SIXTH CHAPTER

PROVING THE PROPOSITION: THE ARGUMENT

FROM EXAMPLE

"Example is the school of mankind and they will learn at no other." BURKE.

THE Argument from Example may be considered under two heads: I, Generalization; and II, Analogy.

I. GENERALIZATION

From what we have seen of the nature of an imperfect induction, which we have called a generalization, it is clear that we have before us a problem quite different from that of deduction. The problem arises from the fact that the conclusion of an imperfect induction, as reached by the process of argument, extends beyond the data on which it is based. It makes a jump from the known to the unknown, a leap in the dark. This has been called the inductive hazard. The problem is, how to justify the leap from verified instances to a conclusion which covers instances beyond the pale of our observation and experiment. How are we to know when we can safely bridge the gap?

The safety of a generalization we may test in at least four ways. We may consider whether the relative size of the unobserved part of the class is so small as to justify its inclusion in our assertion regarding the known part. Or, quite aside from the question of number, we may examine the characteristics of the observed members to ascertain whether those members seem to be fair examples of the class. We may then extend our search beyond the members known or said to fall within the general rule, to see whether any exceptions

to the rule can be found. Finally, apart from the question of the number and characteristics of the known and unknown instances, we may try to estimate the degree of probability that such a general law exists. Although these four tests overlap and test each other, and although they are not always distinct in the mind of one who questions a generalization, yet we can profitably consider them one by one.

A first test of generalization. How many instances will warrant a generalization? Can we prove that all members of the United States Senate are over forty years of age by citing ten, twenty, or even ninety individuals? Clearly not. For such an inference, we are satisfied with nothing short of complete induction. On the other hand, let us examine one diamond, one rectangle, or one falling weight, with scientific accuracy, and we reach a general law from a single instance. We need not multiply examples to determine the specific gravity of all diamonds, the law for the measurement of all rectangles, and the law for the acceleration of falling bodies. Any generalization which stakes its claim to validity on uncontradicted experience" alone may depend, and usually does depend, on experience which is too narrow to warrant the generalization. The child who believes that all people have enough to eat, that all dogs are gentle, and that all children have nursemaids, reasons from the few instances of his own "uncontradicted experience."

From these illustrations it is evident that several examples falling under a general proposition, or several supposed instances of the operation of a principle, may not be sufficient for a trustworthy induction. Indeed, no proportion is always sufficient, for a generalization may be discredited by a single instance.

Accordingly, although we should ask, as a first test, whether the relative size of the unobserved part of the class is so small as to warrant the generalization, we cannot always answer the question without the aid of other tests.

A second test of generalization. The reason why we must consider every member of the Senate, before we can conclude that all senators are over forty years of age, is evident. No members can be selected who are fairly typical of the whole body with respect to the point in question. Another illustration of unwarranted generalization from exceptional instances was furnished by the writer who attempted to draw a sweeping conclusion regarding the beneficence of the tariff from his observations regarding the tariff on shot, barb-wire, and putty. The doubt at once arose how this curious selection of items could fairly represent the whole tariff schedule. Questions like these present the difficulty of finding individual members that embody all those characteristics of the whole class which have anything to do with the disputed principle or general statement.

In the domain of exact sciences, on the other hand, a few specimens, or even a single specimen, may embody all the characteristics of the class which have any bearing on the principle. Diamonds vary greatly in size, shape, value, and brilliancy: but, as these details have nothing to do with the question of specific gravity, we may select a single stone as typical of the whole class with respect to that question. Thus, although isosceles triangles differ infinitely in size and shape, we may deduce from a single specimen various principles which apply to all isosceles triangles; it matters not though their sides extend to the farthest fixed stars, known or unknown. But in such cases, we know that a single specimen is typical only because we have examined many specimens.

Even in more complicated scientific investigations, complete inductions are not considered necessary. The famous scientist Pasteur made many important discoveries by means of generalizations from a few observed instances which, to the best of his keen judgment, were free from exceptional circumstances. In order to find the cause of the blight devastating the silkworms in France, he chose with great care,

from moths known to be free from the suspected germs of the disease, thirty healthy worms. He then fed them with mulberry leaves infected with the germs in question, and watched the results. All died. The natural inference from these specific cases was the general conclusion that the suspected germs really did cause the epidemic among all the silkworms of France. The conclusion would have been untrustworthy, if Pasteur had attempted to generalize from specimens already infected with any fatal disease, or in other ways unfair with respect to the object of his experiments.

We should always test the members upon which a generalization is based to determine whether they are fair specimens of the class.

A third test of generalization. The tendency of the untrained thinker is to conclude that a proposition which is true of all cases he happens to know is true of all possible cases. Accordingly, he generalizes from his limited experience, or accepts the scanty generalizations of other people, unless conflicting instances are thrust upon his attention. The careless reasoner says, "Such and such a fact is true of this member of a class; it is true of this other member of the class; I have observed no member of the class of which it is not true; therefore it is true of the whole class." His error may be due to the non-observation of instances which make against the generalization. The habit of seeking exceptions is a mark of the scientific mind. The observation of the untrained mind is purely passive: it accepts the facts which present themselves, without taking the trouble to search for more: the trained mind tries to determine what facts are needed for a sure conclusion, and then searches for these facts.

As we observed in our discussion of prejudiced testimony, our vision is somewhat distorted by our desires. When we are seeking to establish a principle, verifying instances shine with a deceptive luster which blinds us to exceptions. It is a

trite observation that we find in life what we look for. A man may glance at every periodical on the news-stand for the sole purpose of finding the Atlantic Monthly, and in the end not have a definite idea in his head as to what other magazines he saw. He knows merely that they were not the one he was looking for. He may not be able to tell you the time immediately after looking at his watch. He knows merely that it is not time for his appointment. Well aware as we are of this trait of the mind, we should take definite means to safeguard our generalizations against exceptions. If the nature of the case permits such thorough investigation, we should be able to supplement our conclusions at least by negative evidence; that is, by proving the probability that, if exceptions existed, we should have found them.

The habit of seeking exceptions to a rule is a stanch protection against hasty generalization, not only because of the natural tendency to overlook contradictory evidence, but also because the commonplace "exceptions" may really be far more numerous than the conspicuous cases employed as proof. Much of the every-day reasoning regarding the value of a college education proceeds by exaggerating unusual instances and ignoring instances which make against the conclusion. A man observes a number of college graduates who fail in business; he concludes that a college training unfits men for practical affairs. College graduates who succeed in life provoke little argument on the subject; they are expected to succeed. But a few graduates, who with all their education can do no creditable work, furnish the meager data from which many people draw the generalization that a college education does not pay. In like manner the industrious, upright students, who form a large majority of every college, play no part in the inductive reasoning of those people who judge all college students by the few unworthy ones who make themselves disagreeably conspicuous. Mind-readers gain their reputation largely from the fact that any guess