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the tree move, or that our squeezing of the bulb or our heating of the air around it raised the mercury in the thermometer. For unless we assume our own relative independence it might well be that there was some general state of affairs which made the tree sway and at the same time made our brain-cells discharge and our muscles contract as though we were swaying it; and so with the other examples. On the other hand, if our voluntary acts are spontaneous so far as the events which we are investigating are concerned, -if they are never mere effects of preceding events in the series under consideration,then, though these voluntary acts and the changes around us which follow them may sometimes coincide through mere chance, they can never be joint effects.
If there is any causal relation between them at all, the voluntary acts must be the causes, and the changes that follow must be their effects.*
* A third advantage connected with experiment is that inferences based upon it are accompanied with a greater feeling of satisfaction. The feeling of muscular exertion which comes with our own acts is associated very closely in the minds of most people with the idea of cause and effect or is really a part of it. Consequently the actual production of an effect by our own exertion seems to give an immediate feeling of the causal connection that nothing else can give.
THE JOINT METHOD OF AGREEMENT AND DIFFERENCE.
For a perfect application of the Method of Difference, as we have seen, there must be two cases alike in every respect except that in one a certain effect and its cause
Its function. are both present; and for a perfect application of the Method of Agreement there must be two cases different in every respect except that the causally related circumstances are present (or, it might be, absent) in both. Moreover there is always danger that the method in question has not been applied perfectly, because of the possible presence of other points of difference or resemblance which have not been noticed. But suppose that other points of difference or resemblance are present and are noticed, and that we cannot find any two cases in which they are not; is inference no longer possible?
It is not possible if there are only two such cases; but if there are more and they differ widely from each other, it may be. Suppose, for example, that we have all the following combinations, the letters from A to M standing for known antecedents, the letters from N to Z for known consequents, and the blanks for other possible but unknown antecedents and consequents.
I) ABCDEF-NOPQRS- 4) BCDE-OPQR2) ABGHI-NOTUV- 5) CFGH-PSTU3) ACGKL-NPTXY- 6) EHIJKL-RUVWXY
We notice that where A is present N is present, and that where A is absent N is absent (which is the same thing as saying that where A is present N is present, and where N is present A is present); and this suggests that A is the cause of N. But how shall we prove it? The Method of Difference is inapplicable, because there are no two cases (not even the first and the fourth) that differ in no respect except the presence of A and N in one case and their absence in the other. In the same way there are no two cases from which we can prove the connection by the Method of Agreement.
Yet there is a way in which the Method of Agreement can be applied, and applied doubly. Assuming that the cause of N is to be found amongst the observed antecedents and that it is always the same, we can prove from the first two cases that it is either A or B or the combination AB, for A and B are the only conditions present in both. From the first and third cases we can prove in the same way that the cause is either A or C or AC; and from the second and third that it is either A or G or AG. And if, as we have assumed, the cause is the same in all the cases, it must be A. Thus, though the presence of A and N is not the only respect in which any two cases agree, it is the only known respect in which all the three positive cases agree, and A is therefore the cause of N, if the cause of N is always the same observed circumstance. This is a perfectly legitimate application of the Method of Agreement; but, like all applications of that method, it is subject to the objections that the cause of N may not be the same in all cases, and then even if it is, the real cause may be some unknown circumstance, represented by one of the blanks.
The Method of Agreement can be applied, again, to the negative cases 4, 5, and 6. These all agree in the absence of A and N, and if instead of only three relatively simple cases we had a great number that were quite complex (as we often have in Nature), we might be inclined to say that the absence of A and N was the only respect, or rather the only respect worth considering, in which all these cases do agree. In this way we might have a double assurance, one from the positive cases and one from the negative, that A was the cause of N. The negative cases have this advantage: inference based upon them is not subject to the objection arising from the plurality of possible causes. If the absence of A is always accompanied by the absence of N whether any other antecedent is absent or not, then A not only may be the cause of N, but must be ; and it must also be the only possible cause. On the other hand the negative cases are subject to the tremendous disadvantage that it is practically impossible to prove a negative, to show that a pair of given circumstances are the only ones which can not be found in any of the cases. Consequently, when negative cases are taken by themselves they are much more dangerous to work with than positive. Yet so far as they go they tend to confirm the results based upon the positive cases, and they suggest at least that in all the cases observed there was only one cause. Because results based upon negative instances of this sort can be regarded as confirming those based on the positive, the employment of the two is called by Fowler * the Double Method of Agreement.
But these positive and negative instances can be looked at from another standpoint, and regarded as data for an indirect application of the method of difference. We can say : When N is present and every condition but A can be varied without causing its disappearance, these conditions are necessarily immaterial. In the same way when every condition but the absence of A can be varied without causing its appearance, these conditions also are immaterial. But the distinction between immaterial conditions may be ignored ; therefore the only important distinction between the two sets of cases is that in the one A and N are both present, and in the other they are both absent.' And this is all we need for the method of ing it.
* « Inductive Logic”, Macmillan, 1889.
difference. Hence the double method is called by Mill the Indirect Method of Difference. Because the method of agreement and the method of difference are both involved it is also called by him the Joint Method of Agreement and Difference. Mill's canon for the method is this:
If two or more instances in which the phenomenon occurs have only one circumstance in common, while two or more instances in which it does not occur have nothing in common save the absence of that circumstance, the circumstance in which alone the two sets of instances differ is the effect, or the cause, or an indispensable part of the cause, of the phenomenon." - This method”, Mill
says, may be called the Indirect Method of Difference, or the Joint Method of Agreement Compared
and Difference; and consists in a double employwith simple method of
ment of the Method of Agreement, each proof difference.
being independent of the other and corroborat
But it is not equivalent to a proof by the direct Method of Difference. For the requisitions of the Method of Difference are not satisfied unless we can be quite sure either that the instances affirmative of a [i.e., N, the consequent in question] agree in no antecedent whatever but A [the antecedent in question], or that the instances negative of a agree in nothing but the negation of A. Now, if it were possible, which it never is, to have this assurance, we should not need the joint method; for either of the two sets of instances separately would then be sufficient to prove causation. This indirect method, therefore, can only be regarded as a great extension and improvement of the Method of Agreement, but not as participating in the more cogent nature of the Method of Difference." *
Mill is right in saying that the Joint Method will not give absolute certainty. But then neither will the Method of Difference, applied in our common human ignorance of a vast number of surrounding conditions. A theoretically perfect
* “ Logic”, Bk. III, Chap. VIII, Sec. 4.