European review

TitleStanislaw Leśniewski: rethinking the philosophy of mathematics
Publication TypeJournal Article
Year of Publication2014
AuthorsUrbaniak, R
JournalEuropean review

Near the end of the XIXth century part of mathematical research was focused on unification: the goal was to find ˝one sort of thing˝ that mathematics is (or could be taken to be) about. Quite quickly sets became the main candidate for this position. While the enterpize hit a rough patch with Frege's failure and set-theoretic paradoxes, by the 1920s mathematicians (roughly speaking) settled on a promising axiomatization of set theory and considered it foundational. Quite parallel to this development was the work of Stanislaw Le{\textbackslash}'sniewski (1886-1939), a Polish logician who did not accept the existence of abstract (aspatial, atemporal and acausal) objects such as sets. Lesniewski attempted to find a nominalistically acceptable replacement for set theory in the foundations of mathematics. His candidate was Mereology - a theory which instead of sets and elements spoke of wholes and parts. The goal of this paper will be to present Mereology in this context, to evaluate the feasibility of Lesniewski's project and to briefly comment on its contemporary relevance.

Citation Key4443772