Psychology

by Robert Sessions Woodworth

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.

Of the two facts which, taken together, yield an inferred fact, one is often a general rule or principle, and the inference then consists in seeing how the general rule applies to a special case. A dealer offers you a fine-looking diamond ring for five dollars, but you recall the rule that "all genuine diamonds are expensive", and perceive that this [{467}] diamond must be an imitation. This also is an instance of indirect comparison, the yardstick being the sum of five dollars; this ring measures five dollars, but any genuine diamond measures more than five dollars, and therefore a discrepancy is visible between this diamond and a genuine diamond. You can't see the discrepancy by the eye, but you see it by way of indirect comparison, just as you discover the difference between the heights of Mary and Kate by aid of the yardstick.

If all French writers are clear, then Binet, a French writer, must be clear. Here "French writers" furnish your yardstick. Perhaps it would suit this case a little better if, instead of speaking of indirect comparison by aid of a mental yardstick, we spoke in terms of "relations". When you have before your mind the relation of A to M, and also the relation of B to M, you may be able to see, or infer, a relation between A and B. M is the common point of reference to which A and B are related. Binet stands in a certain relation to "French writers", who furnish the point of reference; that is, he is one of them. Clear writing stands in a certain relation to French writers, being one of their qualities; from which combination of relations we perceive clear writing as a quality of Binet.

Just as an illusion is a false sense perception, so a false inference is called a "fallacy". One great cause of fallacies consists in the confused way in which facts are sometimes presented, resulting in failure to see the relationships clearly. If you read that

"Smith is taller than Brown; and
Jones is shorter than Smith; and therefore
Jones is shorter than Brown,"

the mix-up of "taller" and "shorter" makes it difficult to get the relationships clearly before you, and you are likely [{468}] to make a mistake. Or again, if Mary and Jane both resemble Winifred, can you infer that they resemble each other? You are likely to think so at first, till you notice that resemblance is not a precise enough relation to serve for purposes of indirect comparison. Mary may resemble Winifred in one respect, and Jane may resemble her in another respect, and there may be no resemblance between Mary and Jane.

Or, again,

"All French writers are clear; but
James was not a French writer; and therefore
James was not a clear writer,"

may cause some confusion from failure to notice that the relation between French writers and clear writing is not reversible so that we could turn about and assert that all clear writers were French.

The reasoner needs a clear head and a steady mental eye; he needs to look squarely and steadily at his two given statements in order to perceive their exact relationship. Diagrams and symbols often assist in keeping the essential facts clear of extraneous matter, and so facilitate the right response.

To sum up: the process of reasoning culminates in two facts being present as stimuli, and the response, called "inference", consists in perceiving a third fact that is implicated in the two stimulus-facts. It is a good case of the law of combination, and at the same time it is a case where "isolation" is needed, otherwise the response will be partly aroused by irrelevant stimuli, and thus be liable to error.