Foundations of the General Theory of Sets I

Introduction

Leśniewski published the booklet in Moscow in 1916 as the first part of a planned larger work. It answers Russell’s paradox not with a theory of types but with a different understanding of classes: a class in the collective sense is a concrete whole whose parts are its elements and their parts, as a heap is made of stones. In such a theory the class of all classes that are not elements of themselves cannot be formed in Russell’s sense, and the paradox disappears. He later formalised it on the basis of his ontology. Through Tarski, who used it for a geometry of solids (1929), and Henry Leonard and Nelson Goodman’s “calculus of individuals” (1940), the theory of parts and wholes became an established branch of formal logic and ontology.

Connections

Responds to

• Principia Mathematica1910 · Bertrand Russell