Lesniewski's Analysis of Russell's Antinomy

Notre Dame Journal of Formal Logic 17 (1):19-34 (1976)
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Abstract

This article presents for the first time in english lesniewski's analysis of russell's antinomy as the analysis is given in lesniewski's 1914 paper "czy klasa klas, nie podporzadkowanych sobie, jest podporzadkowana sobie?" is the class of classes which are not subordinate to themselves subordinate to itself? it is shown how the concepts appearing in this paper, written in colloquial polish, were later incorporated and expressed as fundamental axioms and theorems of his theory of collective classes, mereology. in the 1914 paper he asserted: i call any object p an object subordinate to a class k if in some sense of the expression "a" the following two conditions hold: 1) k is a class (of objects) "a", 2) p is an "a". using this explication of "p is subordinate to a class k," he showed that both of the following statements are false: a) the class of classes which are not subordinate to themselves is subordinate to itself, b) the class of classes which are not subordinate to themselves is not subordinate to itself; thus showing that russell's antinomy cannot be generated since its initial assumptions are false

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