A Class Room Logic / Deductive and Inductive, with Special Application to the Science and Art of Teaching

by George Hastings McNair

12. INDUCTION BY ANALOGY.

Induction by analogy assumes that if two (or more) things resemble each other in certain respects, they belong to the same type, and, therefore, any fact known of the one may be affirmed of the other.

THE TYPE.

As the definition implies, analogy involves an extensiveuse of types; let us, therefore, become better acquainted with them as instruments in analogical inductions. A type is one of a group which embodies the essential characteristics of that group. How easy and natural it is to dismiss a complex topic with the citing of an example which may be regarded as a type; how common is the use of examples in the school room! On second thought it becomes apparent that analogical induction by example or type is the most common of all forms of induction either as a method or a mode of inference. Analogy by example (or type) assumes that if two or more things are of the same type, they resemble each other in every essential property.

Illustrations of analogical inductions by example or type.

(1) Mathematics.

Example: a + b

a + b

———————

a² + ab

+ ab + b²

———————

a² + 2ab + b²

Inductive Inference: The square of the sum of two quantities is equal to the square of the first, plus twice the first by the second, plus the square of the second.

(2) Nature.

This corn sent me as a sample produced heavy, full ears, and many of them; hence (inductive inference), if I plant corn like this sample under like conditions, I will receive in return heavy, full ears, and many of them.

(3) Geography.

Cities like New York, located on the coast, possess a larger foreign element than the inland cities like Philadelphia.

(4) Grammar.

A noun is the name of anything, as the examples, “George Washington” and “house” would indicate.

In deriving a generalization from one or two examples the prime essential is to select types which are truly representative. Often the example used is a special type and in consequence does not exemplify all of the essential characteristics of the group. To teach the nature of a parallelogram by using a rectangle only, is an easy way to commit this error; or one may affirm that the class can easily cover the work, when the judgment is based entirely on knowledge concerning the brightest one of the grade.

Type work when judicially used is a positive time saver and a very present help in times of perplexity. Let the skillful teacher use types and examples extensively yet cautiously.

THE MARK OF SIMILARITY.

As opposed to analogy by type there is a second form; namely, analogy by one or more similar marks or qualities. This form is best described by the definition: When two things resemble each other in a few marks or qualities they resemble each other in other marks or qualities.

Illustrations of analogy by marks.

(1) Noting that two students have the same surname, I infer that they are brothers.

(2) A man with a book under his arm rings the door bell and asks to see “the lady of the house.” At once the conclusion is drawn that the caller is a book agent.

(3) Two automobiles, resembling each other in shape of body, force one to the conclusion that the machines are of the same make.

THE ERRORS OF ANALOGY BY MARKS OF SIMILARITY.

It follows that analogy by example gives generalizations of much greater certitude than analogy by one or two marks of resemblance. Here is a field bespattered from boundary to boundary with erroneous thinking. The principle of resemblance being an innate tendency, this form of error is most common with the immature. The child reasons by analogy when he invests the poodle with the despised cognomen of “kitty”; or honors every man who wears glasses with “papa.” In the childhood of the race natural events were interpreted by means of analogy. The wind blowing through the trees made sounds much like the human voice; hence these noises were attributed to spirits. Primeval man was led to believe by analogy that everything which moved was alive. We may, therefore, think of our revered forbear as engaged in the undignified task of running after his shadow, or chasing a leaf around a stump.

THE VALUE OF ANALOGY.

Analogy being rich in its suggestions is the favored process of the scientist and inventor. Newton reasoned by analogy when he tentatively affirmed of the moon what he positively knew of the apple. Franklin’s reasoning was analogical when he discovered the identity of the electric spark and lightning. Because this form of induction so often leads to error and at best involves a degree of probability far below induction by analysis, some logicians are inclined to ignore its generalizations altogether. Others deem this a mistake because of these reasons: First. Analogy is serviceable to a high degree in suggesting hypotheses which may be advanced either for the purpose of explanation or verification. It has already been indicated that analogy is the common instrument used by the inventor and discoverer. Second. The principle of analogy, in reality, lies at the basis of classification; because in this, things are grouped according to their resemblances. Third. Analogical induction affords valuable training in originality and initiative. A mind which easily and naturally discerns analogies is “fertile in new ideas.”

REQUIREMENTS OF A TRUE ANALOGY.

It has been remarked that the certitude of an induction by simple enumeration depends upon the number of uncontradicted instances. In analogy the case is different as the process emphasizes the weight of the points of resemblance rather than the number. In substance the requirements of a logical analogy are three.

First. The points of resemblance must be representative and not exceptional. For example: The argument that Mars is inhabited because it has two moons is of little worth, since we have no proof that moonshine is essential to life; this point of resemblance is not representative. On the other hand, if the basis of argument is the fact that Mars has an atmosphere, the conclusion carries some weight; as air seems to be essential to life.

Second. The points of resemblance must outweigh the points of difference. That is, the ratio of probability must always be in favor of the resembling instances. Since it is not a matter of numbers but of weight, a numerical proportion like this would be misleading: Resemblances: Differences = 10:6. It is obvious that the six differences might more than outweigh the ten resemblances. The safer way, if it were possible, would be to attach a value to each point of resemblance or difference, and then express the proportion in terms of the sums of these values.

Third. There must be no difference which is absolutely incompatible with the affirmation which we wish to prove. For example, the fact that the moon has no atmosphere renders nugatory any attempt to prove the habitability of the moon.