The Doctrine of Relations in Bertrand Russell's Principles of Mathematics

Abstract

The question of the nature of relations is of great importance in the early writings of Bertrand Russell, since his disagreements with British Idealism center around relations, and his philosophy of mathematics depends crucially on relations. Yet there is no extended and systematic discussion of relations in early Russell. After examining Russell's definition of a relation, the author systematically and critically examines Russell's views in Principles of Mathematics on the following issues: whether a relation exists apart from its terms; the intensional character of relations; difficulties in reflexive relations; and whether simple relations can relate more than two relata.