misnamed 'Infinitesimal Calculus' at all. Arithmetic and the theory of
serial order have been shown to be the sufficient basis of the whole
science which, as Plato long ago remarked, is 'very inappropriately
called geometry'. A résumé of the work which has been thus done may be
found in the stately volumes of the _Principia Mathematica_ of Whitehead
and Russell, or--to a large extent--in the _Formulario Matematico_ 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