On Leśniewski’s Ontology

Abstract

The study group which before the Second World War became known as the Warsaw School of Logic, was, throughout its only too short history, dominated by philosophers rather than by mathematicians.² Although Łukasiewicz and Leśniewski, the two founders of the School, held chairs in the Faculty of Mathematics and Natural Sciences in the University of Warsaw, neither of them had a science degree or a degree in mathematics. Both were Arts scholars or, to be more exact, both had graduated in philosophy under Twardowski in Lwów. They had, of course, studied mathematics but within the province of logic philosophy seems to have inspired their research. Łukasiewicz missed no opportunity to acknowledge his debt to Aristotle and Leśniewski meant his logic to be a true, though very general, description of reality, a kind of πρωτη ϕιλοσοϕία. It is significant that the Warsaw School of Logic influenced the development of philosophy in Poland to an extent to which it never succeeded in influencing the development of mathematics.

An earlier version of this paper was read and discussed at a logical colloquium held in Oxford in July 1956.

I am indebted to Mr. F. P. Chambers, Mr. W. C. Kneale, Professor Julius Kraft, Mr. E. C. Luschei, Professor A. N. Prior, Father Ivo Thomas, and Professor H. J. Woodger for their helpful suggestions which enabled me to improve the composition of my essay.

I should also like to express my gratitude to Dr. B. Sobociński for his kind permission to include some of his own unpublished results in the present paper, and for his generous comments, from which I have benefited a great deal.