Lesniewski and Russell's Paradox: Some Problems

Sobocinski in his paper on Lesniewski's solution to Russell's paradox (1949b) argued that Lesniewski has succeeded in explaining it away. The general strategy of this alleged explanation is presented. The key element of this attempt is the distinction between the collective (mereological) and the distributive (set-theoretic) understanding of the set. The mereological part of the solution, although correct, is likely to fall short of providing foundations of mathematics. I argue that the remaining part of the solution which suggests a specific reading of the distributive interpretation is unacceptable. It follows from it that every individual is an element of every individual. Finally, another Lesniewskian-style approach which uses so-called higher-order epsilon connectives is used and its weakness is indicated.