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