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vestigation occurs, and an instance in which it does not occur, have every [other] circumstance in common save one, that one occurring only in the former ; the circumstance in which alone the two instances differ, is the effect, or the cause, or an indispensable part of the cause, of the phenomenon.'' To put the same thing more symbolically : If there is a case in which all the antecedents can be represented by the letters A, B, C, and D and all the consequents by the letters W, X, Y, and Z, and•another case in which all the antecedents can be represented by the letters A, B, and C, and all the consequents by W, X, and Y, then the antecedent D is the cause or part of the cause of the consequent Z.
A girl dressed in a blue gown and carrying some books walks quietly across a room and as she passes over a certain
place a squeaky noise is heard. Soon after, a of Agree- boy dressed wholly differently, talking, and car
rying nothing at all, walks over the same place, and as he does so the noise is heard again. Now if we assume that the noise has the same cause in both cases and if we can be sure that walking over the same spot was the only circumstance except the noise that was the same in both, i.e., the only one in which the two instances agreed, then we cannot help concluding that walking over that spot caused the noise. The italicized words explain why this inference is drawn by the Method of Agreement.
This method, like the last, depends on the principle of exclusion; for we cannot be sure that the circumstance we have picked out is the only point of agreement until we have examined every other circumstance and found that no one of them is the same in both cases.
In the example just given the effect was produced at the time of the observation, so that the things involved underwent a change. But the method of agreement is also applicable to cases in which we cannot observe the origin of the effect. Suppose, for example, that on the top of every high mountain
which we climb we find the air to be cooler than in the surrounding country, no matter where the mountains are, what their shape, or what they are made of. As soon as we can be sure that the elevation is the only point of agreement between them all (except the lower temperature) we can infer that the greater elevation has something to do with the lower temperature. Mill's canon for the method of agreement is this : "
If two or more instances of the phenomenon under investigation have only one circumstance in common [and if that phenomenon is always produced by the same circumstance; then] the circumstance in which alone all the instances agree is the cause (or effect) of the given phenomenon. To put it more symbolically : If all the antecedents in one case can be represented by the letters ABCD and all the consequents by WXYZ, and in another case all the antecedents can be represented by EFGD and all the consequents by KLMZ, and if Z always has the same cause, then D is the cause of Z.
The methods of agreement and difference both depend upon the principle of exclusion, and in both methods this principle has been properly applied only if we Does either have been correct in assu
suming that no point of really exagreement or difference (as the case may be) escaped our observation. But this is no small assumption. How do we know that the mountains we visit do not happen by the merest chance to lie over relatively cool places in the centre of the earth, or to be packed with ice, or to lie in places where cool currents of air turn downwards towards the earth ? How do we know that when the girl and the boy both passed the same spot a cat in the cellar did not happen to catch a mouse which made the noise as it was caught ? How do we know that the ball the child struck was not possessed by a demon which happened to move it at that instant, and that the one swinging in the wind was not similarly possessed ? In short, it is only an infinitesimal part of nature that we can pretend to have observed, and how can we possibly prove that the only point of agreement or the only point of difference we happen to have noticed is the only one there is ?
We can not; and for that reason our inductive argument will always be at least theoretically inconclusive. But all reasoning, even deductive, is for the sake of practice; and from the practical standpoint the force of this objection can be considerably weakened. As mere theorists the thought of the almost infinite search that must be made before we can say we have found the only point of agreement or the only point of difference between two situations appals us. As practical beings it does not ; for when we begin to reason about the connections in Nature we are not in the position of strangers dropped from another universe. We are in the midst of affairs. We have learned in a practical way that a vast number of agreements and differences between situations can be thrown out immediately as immaterial ; and we dismiss them so unhesitatingly that we are inclined to laugh at the theorist instead of answering him when he asks how we know that the ball did not swing because a Chinaman laughed on the other side of the globe, or that the mountains we saw were not cool because people lived in the valleys. Thus the practical man approaches his inductive problem with vastly more data than he states; he does not hesitate to distinguish between kinds of agreement and difference that may be material and those that are certainly immaterial ; and thus most of the elimination is already performed.
Not only have we this practical belief that the possible causes are after all not so very numerous, but we have it in our power to diminish the chance that any of them have been overlooked by observing as many and as different cases as possible.
The more mountains we examine and the more differenc there seems to be between them in every respect except height and coolness, the greater is the chance that there is no other point of resemblance common to them all.
The more often we notice that light things begin to move when the wind begins to blow, the less chance there is that, in every
case we noticed, some entirely different event (which we did not notice but which might have caused the movement) took place at the very instant the wind rose. Mere coincidences-whether in space or in time—may be expected occasionally, but occasionally only.
Whether we shall use the Method of Difference or the Method of Agreement in any particular case often depends upon what data we have to work with; and
Advantages therefore we cannot always choose between them. It is worth while nevertheless to discuss some of their relative advantages and disadvantages.
The methods of Difference and Agreement are both subject to the defect already pointed out that we may fail to observe or consider some essential circumstance, and may thus mistake some merely accidental concomitant for the true cause. With the method of Difference the circumstance overlooked would be a point of difference between the objects compared ; with the method of Agreement it would be a point of agreement.
A much more certain and important difference in the practical application of the two methods grows out of the fact that much the same result can often be pro
Plurality of duced by any one of several causes. You can possible kill a man in a great many different ways; you can poison him with any one of a great many different drugs. Rain is not the only thing that can wet a lawn ; and sunshine is not the only thing that can dry it. This is called the principle of the Plurality of Possible Causes or the Vicariousness of Causes. Let us see how it affects each of our methods.
If we find the antecedents ABC accompanied by the consequents XYZ, and the antecedents AB accompanied by the consequents XY, and if we know that these are all the essential facts, we can conclude that, under the circumstances AB, C is the cause or a necessary part of the cause of Z. This is the method of difference, and it is not affected by the plurality of possible causes,
But suppose that in one case we have the antecedents ABC and the consequents XYZ, and in another the antecedents EFC and the consequents VWZ, and that these are all the essential circumstances. If Z has the same cause in both cases, we know that it cannot be anything but C; but it need not have the same cause in both cases. How do we know, then, that it is not caused by A in one case and by E in the other? If I have coffee, toast, and eggs for breakfast one day, and water, hot biscuit, and eggs the next, and if I have indigestion on both days and know or assume that in each case it was caused by something which I had for breakfast, it may have been caused by the eggs on both occasions ; and in the absence of any further information that is the most natural inference. And yet it is possible that the trouble was due to the coffee on the first day and to the hot biscuit on the second, while the eggs were all the time perfectly harmless.
This plurality of possible causes constitutes what Mill calls or the characteristic imperfection” of the Method of Agreement,-an imperfection which makes it distinctly inferior to the Method of Difference.
Where answers suggested by the method of agreement cannot be tested by some form of the method of difference, the uncertainty arising from the plurality of possible causes can be indefinitely diminished by the multiplication of variations. If we cannot try the eggs alone, it may be that we can try them with different accompaniments on a great many different days, until we are driven to the conclusion that if they do not cause the trouble, they are about the only things one can eat that do not. But farther than this we cannot go by the Method of Agreement; and it is not often we can
go so far.
This difficulty growing out of the plurality of possible causes I have spoken of as practical. It is due partly to the practical impossibility of ascertaining all the antecedents and all the consequents in any set of cases, partly to the practical