a whole, after
religion, it may seem that we have reversed the proper sequence. There are
many reasons for following this course, inasmuch as "knowledge" is the
all-inclusive category of thought; our world is after all a world of
individual consciousness and ideas. In dealing with religion, ethics,
social organization, and human culture, we have been concerned with the
evolution of so many departments of thought and action; and now we are to
develop a final conception of evolution as a universal process in the
progress of all knowledge.

Let us look back over the history of mathematics. The primitive human
individual did not need to count. He dealt with things as he met them, and
he disposed of them singly and individually. A squirrel does not count the
nuts it gathers; it simply accumulates a store, and it perishes or
survives according to its instinctive ability to do this. Just so was
primitive man. The savage, when he organized the first formed tribes,
learned to count the days of a journey and the numbers engaged on opposite
sides in battle. He employed the "score" of his fingers and toes, and our
use of this very word is a survival of such a primitive method of
counting. The abacus of the Roman and Chinese extended the scope of simple
mathematical operations as it employed more symbolic elements. With the
development of Arabic notation capable of indefinite expansion, the
science progressed rapidly, and in the course of long time it has become
the higher calculus of to-day. The conceptions of geometry have likewise
evolved until to-day mathematicians speak of configurated bodies in fourth
and higher dimensions of space, which are beyond the powers of perception,
even though in a sense they exist conceptually. The behavior of
geometrical examples in one dimension leads to the characteristics of
bodies in two dimensions. Upon these facts are constructed the laws of
three-dimensional space which serve to carry mathematical thought to the
remoter conceptual spaces of which we have spoken. It may seem that we are
recording only one phase of mental evolution, but in fact we are dealing
with a larger matter, namely, with the progressive evolution of knowledge
in the Kantian category of number.

Natural science began with the savage's rough classification of the things
with which he dealt in everyday life. As facts accumulated, lifeless
objects were grouped apart from living organisms, and in time two great
divisions of