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O kształtowaniu się intuicyjnej koncepcji zbioru Stanisława Leśniewskiego

Miszczyński R.

Kwartalnik Historii Nauki i Techniki

2013

R. 58, nr 3

99--119

The first vague definitions of a set (Cantor, Dedekind, Hausdorfi) described it as bringing certain objects together. However, in the set theory there appeared some objects which did not originate in this way, for example the empty set. The disadvantages of this theory were clearly revealed in Russell’s antinomy. According to Leśniewski, the con tradictions will disappear when the concept of a set is based on intuition. Therefore, the distributive concept was replaced with the collective one: the relation of the element to the set is based on the relation between the part and the whole. In the new theory, the empty set no longer exists - the non-intuitive distinction between an object and the set composed of this object, disappears. These features allow to prevent Russell’s antinomy.