It has given us ‘philosophers’ whose knowledge about the facts with which serious thinking has to deal has been hopelessly inaccurate; it has also given us ‘men of science’ who have been ‘ageometretes’ and have, by consequence, when forced to offer some account of first principles, taken refuge in the wildest and weirdest improvisation.  For really fruitful work we need the union in one person of the ‘man of science’ and the ‘philosopher’, or at least the most intimate co-operation between the two.  Our theories of first principles require to be constantly revised, purified, and quickened by contact with knowledge of detailed fact; and our representations of fact call for constant restatement in terms of a system of more and more thoroughly thought-out postulates or first principles.  This is perhaps why the department of human knowledge in which the last half-century has seen the most remarkable advances is just that in which unremitting scrutiny of principles has gone most closely hand-in-hand with the mastery of fresh masses of detail, pure mathematics, and again why the present state of what is loosely called ‘evolutionary’ science is so unsatisfactory to any one who has a high ideal of what a science ought to be.  It exhibits at once an enormous mass of detailed information and an apparently hopeless vagueness about the meaning of the ‘laws’ by which all this detail is to be co-ordinated, the reasons for thinking these laws true, and the precise range of their significance.  The work of men like Cantor, Dedekind, Frege, Whitehead, Russell, is providing us with an almost unexceptional theory of the first principles required for pure mathematics.  We are already in a position to say with almost complete freedom from uncertainty what undefined simple notions and undemonstrated postulates we have to employ in the science and to express these ultimates without ambiguity.  ‘Evolutionary science,’ rich as is its information about the details of the processes going on in the organic world, seems still to await its Frege or Russell.  It talks, for example, much of ‘hereditary’ and non-hereditary peculiarities, and some of us can remember a time when our friends among the biologists seemed almost ready to put each other to the sword for differences of opinion about the inheritability of certain characteristics; but no one seems to trouble himself much with the question a philosopher would think most important of all—­precisely what is meant by the metaphor of ‘inheritance’ when it is applied to the facts of biology. (Indeed, it is still quite fashionable to talk not merely as if a ‘character’ were, like a house or an orchard, a thing which can be transferred bodily from the possession of a parent to the possession of the offspring, but even as though an ‘heir’ could ‘inherit’ himself.)