Mathematics First: Russell’s Methodological Response to Bradley

Abstract

Abstract In this article I examine the dispute between F. H. Bradley and Bertrand Russell concerning the reality of relations. I show that Bradley’s objections to Russell’s view, that there are such things as relations which serve to effect the unity of complex items, were rooted in a methodological approach which Russell did not share. On Bradley’s view, one must be able to offer reductive analyses of the items one postulates in order that commitment to those items be justified. I argue that Russell expressly rejected this methodological principle of Bradley’s, and instead adopted the view that one may justifiably postulate entities if doing so aids in the illumination of mathematical truths. I show that the postulation of relations does, on Russell’s view, serve to provide that illumination. Russell held that the truths of mathematics constitute fixed data, and that philosophical positions may be judged as successful according to the extent that they possess explanatory power with respect to this data. I argue that Bradley’s and Russell’s exchanges in print, as well as in private correspondence, reflect Russell’s awareness of a fundamental difference in methodological approach. I conclude that Russell elected not to answer Bradley’s objections on their own terms, but rather rejected the methodological assumptions from which those objections emerged.