When one has laid down with positiveness some supposed general principle, and his attention is called to a fact inconsistent with it, it is not uncommon to hear him say, rather triumphantly, "Oh, that is simply the exception that proves the rule"; and he seems somehow to feel better fortified in his position than before, his generalization being now provided with a necessary equipment. Even respectable writers fall into this absurd mode of speaking. The fallacy consists in taking as a principle, valid in the world of facts, what has no sense at all except in the world of statements. It is taken as if the finding of a black sheep were in some way a confirmation of the generalization that all sheep are white; although, of course, every such case is just so much disproof. But if some person, a lawmaker, an expert, or an authority of some sort, in making statements, excepts a person or thing, then it may be legitimately inferred that he assumes the rule to be the other way. If, for example, one who lives on the shore of Lake Erie speaks of a fine day in March with surprise, his so speaking is equivalent to testimony that bad weather then and there is the rule; but a chance visitor, luckily enjoying bright skies, would not on that account more readily assent to the assertion that March weather on Lake Erie is generally bad. Those who in their youth have been compelled to learn the rules for Latin quantity, find it most convenient to remember them by the exceptions. Knowing that amīcus is given as one of the exceptions in its class, I have no difficulty in recalling the rule that "Words in -icus shorten the penult"; but this proves only the statement of the grammarian, nothing more. In short, the word excep

tion has two senses; first, it means the act of excepting ; secondly, the thing excluded; the popular fallacy consists in substituting the second for the first sense, and in supposing that the discovery of a few words with long i before the termination -cus makes it easier to believe that i so situated is generally short; when in truth the proof is wholly in the fact that a competent authority has declared these words to be exceptions.1

1 See Richard Grant White's Words and Their Uses, 3d edition, Appendix I.

CHAPTER V.

SECONDARY INDUCTIONS.

HAVING by the slow, and often tedious, process of observing many particulars, established our primary inductions, we are prepared to advance with ease and rapidity in the making of Secondary Inductions. A primary induction, we have learned, is a generalization of experience, a truth established by repeated observations. A Secondary Induction is the conclusion of a syllogism of which one premise is a primary induction, and the other premise is the statement of an observed fact. When, for example, it has once been admitted, as a primary induction, that specific gravities are constant, a single experiment upon a newly discovered metal is sufficient to establish its specific gravity to the satisfaction of the scientific world. The single observation is combined deductively with the primary induction, thus:

All specific gravities are constant ;

The specific gravity of this piece of Rubidium is 1.5; Therefore, the specific gravity of Rubidium is always

1.5.

This illustration shows in an interesting manner how induction and deduction are combined. There is discovery here, but it is not reached by anything peculiar in the method of inference; that is simply deductive. But each of the premises records a discovery made by observation; hence the syllogism is inductive. It has

been objected to such syllogisms, that the universal proposition could not be affirmed unless we already knew the conclusion, and that consequently there is only an apparent, and not a real advance in knowledge. The reply is, that no reasoning can ever make a substantial advance in knowledge; to give knowledge is the function of intuition and observation alone. Reasoning can only display explicitly what was already involved implicitly. There is, however, in this case what comes very near to positive discovery. It has appeared in the last chapter that practical certainty is reached, regarding many of the uniformities of nature, long before all instances have been examined; indeed, from the very character of most uniformities, it is impossible that all instances should be examined. We become satisfied that all men are mortal, upon knowledge of what is a very limited part of the experience of the race. When, therefore, it is observed that Socrates is a man, the conclusion that he is mortal comes very near to being a discovery. The fact that Socrates is a man is a discovery of observation; Socrates might be the name of a dog or of a ship. This premise brings into the syllogism an advance in knowledge.

In every-day thinking, primary and secondary inductions are constantly mingled, and almost all of our generalizations partake of the nature of both, or are proved in both ways. There is, for instance, a perpetually accumulating mass of experience that lead is heavy, that aluminum is light, and so on. Independently of anything else, a primary induction can be made regarding each one of the metals. But at the same time the broader primary induction that specific

gravities are constant is receiving perpetual confirmation, so that each single experience with lead or aluminum abundantly warrants a secondary induction covering the whole existing amount of that metal.

After observing a thousand uniformities, every one perceives that objects and events in this world run in lines of similarity; a strong presumption, therefore, arises that any given object is only one of a class. Finding several similar things, we combine the observation with the previously established generalization that several similarities indicate the line of a uniformity, and make an induction accordingly. This is what Dr. Fowler has called "the mode of generalization natural to immature and uninstructed minds"; but in truth it is the necessary procedure of all sane minds. The immaturity and inexperience appear in neglecting care in determining the exact course and limits of the lines of uniformity.

Archbishop Whately regarded the uniformity of the course of nature as the ultimate major premise in all inductions. That is, he did not provide for any primary inductions at all. But the uniformity of nature is too vast and indefinite an induction for immediate use, even in most cases of secondary induction. The doctrine does not mean that all objects are alike, and all events alike; it only means that all particular lines of uniformity persist. What these lines are, must be determined simply by accumulating instances and making generalizations. We must have observed a number of lines of particular uniformity, before we could ascend to the induction of the general uniformity of nature. Το quote Mr. Mill: