In abstract, intellectual conceptions, such as those of equality,
distance, number, and the like, the same faculty and the same elements
are at work as in those which express physical and moral qualities.
These conceptions, which as civilization advances ultimately become mere
intellectual symbols necessary for logical speech, are at first formed
by the actual comparison of things, and therefore by the aid of the
senses. Even if we were to assert with some schools of thought that they
were formed _a priori_ in the mind, sensation would still be necessary
as the occasion of displaying them. When such conceptions are expressed
in words there is a physiological recurrence to the mind of what may be
termed the shadow of previous sensations or perceptions, which are
united in an intellectual type to give rise to such conceptions. And in
the appearance of this phenomenal basis, thought unconsciously fulfils
the fundamental law of assuming, or I might say of actually _feeling_,
the reality of the subject.

It must be remembered that in speaking of these entities created by the
intellect, I refer to the primitive ages of human thought, or to the
notions of ignorant people, and also to the spontaneous language of
educated men, who in ordinary conversation do not pause to consider the
simple and logical value of their expressions. We are only giving the
natural history of the intelligence, which necessarily excludes the
analytic and refining processes of rational science. An educated man
will, for example, say or write that identity is a most important
principle of logic as well as that of contradiction, although he is
perfectly aware that such expressions only imply an abstract form of
cognition; he follows the natural and primitive process of the
intellect, and for the moment expresses these conceptions as if they
were real entities in the organism of science and of the world. Any one