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.