor never discussed the paradox in his writings. Far from regarding the foundations of set theory to be shaken, he showed no apparent concern over the paradox and its implications whatever. Against this account, I will argue here that in fact Cantor never saw any paradox at all, but that his conception of set at that time, and already as far back as 1883, was one in which the paradoxes cannot arise. 2 The main sources I will draw on are Cantor's great 1883 work Grundlagen einer .al1gemeinen Mannigfaltigkeitslehre3 and his "Mitteilungen zur Lehre vom Transfiniten. "4