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application of the Method of Difference will give a theoretically perfect proof; but none of our applications of the method are theoretically perfect, and a good many of them are not practically perfect either. Mill and other writers on
logic tell us that experiments are usually based upon the - Method of Difference and that that is one reason why experi
ment is better than mere observation. It is true that they are based on that method in any single experiment,- -we add one new circumstance and see if the effect in question follows. But why are the conclusions based on experiment sometimes erroneous ? Why do scientists all over the world try to repeat and thus 'verify' each others' experiments, if any one could be sure that the method was rigorously applied the first time? The fact of the matter is that in all cases where experiment is possible, whether in common life or in science, the final appeal is not usually to the Method of Difference, but to the Joint Method. I destroy a frog's brain, suspend the creature by the nose, and dip its foot into a solution of acid ; and a second or two later I see the foot lifted out of the acid just as if the brainless frog knew what it was doing. By the Method of Difference I reason that the contact with the acid was what made the frog lift the foot up. But am I satisfied with this one experiment? If such an occurrence happens to be unfamiliar and I am really interested in the question, will I not try the experiment again under as many different conditions as I can think of, and ask others to do the same? And if everybody gets the same result, will they not then have two groups of cases to compare, the members of each group varying in as many respects as possible except the two in question ? In one group there are all the cases in which the foot has not yet touched the acid and has not been drawn up; in the other are all the cases in which the foot has touched the acid and has been drawn up. And these are the kind of data to which we apply the Joint Method.
In conditions known to be theoretically perfect one experiment based on the Method of Difference would be sufficient to give absolute proof of a causal relation; but because there are always a great many possible sources of error, we can always feel surer of conclusions when the experiments upon which they are based have been performed many times under different conditions than when they have been performed only once. And thus even where the Method of Difference is most applicable we appeal from it to the Joint Method.
COUNTERACTING AND COMPLEX CAUSES.
We have reasoned thus far on the assumption that an adequate cause is invariably accompanied by its effect. We have virtually said: “The effect may be present without this particular cause, because the same effect may be due to any one of several causes; but ing causes. that does not imply that the cause can be present without its effect, and if what we supposed to be a cause of a given effect is ever found to be present without the effect, we were mistaken in supposing it was the cause (though it might have been part of the cause).
If A causes N, N
may sometimes be present without A, but A can never be present without N.' This is the principle on which we have been reasoning up to the present, and if we were in a world in which nothing else could come between 'A and N, or affect their relations to each other, reasoning based on this principle would always be correct. As it is, it is not. It
be that A is a perfectly adequate cause of N and yet that it is sometimes present without N. In the presence of a 'Counteracting Cause' a cause perfectly adequate in itself will fail of its effect. The swift current of a river causes things floating in it to drist down the stream; and yet if there is a hurricane blowing in the opposite direction, the things may drift up and not down. The working of the engines makes the ship move; but now she is fast on the rocks and for all their work the engines cannot move her.
Without going into any theoretical discussion, the practical lesson to draw from such cases is this: There is a difference between saying that a cause always produces its natural effects and saying that it always tends to produce them; and this latter is all we have a right to say. Put more concretely, this rule means that if we are searching for the cause of a given effect N and find that A is sometimes present when N is not, we must not conclude from this that A is not the cause of N, until we are sure that there is nothing present which can counteract A's effect.
If we know what can counteract the effect of A, or, what amounts in this case to the same thing, what can prevent the production of N, our task of discovering the relation between A and N will be easy enough. But if we do not know enough about either A or N to say what would prevent the one from causing the other, then our task will be very much more difficult. If A and N occur together often enough to make us suspect that A is really a cause of N, though sometimes counteracted in its working by G, H, or J, we must simply leave the matter doubtful until we can make or find conditions simple enough or varied enough to let us infer something about the real nature of some of these influences.
Sometimes a situation may be so complicated that we have to deal not only with several kinds of causes and counteracting causes, but with still other antecedents that counteract the counteracting causes.
But however complicated our problem may be, the principle of exclusion upon which we must depend for its solution remains the same.
The possibility of counteracting causes makes it possible to commit a blunder of precisely the opposite kind from that made possible by the plurality of possible causes. forget that practically the same effect can be produced by any one of several causes, we may assert that something is the cause of this effect, when it is not the cause at all, simply because it happens to be the only one thing present in all
the cases we have observed. On the other hand, if we forget that a cause is sometimes counteracted, we may deny that something is the cause, when it really is, because it is sometimes present without the effect. Thus, if we are careless, the
presence of a plurality of causes may make us find false causes, and the presence of a counteracting cause may make us overlook true ones.
Methods of investigating causal relations have been discussed thus far as though we assumed that every effect had some one simple cause and every cause some one
simple effect. But it often happens that several pounded or
combined'. causes act together to produce a given effect and that there is some reason why we should not regard them as
There are two ways in which causes can act together to produce a joint effect. Sometimes the effect of each one of them separately is like that of each of the others and like that of the group as a whole. Sometimes the separate effect of each is unlike the effect of each of the others, and the effect of all together is unlike the effect of any one.
Here is a case of the first sort. The amount of money that a man has at the end of the year depends upon how much he had to start with, what he made or lost each day in his regular business, what he made or lost in other ways, what he spent for regular household purposes, what he spent for amusement, what he gave away. In his cash account he sets down all the expenditures on one page and all the receipts on another, adds all the items on the same page together, and subtracts them from the total of the other page. In his balance it makes absolutely no difference what the money that he spent was spent for. If he wants a certain balance and finds before the end of the year that he is spending too much for rent and groceries, he may make up for it by cutting down his expenditures for recreation and charity. All the forces dealt with in mechanics are causes of this sort. When one is ' added to' or 'subtracted from another the