COLLINGWOOD'S VIEW OF HISTORY 729
of contemporary and posterior civilizations, down to and including
Collingwood's and Toynbee's own seventeenth-century forebears in the
West, who had fallen like ninepins to the fascination of this professedly
scientific system of ideas.
'The human interest' which attaches to the history of astrological
beliefs, and which is just as well served by a study of them if they happen
to be scientifically false as if they-happen to be scientifically true, is the
hidden treasure1 that is the historian's lodestone. Nothing else except
the quest for this trove would induce the historian to give his mind to
scientific and mathematical propositions which for the historian have
no intrinsic professional interest either a priori or even in consequence
" of the historian's being told by a savant that the savant believes them to
be true—and, perhaps, not only true but momentous—in the inhuman
realm of scientific and mathematical reality.
It will be seen that the mathematician's and the historian's respective
professional interests in the same mathematical proposition are mutually
exclusive; and consequently either party's interest is at best boring to
the other party and at worst exasperating to him. The historian has no
professional use for a system of mathematical or scientific truth if he is
asked to study it for its own sake; for he is not concerned to certify the
permanence of 'a permanent addition to mathematical knowledge' in
thinking this mathematical thought for himself, any more than he is
concerned to certify the permanence of 'a permanent addition to political
ideas' in entering into the thoughts and aims of Augustus. If he sets
himself to think thoughts that were once entertained by the mind of
either an Augustus or a Pythagoras, his purpose is to utilize the political
calculation or the mathematical theorem as an intellectual spring-board
from which his imagination can make an attempt, by taking a flying
leap, to establish psychic communications with other human souls whose
intellects have thought the same thought at other times and places. Con-
versely, the mathematician or natural scientist has no professional use
for the history of mathematical or scientific beliefs.
It is true that the beliefs which mathematicians and scientists will be
found to be holding at any date will always also be found to be the his-
torical product of beliefs held by their predecessors, some of which will
have been retained, and others discarded, by these past thinkers' present
epigoni; and this is an aspect of mathematical and scientific beliefs that
is of greater professional interest to an historian than the mathematician's
or scientist's professional question whether these beliefs happen to be
intrinsically true or false. At any date at which the historian takes a
sounding, he is apt to find the mathematicians and scientists of that
generation indebted to the past beliefs that they have discarded, not
much less deeply than to those that they have retained; but the his-
torian is also apt to find himself being astonished by his own mathe-
matical and scientific contemporaries' ingratitude. If they are confronted
with one of their predecessors' beliefs, their first question is not, 'What
do we owe to it?' but, Is it true or false?' And, if once they have pro-
nounced it to be false according to their own present lights, they suffer
i Matt. xiii. 44-