The extension of the concept abolished?

reflexions on a fregean dilemma

Christian Thiel

pp. 269-273

in: Jaakko Hintikka, Tadeusz Czarnecki, Tomasz Placek, Artur Rojszczak (eds), Philosophy and logic in search of the Polish tradition, Berlin, Springer, 2003

Abstract

Scores of expositions and technical analyses have been devoted to the materialization of the Zermelo-Russell antinomy in naive set theory as well as in Frege's system of Grundgesetze der Arithmetik.¹ The origins of the antinomy have been studied with great circumspection, and the impossibility of Frege's attempted "Way Out" has been demonstrated, with essential participation of Polish logicians.² Yet, there is no unanimity as to the ultimate cause of the deadlock up to now, and no full comprehension of Frege's wavering between some hope for a conclusive repair of his system and the relinquishment of all hope for a secure foothold of our talk about classes, extensions of concepts, or—in his own terminology—courses-of-values. Reflection on the dilemma Frege found himself facing is certainly not out of place.

Cited authors

Frege Gottlob