unfinished third edition than in the second.  So far, then, as the problem of the unification of the sciences is concerned, the old prejudices which divided the rationalist philosopher from the sensationalist scientific man seem to have been, in the main, dissipated.  We can see now that what used to be called Philosophy and what used to be called Science are both parts of one task, that they have a common method and presuppose a common body of principles.

So far it may be said with truth that Philosophy is becoming more faithful than Kant was himself to the leading ideas of ‘Criticism’, and again that it is reverting once more, as it reverted in the days of Galileo, to the positions of Plato.  I do not mean that the whole programme has been completely executed and that there is nothing for a successor of Frege or Russell to do.  It is instructive to observe that at the very end of the great work on arithmetic to which I have referred Frege found himself compelled by difficulties which had been overlooked until Russell called attention to them to add an appendix confessing that there was a single important flaw in his elaborate logical construction of the principles of arithmetic.  He had shown that if there are certain things called ‘integers’, defined as he had defined them, the whole of arithmetic follows.  But he had not shown that there is any object answering to his definition of an integer, and the logical researches of Russell had thrown some doubt on the point.  This proved that some restatement of the initial assumptions of the theory was needed.  Since the date of Frege’s appendix (1903), Mr. Russell and others have done something towards the necessary rectification, and the resulting ‘Theory of Types’ is pretty certainly one of the most important contributions ever made to logical doctrine, but it may still be reasonably doubted whether the ‘Theory of Types’, as expounded by Whitehead and Russell in their Principia Mathematica, is the last word required.  At any rate, it seems clear that it is a great step on the right road to the solution of a most difficult problem.

There still remains the greatest problem of all, the harmonization of Science and Life.  I cannot believe that this problem is an illegitimate one, or that we must sit down content to accept the severance of ‘fact’ and ‘value’ as final for our thought.  Even the unification of the sciences itself remains imperfect so long as we treat it as merely something which ‘happens to be the case’ that there are many things and many kinds of things in the universe and also a number of relations in which they ‘happen’ to stand.  It is significant that in his later writings Mr. Russell has been driven to abandon the concept of personal identity, which is so fundamental for practical life, and to assert that each of us is not one man but an infinite series of men of whom each only exists for a mathematical instant.  I am sure that such a theory requires the abandonment of the whole notion