Sobocinski in his paper on Leśniewski's solution to Russell's paradox (1949b) argued that Leśniewski 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 Leśniewskian-style approach which uses so-called higher-order epsilon connectives is used and its weakness is indicated. (shrink)

The discovery of the importance of mereology follows and does not precede the formalisation of the theory. In particular, it was only after the construction of an axiomatic theory of the part-whole relation by the Polish logician Stanisław Leśniewski that any attempt was made to reinterpret some periods in the history of philosophy in the light of the theory of parts and wholes. Secondly, the push for formalisation - and the individuation of mereology as a specific theoretical field - arise (...) from several particular theories, first from biology and then from psychology. Mereological considerations were explicitly developed within the school of Brentano, by Brentano himself- starting from the problem of the unity of consciousness - and by his students, particularly Stumpl, Twardowski and the Gestaltists. The most complete result of this tradition is undoubtedly the third of Husserl's Logical Investigations, called "the single most important contribution to realist (Aristotelian) ontology in the modern period". (shrink)

Leśniewski is known for his pedantry and idiosyncratic notation, which make it extremely difficult to read and follow. As reading comes before understanding, this paper therefore attempts only one...

Leśniewski’s metalogic is often considered to be difficult to understand because it differs greatly from its standard formulation. In this paper I try to explain the reasons of these idiosyncrasies. I claim that they have mainly two sources. First of all there is Leśniewski’s conviction that a formal system should be conceived as a set of concrete marks that can always physically and syntactically be expanded by the addition of new theses. Secondly there is Leśniewski’s conviction that definitions should neither (...) be formulas belonging to the metalanguage, nor deduction rules, but formulas belonging to the object-language and expressed with the help of the biconditional functor. The realisation of the first point is linked to the second one in so far as the metalinguistic rule for the writing out of definitions has to be formulated in a way that makes it possible to build the formal system in agreement with Leśniewski’s conception. While explaining these points I give an overview of the main peculiarities of Leśniewski’s metalogic. (shrink)