Consistency of Leśniewski’s Mereology

Abstract

According to Sobociński’s recollection, the consistency of Mereology was proved by Leśniewski by means of an appropriate interpretation within the framework of the theory of real numbers. His proof was never published, but in a recent paper R. E. Clay has succeeded in reconstructing a version of it.¹ Clay’s result amounts to showing that if Leśniewski’s Ontology expanded by the addition of the axioms for the real numbers is consistent then Mereology is consistent. Without casting any doubts on the validity of the proof one can hardly fail to note that here we have a case where the consistency of a conceptually simple theory is made to depend on the consistency of a theory which from the point of view of intuition is far from being obvious. What we would like to be in a position to do is to prove the consistency of Mereology relative to a theory which is more obvious than Mereology, or, preferably, relative to a theory which is, in fact, a much weaker subsystem of Mereology. It is with this methodological principle in mind that I propose to outline, in what follows, a new proof of the consistency of the theory under consideration.