Logic, Inductive and Deductive

by William Minto

The principle on which we decide that there is causal connexion is the same whether we make the experimental changes ourselves or merely watch them as they occur—the only course open to us with the great forces of nature which are beyond the power of human manipulation. In any case we have proof of causation when we can make sure that there was only one difference in the antecedent circumstances corresponding to the difference of result.

Mill's statement of this principle, which he calls the Canon of the Method of Difference, is somewhat more abstract, but the proof relied upon is substantially the same.

If an instance in which the phenomenon under investigation occurs, and an instance in which it does not occur, have every 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][¹] the cause, or an indispensable part of the cause, of the phenomenon.

Mill's statement has the merit of exactness, but besides being too abstract to be easy of application, the canon is apt to mislead in one respect. The wording of it suggests that the two instances required must be two separate sets of circumstances, such as may be put side by side and compared, one exhibiting the phenomenon and the other not. Now in practice it is commonly one set of circumstances that we observe with a special circumstance introduced or withdrawn: the two instances, the data of observation, are furnished by the scene before and the scene after the experimental interference. In the case, for example, of a man shot in the head and falling dead, death being the phenomenon in question, the instance where it does not occur is the man's condition before he received the wound, and the instance where it does occur is his condition after, the single circumstance of difference being the wound, a difference produced by the addition or introduction of a new circumstance. Again, take the common coin and feather experiment, contrived to show that the resistance of the air is the cause of the feather's falling to the ground more slowly than the coin. The phenomenon under investigation is the retardation of the feather. When the two are dropped simultaneously in the receiver of an air-pump, the air being left in, the feather flutters to the ground after the coin. This is the instance where the phenomenon occurs. Then the air is pumped out of the receiver, and the coin and the feather being dropped at the same instant reach the ground together. This is the instance where the phenomenon does not occur. The single circumstances of difference is the presence of air in the former instance, a difference produced by the subtraction of a circumstance.

Mill's Canon is framed so as to suit equally whether the significant difference is produced by addition to or subtraction from an existing sum of circumstances. But that is misleading in so far as it suggests that the two instances must be separate sets of circumstances, is shown by the fact that it misled himself when he spoke of the application of the method in social investigations, such as the effect of Protection on national wealth. "In order," he says, "to apply to the case the most perfect of the methods of experimental inquiry, the Method of Difference, we require to find two instances which tally in every particular except the one which is the subject of inquiry. We must have two nations alike in all natural advantages and disadvantages; resembling each other in every quality physical and moral; habits, usages, laws, and institutions, and differing only in the circumstance that the one has a prohibitory tariff and the other has not." It being impossible ever to find two such instances, he concluded that the Method of Difference could not be applied in social inquiries. But really it is not necessary in order to have two instances that we should have two different nations: the same nation before and after a new law or institution fulfils that requirement. The real difficulty, as we shall see, is to satisfy the paramount condition that the two instances shall differ in a single circumstance. Every new enactment would be an experiment after the Method of Difference, if all circumstances but it remained the same till its results appeared. It is because this seldom or never occurs that decisive observation is difficult or impossible, and the simple method of difference has to be supplemented by other means.

To introduce or remove a circumstance singly is the typical application of the principle; but it may be employed also to compare the effects of different agents, each added alone to exactly similar circumstances. A simple example is seen in Mr. Jamieson's agricultural experiments to determine the effects of different manures, such as coprolite and superphosphate, on the growth of crops. Care is taken to have all the antecedent circumstances as exactly alike as possible, except as regards the agency whose effects are to be observed. A field is chosen of uniform soil and even exposure and divided into plots: it is equally drained so as to have the same degree of moisture throughout; the seed is carefully selected for the whole sowing. Between the sowing and the maturing of the crop all parts of the field are open to the same weather. Each plot may thus be regarded as practically composing the same set of conditions, and any difference in the product may with reasonable probability be ascribed to the single difference in the antecedents, the manures which it is desired to compare.

II.—Application of the Principle.

The principle of referring a phenomenon to the only immediately preceding change in antecedent circumstances that could possibly have affected it, is so simple and so often employed by everybody every day, that at first we do not see how there can be any difficulty about it or any possibility of error. And once we understand how many difficulties there are in reaching exact knowledge even on this simple principle, and what care has to be taken, we are apt to overrate its value, and to imagine that it carries us further than it really does. The scientific expert must know how to apply this principle, and a single application of it with the proper precautions may take him days or weeks, and yet all that can be made good by it may carry but a little way towards the knowledge of which he is in search.