Chapter V.
METHODS OF OBSERVATION.—ELIMINATION.—SINGLE AGREEMENT.
I.—The Principle of Elimination.
The essence of what Mill calls the Method of Agreement is really the elimination[1] of accidental, casual, or fortuitous antecedents. It is a method employed when we are given an effect and set to work to discover the cause. It is from the effect that we start and work back. We make a preliminary analysis of the antecedents; call the roll, as it were, of all circumstances present before the effect appeared. Then we proceed to examine other instances of the same effect, and other instances of the occurrence of the various antecedents, and bring to bear the principle that any antecedent in the absence of which the effect has appeared or on the presence of which it has not appeared may be set aside as fortuitous, as being not an indispensable antecedent. This is really the guiding principle of the method as a method of observation.
Let the inquiry, for example, be into the cause of Endemic Goitre. Instances of the disease have been collected from the medical observations of all countries over many years. Why is it endemic in some localities and not in others? We proceed on the assumption that the cause, whatever it is, must be some circumstance common to all localities where it is endemic. If any such circumstance is obvious at once, we may conclude on the mere principle of repeated coincidence that there is causal connexion between it and the disease, and continue our inquiry into the nature of the connexion. But if no such circumstance is obvious, then in the course of our search for it we eliminate, as fortuitous, conditions that are present in some cases but absent in others. One of the earliest theories was that endemic goitre was connected with the altitude and configuration of the ground, some notorious centres of it being deeply cleft mountain valleys, with little air and wind and damp marshy soil. But wider observation found it in many valleys neither narrower nor deeper than others that were exempt, and also in wide exposed valleys such as the Aar. Was it due to the geological formation? This also had to be abandoned, for the disease is often incident within very narrow limits, occurring in some villages and sparing others though the geological formation is absolutely the same. Was it due to the character of the drinking-water? Especially to the presence of lime or magnesia? This theory was held strongly, and certain springs characterised as goitre-springs. But the springs in some goitre centres show not a trace of magnesia. The comparative immunity of coast regions suggested that it might be owing to a deficiency of iodine in the drinking-water and the air, and many instances were adduced in favour of this. But further inquiries made out the presence of iodine in considerable quantities, in the air, the water, and the vegetation of districts where goitre was widely prevalent; while in Cuba it is said that not a trace of iodine is discoverable either in the air or the water, and yet it is quite free from goitre. After a huge multiplication of instances, resulting in the elimination of every local condition that had been suggested as a possible cause, Hirsch came to the conclusion that the true cause must be a morbid poison, and that endemic goitre has to be reckoned among the infectious diseases.[2]
On this negative principle, that if a circumstance comes and goes without bringing the phenomenon in its train, the phenomenon is causally independent of it, common-sense is always at work disconnecting events that are occasionally coincident in time. A bird sings at our window, for example, and the clock ticks on the mantelpiece. But the clock does not begin to tick when the bird begins to sing, nor cease to tick when the bird flies away. Accordingly, if the clock should stop at any time, and we wished to inquire into the cause, and anybody were to suggest that the stoppage of the clock was caused by the stoppage of a bird's song outside, we should dismiss the suggestion at once. We should eliminate this circumstance from our inquiry, on the ground that from other observations we knew it to be a casual or fortuitous concomitant. Hotspur's retort to Glendover (p. 297) was based on this principle. When poetic sentiment or superstition rejects a verdict of common-sense or science, it is because it imagines a causal connexion to exist that is not open to observation, as in the case of the grandfather's clock which stopped short never to go again when the old man died.
II.—The Principle of Single Agreement.
The procedure in Mill's "Method of Agreement" consists in thus eliminating fortuitous antecedents or concomitants till only one remains. We see the nature of the proof relied upon when we ask, How far must elimination be carried in order to attain proof of causal connexion? The answer is that we must go on till we have eliminated all but one. We must multiply instances of the phenomenon, till we have settled of each of the antecedents except one that it is not the cause. We must have taken account of all the antecedents, and we must have found in our observations that all but one have been only occasionally present.
When all the antecedents of an effect except one can be absent without the disappearance of the effect, that one is causally connected with the effect, due precautions being taken that no other circumstances have been present besides those taken account of.
Mill's Canon of the Method of Agreement is substantially identical with this:—