senses, and showing the non-serial
evolution of its divisions, to note the non-serial character of those
preliminary processes of which all after development is a continuation.
On reconsidering them it will be seen that not only are they divergent
growths from a common root, not only are they simultaneous in their
progress; but that they are mutual aids; and that none can advance
without the rest. That completeness of classification for which the
unfolding of the perceptions paves the way, is impossible without a
corresponding progress in language, by which greater varieties of
objects are thinkable and expressible. On the one hand it is impossible
to carry classification far without names by which to designate the
classes; and on the other hand it is impossible to make language faster
than things are classified.

Again, the multiplication of classes and the consequent narrowing of
each class, itself involves a greater likeness among the things classed
together; and the consequent approach towards the notion of complete
likeness itself allows classification to be carried higher. Moreover,
classification necessarily advances _pari passu_ with rationality--the
classification of _things_ with the classification of _relations_. For
things that belong to the same class are, by implication, things of
which the properties and modes of behaviour--the co-existences and
sequences--are more or less the same; and the recognition of this
sameness of co-existences and sequences is reasoning. Whence it follows
that the advance of classification is necessarily proportionate to the
advance of generalisations. Yet further, the notion of _likeness_, both
in things and relations, simultaneously evolves by one process of
culture the ideas of _equality_ of things and _equality_ of relations;
which are the respective bases of exact concrete reasoning and exact
abstract reasoning--Mathematics and Logic. And once more, this idea of
equality, in the very process of being formed, necessarily gives origin
to two series of relations--those of magnitude and those of number: from
which arise geometry and the calculus. Thus the process throughout is
one of perpetual subdivision and perpetual intercommunication of the
divisions. From the very first there has been that _consensus_ of
different kinds of knowledge, answering to the _consensus_ of the
intellectual faculties, which, as already said, must exist among the
sciences.

Let us now go on to obs