characters is a hero. We may try any one of the characters in a minor premise and find out whether the conclusion logically deduced is true. If the conclusion is not true, we have discovered an exception to the general assertion. Thus

None of Shakespeare's characters is a hero,

Romeo is one of Shakespeare's characters,

.. Romeo is not a hero.

In place of Romeo, we may insert, one by one, Cæsar, Hamlet, Kent, and all the rest. When we come to Brutus, we may object to the conclusion that Brutus is not a hero. If so, we have proved that the generalization is unwarranted, according to our definition of a hero. Ordinarily we do not go through all the steps of this formal process in testing a generalization; nevertheless, so far as we examine particular cases, this method in abridged form is precisely the one we must employ.

We should look beyond the members upon which a generalization is based in order to discover possible exceptions.

So far we have

A Fourth Test of Generalization. considered the means of testing inductive reasoning by observation and experiment. But our generalizations are usually unsafe in so far as they depend on experience, for our experience is usually confined to a small part of the class concerning which we seek to discover a universal truth. As we have seen, the appearance of universality may be due to the very limitations of experience, as when a child, who has seen only two dogs, concludes that all dogs have shaggy hair. Uncontradicted experience is insufficient to establish a general truth. How, then, can we finally test a generalization? In those many cases where even the most extensive possible observation and experiment fail to cover the class, how

can we finally justify the leap from the known to the unknown? Not by the mere number of verifying instances, not by their apparently universal characteristics, not by the absence of known, exceptions, but by a revealed order of nature beyond the likelihood of chance. The ultimate warrant for a generalization is our belief in the universal laws of causation; nothing happens without sufficient cause; or, in common language, “if it is true, there must be a reason for it." And so, to look for uniformity in the course of nature where uniformity is not to be expected to hold that every seventh Class Day at Harvard will be rainy — is rightly ridiculed as superstitious. Accordingly, as a final test of an imperfect induction, we try to estimate, by a consideration of underlying causes, the degree of probability that such a general law or statement is true.

Suppose that misfortune has several times followed the appearance of three black cats, that the instances seem fairly typical, and that we have heard of no contradictory instances. Then, without a search for the causal connection, we at once conclude that the two events are regularly associated in the course of nature. We jump to the broad statement that the appearance of three black cats is a sign of bad luck. We have made some pretense of generalizing, — a weak attempt, to be sure, since our induction is based on "simple enumeration," but still an attempt. It illustrates the typical fault of inductive reasoning, hasty generalization from insufficient data without even a probable causal connection.

The outrageous advertisements of cheap family papers which still flood the mails are veritable encyclopedias of unwarranted generalization. In proof that Professor Fakir's lucky box will bring good fortune to

all men, a dozen testimonials are presented; and the reader, unless he has tried the charm, finds no exception to disprove the rule. In proof that Madam Fakir possesses occult powers, the remarkable assertion is made that she is the seventh daughter of a seventh daughter! In proof that the Genuine Fakir Balsam will cure all men of all maladies, a reward of a hundred dollars is offered for a single case of failure! To such amazing generalities, expressed or implied, the ignorant and the grossly superstitious apply no tests at all; and on their money the Fakir business thrives. The rest of us escape by instinctively asking how such things can be. The demand on our credulity is so great that we need not even examine the alleged cases; it is enough that we cannot conceive the possibility that such general laws exist.

Generalizations range all the way from the mistakes of children, plainly caused by the limitations of experience, to the scientific generalizations at the other end of the scale, such as the law for falling bodies. Our generalizations go through this progression: at the outset they are based on the simple enumeration of a few chance observations, and at the end they are explained, to a greater or less extent, by the relation of cause and effect. Toward the lower end of the scale we must place most of our generalizations about the weather, about national characteristics, and about the fluctuations in the money market. Such generalizations owe little to our perception of causal relations. And yet they are gradually approaching the scientific end of the scale. We have lately acquired some knowledge of the causes of epidemics which formerly seemed capricious. As our generalizations thus become explained by causal theory, they are narrowed and safeguarded against error. When

we ask why the black cats and misfortune have appeared in succession, when we attempt to fix the links of causation between the two events, we are in a fair way to reveal the absurdity of the idea.

In testing our generalizations, we should endeavor to place them near the scientific end of the scale by discovering the underlying relations of cause and effect.1

SUMMARY OF THE TESTS OF GENERALIZATION

1. Is the relative size of the unobserved part of the class so small as to warrant the generalization? 2. Are the members observed fair examples of the class?

3. Are we reasonably sure that there are no exceptions?

4. Is it highly probable that such a general rule or statement is true?

II. ANALOGY

"In the argument from analogy the ground of inference is the resemblance between two individual objects in a certain number of points; and the inference is that they resemble one another in some other point, known to belong to the one, but not known to belong to the other."" In other words, we infer by analogy that a

1 This subject is well treated in Alfred Sidgwick's The Process of Argument.

2 This definition is from Minto (Logic: Inductive and Deductive, p. 368). Professor Baker, on the other hand, agrees with Whately in confining the term analogy to resemblances "not so much in the things themselves as in the relations in which the things stand to other things." "Thus an egg and a seed are not in themselves alike, but bear a like relation to the parent bird and to her young nestling, on the one hand, and to the old and young plant on the other, respectively." Professor Genung regards an argument from analogy as one

certain fact, known to be true of A, is more likely to be true of B if B resembles A in essential properties, than if B were not known to resemble anything of which the certain fact is true. An argument from analogy is, therefore, that kind of argument from example which steps from one particular case to another particular case. It does not amount to a complete or even attempted generalization.

For example, sodium and potassium are included in the same group, called alkaline metals, because of their common characteristics: both combine with oxygen to decompose water at all temperatures; their carbonates are soluble in water; and each metal forms only one chloride. Now, if chemists discovered a new property of one of these metals, they might infer by analogy that the other metal had the same property. Or, to take another example, we observe that one college student, of good health and fair ability, indulges in repeated dissipation. Finally, his health breaks down, he fails to pass his examinations, and he is dropped from college. We argue from analogy that another student, of equal health and ability, who makes the same mistakes, will which takes "relations that exist in one sphere of life or experience, as indications of what may be regarded as true of another sphere whose relations are similar." But whether the argument is based on similarity between objects in the same sphere of life or in different spheres of life, and whether the argument is based on similarity in the objects or in relations, the force of the argument depends on precisely the same conditions; we should apply the same tests, and expose its insufficiency by the same methods. For practical purposes, therefore, the distinctions would hardly be worth insisting upon, even if there were any agreement among writers. In this chapter, the term Argument from Analogy is used in the wider sense to include all arguments from example which do not amount to an induction, that is to say, all arguments from resemblance in which the operating principle is suppressed. Any one who prefers the term Argument from Resemblance for the whole class, with the Argument from Analogy as a sub-class, can readily make the distinction.