The behavior of human beings, placed figuratively in a cage, sometimes differs very little from that of an animal. Certainly it shows plenty of trial and error and random motor exploration; and often the puzzle is so blind that nothing but motor exploration will bring the solution. What the human behavior does show that is mostly absent from the animal is (1) attentive studying over the problem, scrutinizing it on various sides, in the effort to find a clue; (2) thinking, typically with closed eyes or abstracted gaze, in the effort to recall something that may bear on the problem; and (3) sudden "insights" when the present problem is seen in the light of past experience.
Though reason differs from animal trial and error in these respects, it still is a tentative, try-and-try-again process. The right clue is not necessarily hit upon at the first try; usually the reasoner finds one clue after another, and follows each one up by recall, only to get nowhere, till finally he notices a sign that recalls a pertinent meaning. His exploration of the situation, 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.
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 up in the other two.
You do not infer what you can perceive directly by the senses. If Mary and Kate are standing side by side, you can see which is the taller. But if they are not side by side, but Mary's height is given as so much and Kate's as an inch more, then from these two facts you know, by inference, that Kate is taller than Mary.
"Have we set the table for the right number of people?" "Well, we can see when the party comes to the table." "Oh! but we can tell now by counting. How many are there to be seated? One, two, three--fifteen in all. Now count the places at table--only fourteen. You will have to make room for one more." This reducing of the problem to numbers and then seeing how the numbers compare is one very simple and useful kind of inference.
Indirect comparison may be accomplished by other similar devices. I can reach around this tree trunk, but not around that, and thus I perceive that the second tree is thicker than the first, even though it may not look so. If two things are each found to be equal to a third thing, then I see they must be equal to each other; if one is larger than my yardstick and the other smaller, then I see they must be unequal.