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circumstances; inductive reasoning about relations of cause and effect must eliminate them. This is often very difficult; and when the elimination has been made and we are thus able to conclude from the cases examined that A's action was the cause of B's, we must not conclude from this that this same act on A's part will always be followed by the same act on B's; but only that such will always be the case as long as nothing else interferes. *
This fact that one cause can interfere with another is what makes a knowledge of causal relations so very important practically as well as theoretically. No human effort can
. change a thing's identity, but if we know enough we can use our bodies in such a way as to pit one cause in the world against another and change its effects in accordance with
This is why knowledge is power. The thing that makes the knowledge of causal relations most difficult is the very thing that makes it useful.
* In this connection the reader may recall the statement made on p. 80 that causal relations seem to penetrate into the very being of things, while non-dynamic relations exist only externally for some observer. In this respect identity is like causation.
THE METHOD OF EXHAUSTION AND THE SEARCH FOR
We use the method of exhaustion when we base a conclusion upon the results of a more or less direct and serious attempt to examine every case of a given sort in the universe.
The simplest application of this principle is found in the so-called Aristotelian, or Perfect, Induction. The first ex
ample of induction given on page 224 was of this induction.'
sort, namely: This, that, and the other member
of a certain family each has light hair; these members constitute the whole family; therefore every member of the family has light hair. In the same way we can say: ‘The apostle James was a Jew; so was John; so was Peter’; and so on through the twelve; “therefore the twelve apostles were all Jews'. January contains less than thirtytwo days; so do February, March, etc.; therefore each month of the year contains less than thirty-two days. In this 'perfect induction' the conclusion is something more than a mere summary of the particular facts stated in the premises; for we might know that James was a Jew and that John was a Jew, and so on through the twelve, without knowing or without thinking that these twelve were all the apostles.
This Perfect Induction is relatively rare; for it is only in comparatively few cases that we can be sure that the individuals named constitute the whole class in question.
“The assertion that all the months of the year are of less length than thirty-two days . . . is a certain conclusion because the calendar is a human institution, so that we can know beyond doubt how many months there are. But the assertion that all the planets move in one direction round the sun, from West to is derived from Imperfect Induction; for it is possible that there exist planets more distant than the most distant known planet Neptune, and” of " such a planet of course the assertion would ” not hold true. *
If a being who was purely rational found that a Perfect Induction was impossible, he might go no further. men are animals as well as rational, and have an
Why we animal's tendency to react to every impression, accept less. and to react in the same way when the impressions are similar. Consequently we will often risk a conclusion that the premises will not altogether warrant, and when all the individuals with a given general appearance that we have examined have a certain particular characteristic we almost always take it for granted that those we have not examined have it also. Practically in inductive argumentan opponent” who maintains that some general statement is not true is worsted when he cannot produce an instance to the contrary. Suppose he admits the predicate in ques
tion to be true of this, that, and the other, but denies that } this, that, and the other constitute the whole class in ques
tion, he is defeated in common judgment if he cannot instance a member of the class about which the predicate does not hold. Hence this mode of induction becomes technically known as Inductio per enumerationem simplicem ubi non reperitur instantia contradictoria. When this phrase is applied to a generalization of fact, Nature or Experience is put figuratively in the position of a Respondent unable to contradict the inquirer." + Thus we see how the inductive process by which we make
Jevons' "Lessons ”, p. 213. † Minto, pp. 236-7.
When may we guess ?
and try to justify a universal proposition falls short of its
ideal. We set out to exhaust the universe, and Justification practical.
stop when we have exhausted our own knowledge
or when we get tired of going any further, but we draw our conclusion nevertheless. The only justification we can give for such a proceeding is practical; that on the whole we get along better if we jump to such conclusions after a reasonable amount of investigation than if we always suspend our judgment and refuse to act until our data are absolutely complete.
How many cases constitute a 'reasonable' number upon which to base a general conclusion depends altogether upon
circumstances. If the general conclusion in question fits in with what we know about other
things it will not usually require so much evidence in its favor as it would if it did not. In view of what everybody knows about other animals it requires very little evidence to prove that all sheep are mortal. cases make a reasonable number depends too upon how likely it is that we should know of an exception to the general rule if one existed. That every man in the civilized world is less than twenty feet tall we have a right to say at once, because we know that if taller men than that existed anywhere within the bounds of civilization we should be sure to have heard of them. A third consideration which helps to determine how many cases we should investigate before venturing upon a general statement is the practical importance of the question at issue. If the eternal salvation of every human being depended upon the truth of our statement the number of cases investigated would have to be very great indeed before any one of us would think it reasonable to draw the general conclusion. Anything short of an absolute exhaustion of the group in question fails to give absolute certainty, and the completeness of the exhaustion which we feel compelled to make will always depend upon the amount of certainty that we require.
Though the circumstances which help to determine how much evidence for a general conclusion is reasonable are related to the case in question, they all lie outside of it. That is to say, the question of how much evidence is reasonable does not depend so much upon the nature of the problem in itself as upon its relation to what we know about other things—e.g., the constitution of society that makes it likely that we shouid hear of a man twenty feet tall if he existed, the supposed divine law that would lead to our damnation for a false guess, etc.
The one thing in this connection which the student of logic should not overlook is this: As civilization advances, the need for accuracy and certainty of thought and action constantly increases. Our environment in this respect is changing very rapidly, while our natures change very slowly. The consequence is that the average man is apt to be too impatient of suspense and to jump to his conclusions too rapidly for his own good. And if the individual happens to be concerned with science, in the very front of the forward movement, where the need for accuracy and the means of attaining it are growing most rapidly, then intellectual patience becomes a virtue of which he can hardly have too much. An incautious or inaccurate farmer may get along after a fashion even in this day; but an inaccurate scientist is almost certainly bound to be an utter failure.
Perfect Induction and the Inductio per Enumerationem Simplicem may be regarded as the inductive processes corresponding to the first figure of the syllogism. They are not concerned pre-eminently with any problems particular kind of relations; they involve no tions are refined analysis; and their only positive characteristic is the generality of their conclusions.
On page 225 we saw how the principle of exhaustion is used to ascertain relations of identity and causation as well as to prove propositions that are merely general; and how the principle therefore furnishes an inductive process correspond