eometrical
conceptions. Strange to say, a large body of respectable mathematicians
have been found to favour the extraordinary view that our mathematical
conceptions are derived from Sensation. We do not propose here to
discuss at length this idea. It is merely another form of the old
sensationalist view of Knowledge, but we suggest that the conditions of
the problem will readily appear in their true light and real nature
whenever such inquirers realise the fact that our exertional activity is
the source of our cognitions of the external, and that therefore our
pure exertional activity is the source of the basal concepts of
geometry.

Here lies the root of the distinction between pure and empirical
science. The propositions of geometry, being derived from our own pure
activity, are of the former class; the inductive conclusions of physical
experimental science, being gathered by observation and measurement
from sensible data, are empirical and approximate. A geometrical
proposition--such, for example, as the assertion that the three angles
of a triangle are equal to two right angles--is not merely approximate.
It has no dependence on measurement. It is absolutely true. It is
ascertained deductively, and therefore measurement is not involved, and
is never employed. Its truth is not ascertained by measurement. It is
not verified by measurement. It in no degree depends upon the sensible
figure. It is equally true for every human being whatever be the degree
of accuracy of the figure by the aid of which he studies it, or indeed
whether he studies it by figure or otherwise, as must necessarily be the
case with the born blind.

There may be many different forms of energetic transmutation which may
determine many other forms of space besides that form of tridimensional
space in which our Activity is involved. For such, a different geometry
may and will be applicable; but for the tridimensional conditions of
_our activity_ the proposition is necessary and absolute. No measurement
of any stellar parallax, however minute and whatever the result might
be, could have any bearing on its truth. Geometry is the science of the
pure forms of our motor activity amidst corporeal bodies.

A useful illustration of our argument is to be drawn from a
consideration of the question of phonetic spelling. Occasionally we find
persons urging that all spelling should be an exact reproduction of
sound. Indeed, an improved alphabet has been design