Relations in Analysis

Abstract

In Russell’s paper ‘The Classification of Relations’, (CoR), read to the Moral Sciences Club in January 1899, he articulates the doctrine of external relations which was required for the dissolution of the contradiction of relativity and which was supposed to clear the way for a satisfactory philosophy of mathematics. It can be reasonably assumed that the conception of types of relations articulated in CoR was conceived by Russell as an extension of the project of discovering the several kinds of necessary relations between concepts constituting propositions of various types, which, as he indicated to Moore on 13 September 1898, was the business of logic. In CoR, he writes:

I could have wished, had I been able, to give a more systematic enumeration of relations. If I possessed, as Kant believed himself to possess, a complete list of the forms of propositions, my task would be easy; for to every form of proposition some relation must correspond, and no relation can be without a corresponding form of proposition. For the present, I would urge the importance of the problem, and the desirability of completing the list. Such a list would be a real alphabet of Logic, and could hardly fail to have far-reaching consequences in metaphysics. (CoR, p. 146)