_qualitative_ prevision in respect to
the commoner phenomena with which savage life is familiar; and we have
now to inquire how the elements of _quantitative_ prevision are evolved.
We shall find that they originate by the perfecting of this same idea of
likeness; that they have their rise in that conception of _complete
likeness_ which, as we have seen, necessarily results from the continued
process of classification.

For when the process of classification has been carried as far as it is
possible for the uncivilised to carry it--when the animal kingdom has
been grouped not merely into quadrupeds, birds, fishes, and insects, but
each of these divided into kinds--when there come to be sub-classes, in
each of which the members differ only as individuals, and not
specifically; it is clear that there must occur a frequent observation
of objects which differ so little as to be indistinguishable. Among
several creatures which the savage has killed and carried home, it must
often happen that some one, which he wished to identify, is so exactly
like another that he cannot tell which is which. Thus, then, there
originates the notion of _equality_. The things which among ourselves
are called _equal_--whether lines, angles, weights, temperatures, sounds
or colours--are things which produce in us sensations that cannot be
distinguished from each other. It is true we now apply the word _equal_
chiefly to the separate phenomena which objects exhibit, and not to
groups of phenomena; but this limitation of the idea has evidently
arisen by subsequent analysis. And that the notion of equality did thus
originate, will, we think, become obvious on remembering that as there
were no artificial objects from which it could have been abstracted, it
must have been abstracted from natural objects; and that the various
families of the animal kingdom chiefly furnish those natural objects
which display the requisite exactitude of likeness.

The same order of experiences out of which this general idea of equality
is evolved, gives birth at the same time to a more complex idea of
equality; or, rather, the process just described generates an idea of
equality which further experience separates into two ideas--_equality of
things_ and _equality of relations_. While organic, and more especially
animal forms, occasionally exhibit this perfection of likeness out of
which the notion of simple equality arises, they more frequently
exhibit only that kind of