Lesniewski's logic aspects of his protothetic, ontology and mereology

Abstract

Stanislaw Lesniewski (1886-1939) was professor of Philosophy of Mathematics at the University of Warsaw from 1919 until his death. He played a leading role in the Warsaw school of logic and had a lasting influence on many of its members. Lesniewski constructed his first description of mereology in colloquial language and in the absence of a secure logical foundation. In order to effectively distinguish between the collective and distributive notions of class, further description of the distributive notion was necessary. He therefore formalized the distributive concepts in his theory of ontology. Henceforth "ontology" will be used specifically to refer to this theory of Lesniewski. Finally, the construction of protothetic (a system of propositional logic) provided a sound logical foundation of Lesniewski's ontology and mereology. Protothetic, together with his prescribed rules of procedure and his grammar of semantic categories, also facilitated the formalization of his systems in a logically rigorous manner. All of the researchers acknowledge that one of Lesniewski's most fundamental achievements was the development of his deductive systems (protothetic, ontology and mereology).