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presence of change in the world. It may be remembered that the relations of things (as distinguished from the laws on thought pure, and simple) upon which deductive reasoning turns are individual identity, similarity, and the coexistence of qualities or other attributes. Now all three of these relations could exist-identity after a fashion and the other two very well—in a world in which there was no change, in which nothing ever happened or came to pass; and it may be remembered that this notion of change was so remote from the conception of the universe involved in deduction that the rules of the syllogism have been declaring for centuries that contrary relations prove objects to be non-identical, without ever stopping to say that this ruie only holds when the objects in question are observed at the same time, or at least nearly enough at the same time to make it certain that these particular relations could not have changed. Induction on the other hand has to do almost altogether with a world of change; and for it the most important relation of all is the relation of one change or event to another.
A third characteristic of induction is that it rests at bottom upon a tendency, unconscious or conscious, vague or definite, to act as though we took for granted that in the changes and other relations of things we might expect a certain uniformity. This tendency is so important that we must presently give a longer account of it.
The fourth characteristic of Induction is that when it reaches the critical stage it attempts more or less seriously to find out and examine every case of a given sort in the world or the part of the world under consideration. Let us explain this with reference to each of the figures separately.
If we wish to find out whether it is true that every member of a certain family has light hair, the simplest inductive method is to look at each one of them, and if we find none that have not and if we are sure that we have examined them all, we can be sure that the statement is true. we are able to gain the singular or the universal proposition
In this way
which is required as one of the premises of a deductive argument in the first figure.
According to the second figure dissimilarity proves that objects are not identical, but similarity does not prove that they are.
What then will prove it? If I leave a book of mine in a library and the next day find one there which looks precisely like it, how can I make sure that it is mine, and not some other copy of the same work? I can make sure of it if I make sure that no book has gone out of the library since mine was left there, and then examine every book in it, but find no other that looks precisely like the one that I left. Similarity will not ordinarily prove identity, for there is no limit to the number of things that may resemble each other ; but if we are certain that some former object still exists in a certain part of the world and still retains its former appearance, and if we are equally certain that in that part of the world there is now only one object with that appearance, we may be certain that the two are identical. Thus by a sufficiently exhaustive examination of other things we can prove the identity of those in question, where the second figure of the syllogism which does not look beyond the objects given can prove only non-identity.
The third figure proves from the coincidence of two given relations that they are compatible; but it can never go further and prove that they are necessarily connected. Induction can; and again it proceeds by going beyond the two given relations and attempting to consider a worldful. Suppose for example that an event A is immediately followed by the event K.
For deduction this proves that the succession of these two events, A and K, is not impossible ; and for induction this one case taken by itself proves nothing more. But if we assume, as induction does, that every event has a cause with which it is necessarily connected, and if there is any way—whether direct or indirect—of going over all the events which preceded K and of showing that there was no event but A which could have caused it, then we can be
quite sure that A did cause it. And something of this sort is what induction attempts.
Thus there is an inductive process corresponding to each figure of the syllogism, and in each case the inductive process attempts to reach conclusions which the deductive does not, by looking beyond a mere pair of given relations and attempting to exhaust the universe.
One of the most obvious differences between deduction and induction is that in deduction any conclusion that fol
lows from the given premises at all seems to folDifference
low with absolute certainty, while in inductive certainty.
reasoning it only follows with a greater or less degree of probability. This difference is striking and important, and it is sometimes thought to depend upon some absolutely fundamental difference between the two methods. But it does not. So far as the strictly demonstrative side of the two is concerned their problems are precisely the same, namely: to find whether the conditions named in the premises could exist in the assumed universe in the absence of the conditions named in the conclusion. The difference in certainty is due merely to the greater complexity of the material which induction attempts to handle. In the first place, the relations of things—the laws of the universe—which induction has to assume are more complex; in induction we must reckon with the uniformity of nature and all that that implies as well as with the simpler relations of things assumed in deduction. Then, in the second place, the particular facts that have to be built together according to the general relations of our universe are—as we have seen-ever so much more numerous in induction-often indeed innumerable, and even when we know that all the facts are in our possession it is a much more difficult and uncertain thing to realize how they must all fit together when there are a great number of them than when there are only two. Moreover, in induction, where the ideal is to search through the whole world and find every fact of a given sort, we usually know perfectly well that the search has been incomplete, and even when we have tried to make it complete there is always the chance that something has been overlooked and that we really have not exhausted the universe after all. This is why the inductive sciences are being continually corrected, while such a science as geometry (which does not demand this exhaustive search through the world) stands from the first with little or no correction. Assume the uniformity of nature, and a ' perfect induction', or one which really exhausted the universe in question, would give quite as much certainty as deduction ; but in this complex world of which we are so ignorant, perfect induction is little more than an ideal. We come as near to it as we conveniently can and then begin to guess, trusting to future experience to correct us if the guess
But the fact that in induction we often have to guess for lack of premises or for lack of skill to put them together does not prove that if anybody had the premises and had the skill his inductive construction of facts would be any less infallible than his deductive.
THE UNIFORMITY OF NATURE.
How we come to
ACCORDING to the old definition, “Man is a rational animal”; and to say this means much more than merely to say he is rational. Animals are distinguished from sticks and
stones by the fact that they can feel and move. believe in it. The movement comes in response to the feeling; but animals differ from each other with respect to the connection between the two. With some the movement follows upon the feeling directly, uniformly, and, so far as we can judge, inevitably. Others can postpone the movement until they have stopped and considered. Man can stop longer and consider more than any other animal, and for that reason he is called pre-eminently rational. But even man cannot always stop and consider how to act in response to his impressions. He cannot help swallowing anything which has begun to go down his throat; he cannot endure more than a certain amount of pain without crying out; and without considerable training he cannot avoid raising his arms, shutting his eyes, or drawing his head back when a blow is aimed at his face. Reflex acts like these shade so imperceptibly into the acts which we call purely voluntary that it is often impossible to say whether some act, even if it is our own, belongs to the one class or to the other. Moreover, there is good reason to believe that all voluntary acts are built up on a basis