tion, though carried on by aid of
recalled experience instead of by locomotion, still resembles finding
the way out of a maze with many blind alleys. In short, reasoning may
be called a trial and error process in the sphere of mental reactions.

{465}

The reader familiar with geometry, which is distinctly a reasoning
science, can readily verify this description. It is true that the
demonstrations are set down in the book in a thoroughly orderly
manner, proceeding straight from the given assumption to the final
conclusion; but such a demonstration is only a dried specimen and does
not by any means picture the living mental process of reasoning out a
proposition. Solving an "original" is far from a straight-forward
process. You begin with a situation (what is "given") involving a
problem (what is to be proved), and, studying over this lay-out you
notice a certain fact which looks like a clue; this recalls some
previous proposition which gives the significance of the clue, but
often turns out to have no bearing on the problem, so that you shift
to another clue; and so on, by what is certainly a trial and error
process, till some fact noted in the situation plus some knowledge
recalled by this fact, taken together, reveal the truth of the
proposition.

Reasoning Culminates in Inference

When you have described reasoning as a process of mental exploration,
you have told only half the story. The successful reasoner not only
seeks, but finds. He not only ransacks his memory for data bearing on
his problem, but he finally "sees" the solution clearly. The whole
exploratory process culminates in a perceptive reaction. What he
"sees" is not presented to his senses at the moment, but he "sees that
something _must_ be so". This kind of perception may be called
_inference_.

To bring out distinctly the perceptive reaction in reasoning, let us
cite a few very simple cases. Two freshmen in college, getting
acquainted, ask about each other's fathers and find that both are
alumni of this same college. "What class was your father in?" "In the
class of 1900. And {466} yours?" "Why, he was in 1900, too. Our
fathers were in the same class; they must know each other!" Here two
facts, one contributed by one person and the other by another person,
enable both to perceive a third fact which neither of them knew
before. Inference, typically, is a response to two facts, and the
response consists in perceiving a third fact that is bound u