obvious that the truth of mathematics, if mathematics are true, is a
fatal stone of stumbling for this type of philosophy. Mathematics never
attempts to say anything about the 'Absolute'--the only 'Absolute' of
which it knows is only a 'degraded conic'--yet it claims that its
statements, if once they have been correctly expressed, are not
'partial' but complete.

Over against the Hegelianizing philosophers, we had, of course, the men
of science. No one could wish to speak of the scientific men of the
days of Huxley without deep respect for their success in adding to our
positive knowledge of facts. But it may perhaps be said at this distance
of time that it was not precisely the greatest among them who were most
prominent as mystagogues of Science with the big S, and it may certainly
be said that when the mystagogues, the Cliffords, Huxleys, and the rest,
undertook to improvise a theory of first principles, their achievement
was little better than infantile. They took it on trust from Hume that
the whole of knowledge is built up of sensations, actual or 'revived',
and quite missed Kant's point that their empiricism left the formal
constituent in knowledge, the type of order by which data are organized
into an intelligible pattern, wholly out of account. Even when they
deigned to read Kant, they read him without any inkling of the character
of the 'critical' problem. Hence they taught dogmatically as true a
theory of scientific method which Hume himself had elaborately proved
impossible. It was just because Hume had seen so clearly that no
universal scientific truths can be derived from premisses which merely
record particular facts that he professed himself a follower of the
'academic' or 'sceptical' philosophy. He recognized the impossibility of
constructing scientific knowledge out of its material constituent alone,
but did not see where the formal constituent could come from, and so
resigned himself to regarding the actual successes of science as a kind