The significance of Our Knowledge of the External World is that it proposed a new method for philosophizing. Although the method suggested was not strictly novel (it had been previously used by such mathematical logicians as George Boole, Giuseppe Peano, and Gottlob Frege), it was modified by Bertrand Russell and transferred from mathematical to philosophical subject matter. Russell called it the “logical-analytic” method or the method of “logical atomism.” Since the publication of these lectures, the method has been taken over and radically modified and broadened by a large school of philosophers who call themselves “analysts” and who constitute an important group in the modern philosophical world.
The analytic method, as Russell formulated it, is less ambitious than that of classical philosophy in that it does not claim to determine the nature of reality or the universe as a whole. What it does is both less speculative and less sweeping, but more scientific. It uses the techniques of modern logic and modern mathematics and employs such concepts as class, relation, and order for the purpose of clarifying and solving some of the perennial problems of philosophy that have not yet yielded to satisfactory solution. There are many such problems, but Russell here considers those concerned with the nature of the external world, with how the world of physics is related to the world of ordinary sense experience, and with what is meant by space, time, continuity, infinity, and causation. The book consists of illustrations of the application of the logical-analytic method to these problems for the purpose of showing its fruitfulness. Russell insists that his results are to be taken as tentative and incomplete, but he believes that if any modification in his method is found necessary, this will be discovered by the use of the very method that he is advocating.
The Faults of Traditional Logic
The philosophies of two typical representatives of the classical school—F. H. Bradley and Henri Bergson—are first examined in order to show the errors that these men made. Bradley found the world of everyday life to be full of contradictions, and he concluded that it must be a world of appearance only, not of reality. His error lay in his attempt to determine the character of the world by pure reasoning rather than by going to experience and examining what he found. Bergson believed that reality is characterized fundamentally by growth and change; he then concluded that logic, mathematics, and physics are too static to represent such a world and that a special method called “intuition” must be employed. His mistake was twofold: First, he supposed that because life is marked by change and evolution, the universe as a whole must be so described; he failed to realize that philosophy is general and does not draw conclusions on the basis of any of the special sciences. Second, his emphasis on life suggests that he believed philosophy to be concerned with problems of human destiny. However, such is not the case; philosophy is concerned with knowledge for its own sake, not with making people happier.
One reason why the logical-analytic method was not more widely employed earlier, according to Russell, is that it was new and only gradually replaced some of the earlier and erroneous conceptions of logic. Traditional (syllogistic) logic had been quite generally abandoned as inadequate. The inductive logic of Francis Bacon and John Stuart Mill had been shown to be unsatisfactory because it cannot really show why people believe in such uniformities as that the sun will rise every morning. Belief in universal causation cannot be a priori because it is very complicated when formulated precisely; nor can it be a postulate, for then it would be incapable of justifying any inference; nor can it be proved inductively without assuming the very principle that one is trying to prove. Russell claims that Georg Wilhelm Friedrich Hegel made the mistake of confusing logic with metaphysics, and...
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