of Professor Peano.  Of other works dealing with the subject, the finest from the strictly philosophical point of view is probably that of Professor G. Frege on The Fundamental Laws of Arithmetic.  The general result of the whole development is that we are now at last definitely freed from the haunting fear that there is some hidden contradiction in the principles of the exact sciences which would vitiate all our knowledge of universal truths.  This removes the chief, if not the only ground for the view that all the truths of Science are only ‘partial’.  At the same time, the proof that pure mathematics is a strictly logical development and that all its conclusions are of the hypothetical form, ‘if a b c ..., then x’ definitely disproves the popular Kantian doctrine that sense-data are a necessary constituent of scientific knowledge.  And with this dogma falls the main ground for the denial that knowledge about the soul and God is attainable.  The recovery of a sounder philosophical method has, as Mr. Russell himself says, disposed of what was yesterday the accepted view that the function of Philosophy is to narrow down the range of possible interpretations of facts until only one is left.  Philosophy rather opens doors than shuts them.  It multiplies the number of logically possible sets of premisses from which consequences agreeing with empirical facts may be inferred.  Mr. Russell’s unreasoned anti-theism seems to me to make him curiously blind to an obvious application of this principle.  On the other side, the revived attention to the logical methods of the sciences is killing the crude sensationalism of the days which saw the first publication of Mach’s Science of Mechanics and Pearson’s Grammar of Science.  The claims of ‘induction’ to be a method of establishing truths may be fairly said to have been completely exposed.  It is clearer now than it was when Kant made the observation that each of the ‘sciences’ contains just so much science as it contains mathematics, and that the Critical Philosophy was fully justified in insisting that all science implies universal a priori postulates, though it went wrong in thinking that these postulates are laws of the working of the human mind or are ’put into’ things by the human mind.  How far Science has moved away from crude sensationalistic empiricism may be estimated by a comparison of the successive editions of the Grammar of Science.  It must always have been apparent to an attentive reader that the chapters of that fascinating book which deal directly with the leading principles of Physics and Biology are of very different quality from the earlier chapters which expound, with many self-contradictions and much wrath against metaphysicians and theologians whom the writer seems never to have tried to understand, the fantastic ’metaphysics of the telephone-exchange’.  But the difference of quality is more marked in the second edition than in the first, and in the (alas!)