On Leśniewski’s Elementary Ontology

Abstract

S. Leśniewski’s calculus of names, often referred to as ontology, originated in 1920. This system like his other systems, mereology and prosthetics, was constructed with the aim on the one hand of bringing logic closer to the intuitions of natural language and on the other of searching for foundations for mathematics. Leśniewski’s ontology, in spite of numerous intuitive and formal advantages and in spite of its considerable expressive potential, has been underrated and little known for a long time; although half a century has passed since the construction of the system no precise elaboration of it has yet appeared which takes account of its methodological aspect. This situation seems fundamentally to be due to the fact that Leśniewski published no paper presenting his system in more or less final form. The manuscripts that Leśniewski left and which covered the results of the years of his investigations into ontology were destroyed during world war II. Nor should one ignore the fact that most of the published papers, in which Leśniewski presented his system at the stage of formalisation, were written in a difficult and not easily intelligible style. Leśniewski’s complicated symbols, although abounding in interesting ideas, differ from the familiar logical and set-theoretic symbols and thus create an obstacle to the appreciation of his ideas. This explains the scarcity of extensive discussions of the ontology.