Several recurrent strains of considerable importance can, however, be found in his writings. I believe it is possible to give a brief account of these aspects that will still present the relevant issues involved and even permit some evaluation of Russell's conclusions. In his later work we find that Russell is concerned with a problem that has been of great importance to philosophers, traditional and contemporary, the problem of the basis of our knowledge of the external world, both as it is known to common sense and to science. Russell's own solution of this problem underwent development as he reconsidered his philosophy; for he is an example of a philosopher who does not maintain that his answer is the final truth. In the study of this problem he found he could utilize certain methodological principles, especially the employment of 'logical constructions', which he had developed in his earlier, more specialized, investigations. In these earlier writings, Russell made important contributions to the foundations of mathematics and symbolic logic, of such importance that if he had done no further work those contributions would themselves have given him a secure place among contemporary philosophers.

Russell's early interest in mathematics and logic led to two of his important works, the Principles of Mathematics ( 1903) and Principia Mathematica (with Whitehead's collaboration, 1910-13). He was concerned with the nature of mathematical knowledge, with that abstract, formal quality that is referred to when mathematics is said to be 'necessary' or a priori. Russell was not convinced that the solutions found, e.g. by Hume or Kant, were valid; and he looked for some other explanation. Further, certain mathematical notions, especially those of the nature of number, infinity, and continuity, he felt had never adequately been explained, and attempted explanations had led to philosophic theories--such as Kant's account of space, which Russell felt he could not accept. The general philosophic view which Russell had at this time was a rather extreme realism, believing in the reality of many kinds of entities, especially physical objects, minds and universals. He used in his mathematical investigations also the work of preceding mathematicians such as Cantor, Dedekind and Weierstrass, and more important, the discoveries made in symbolic logic by the Italian school. He found that by the help of the new logic it was possible to answer the mathematical problems he was investigating. The question of the nature of mathematical knowledge was answered, or at least shown to be another problem, by finding that it was possible to 'identify' mathematics and logic. He showed that the propositions of pure mathematics could be derived from those of logic, and consequently the 'necessity' and 'truth' of mathematics were the same as those of logic. The further problem important for his later philosophy that he found he could answer was the nature of 'number'. Previously, on the basis of his realistic philosophy, it had been necessary to assume that numbers were real entities, but employing a procedure which he later came to call 'logical constructions' he was able to show that numbers do not refer to real entities 'numbers' but to classes of classes, entities already known. . .