Antinomies of Set Theory

Abstract

The main aim of the study - written by Ajdukiewicz in 1913 in order to fulfil the requirements for a teaching certificate - is to provide a clear classification of set-theoretic paradoxes (Russell's, Burali-Forti's, Richard's, König's, and Berry's) and to present a uniform way of framing them, which combines ideas put forward by Grelling, Nelson, and Russell. In the last part of the study, Ajdukiewicz surveys available solutions (Poincaré, Richard, Russell, Frege, Bernstein, Jourdain) and comments on their validity. The edition is based on a typescript.