Relations in Mathematical Philosophy

Abstract

According to Russell, “the importance of relations” is “a matter which concerns philosophy and mathematics in equal measure”.¹ His book on Leibniz “had emphasised the importance of relational facts and propositions as opposed to facts consisting of substance-and-attribute and propositions consisting of subject-and predicate.” Russell found that “the prejudice against relations had had bad consequences in mathematics as well as in philosophy.” In mathematical logic the tendency was to emphasise classes, with relations at best being treated as classes of couples. For Russell it was a disaster for mathematical logic that technical considerations had been allowed to obscure the philosophical importance of relations. “What is important in the logic of relations is what is different from the logic of classes. . . . ” Just what the important philosophical principles are that derive from the logic of relations will unfold as this chapter proceeds.