The early Russell's view of the universe as fully describable

Abstract

    A standard interpretation of Bertrand Russell’s early work on logic revolves around the doctrine of the unrestricted variable—the idea that the genuine variable of logic must range over all the objects in the universe. Those who endorse this interpretation view the doctrine as ‘the centerpiece’ of The Principles of Mathematics. My aim in this essay is to examine some of the given and possible grounds for this view. I attempt to show that Russell in that book does not endorse the doctrine as it stands but the idea that there are no objects that cannot, in principle, be fully described—the idea that there is no logical bar to making simply true judgments about objects.