From 1914 on Russell's epistemology was dominated by the attempt to show how we come by our knowledge of the external world. As he gradually became aware of the inadequacies of the "pure empiricist" approach, Russell realized that his program was viable only insofar as certain postulates of inference were allowed. In this paper I trace the development of the structural postulates from Analysis of Matter to Human Knowledge. The basic continuity of Russell's thought is established. Certain confusions implicit in (...) the various formulations of the postulates are brought to light. Finally, it is argued that the viability of Russell's program rests on a larger number of independent postulates than he thought were needed. Some implications of Russell's work for current work in the philosophy of science are briefly sketched. (shrink)