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Leśniewski, Stanisław and Polish Mereology

Jan Woleński

Pages 287 - 293

Due to Stanisław Leśniewski and his influence, mereology became one of the main specialties of the Polish School of Logic. For Leśniewski mereology was the third and last part of the system of foundations of mathematics, a kind of grand logic, next to protothetic (extended propositional calculus) and ontology (the calculus of names, in particular, the theory of the copula ‘is’). However, the historical order of the origin of particular parts of Leśniewski’s system was just the reverse. He first constructed mereology in 1914 – 1916 and then supplemented it by ontology and protothetic in the early 1920s (see Luschei 1962, Rickey 1977, Miéville 1984, Woleński 1989, Chapter VII and Gessler 2005 for historical and other details). Leśniewski’s mereology was motivated by the Russell paradox of the set of all sets which are not members of themselves. He learned about this antinomy from a book by Jan Łukasiewicz on the principle of contradiction in Aristotle and decided to look for a solution. Leśniewski came to the conclusion that the concept of set used by Russell and other mathematicians should be replaced by the mereological notion of class (in the following I will use the term ‘set’ in the context of the standard set-theory, but the name ‘class’ in the context of mereology in most cases). Although Russell’s paradox determined the main motivation, one should also remember that Leśniewski studied with Twardowski (who was his PhD supervisor) and knew Husserl very well (he planned to translate Logische Untersuchungen into Polish, but later abandoned this project). Since recent historical investigations discovered mereological elements in the Brentano school (including early phenomenology), it is plausible to speculate that Leśniewski’s mereology was also influenced by this radition, at least indirectly. Unfortunately, the connection cannot be documented—although Leśniewski noted many times his links with Austrian philosophy and phenomenology, his remarks do not concern mereology.

1Department of Social Sciences, University of Information, Technology and Management at Rzeszow

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