CHAPTER IV.

METHODS OF OBSERVATION.--SINGLE DIFFERENCE.

I.--THE PRINCIPLE OF SINGLE DIFFERENCE.--MILL'S "CANON".

On what principle do we decide, in watching a succession of phenomena, that they are connected as cause and effect, that one happened in consequence of the happening of another? It may be worded as follows:--

_When the addition of an agent is followed by the appearance or its subtraction by the disappearance of a certain effect, no other influential circumstance having been added or subtracted at the same time or in the meantime, and no change having occurred among the original circumstances, that agent is a cause of the effect._

On this principle we would justify our belief in the causal properties of common things--that fire burns, that food appeases hunger, that water quenches thirst, that a spark ignites gunpowder, that taking off a tight shoe relieves a pinched foot. We have observed the effect following when there was no other change in the antecedent circumstances, when the circumstance to which we refer it was simply added to or subtracted from the prior situation.

Suppose we doubt whether a given agent is or is not capable of producing a certain effect in certain circumstances, how do we put it to the proof? We add it singly or subtract it singly, taking care that everything else remains as before, and watch the result. If we wish to know whether a spoonful of sugar can sweeten a cup of tea, we taste the tea without the sugar, then add the sugar, and taste again. The isolated introduction of the agent is the proof, the experiment. If we wish to know whether a pain in the foot is due to a tight lacing, we relax the lacing and make no other change: if the pain then disappears, we refer it to the lacing as the cause. The proof is the disappearance of the pain on the subtraction of the single antecedent.

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.

When the circumstances are simple and the effect follows at once, as when hot water scalds, or a blow with a stick breaks a pane of glass, there can be no doubt of the causal connexion so far, though plenty of room for further inquiry into the why. But the mere succession of phenomena may be obscure. We may introduce more than one agent without knowing it, and if some time elapses between the experimental interference and the appearance of the effect, other agents may come in without our knowledge.

We must know exactly what it is that we introduce and all the circumstances into which we introduce it. We are apt to ignore the presence of antecedents that are really influential in the result. A man heated by work in the harvest field hastily swallows a glass of water, and drops down dead. There is no doubt that the drinking of the water was a causal antecedent, but the influential circumstance may not have been the quantity or the quality of the liquid but its temperature, and this was introduced into the situation as well as a certain amount of the liquid components. In making tea we put in so much tea and so much boiling water. But the temperature of the pot is also an influential circumstance in the resulting infusion. So in chemical experiments, where one might expect the result to depend only upon the proportions of the ingredients, it is found that the quantity is also influential, the degree of heat evolved entering as a factor into the result. Before we can apply the principle of single difference, we must make sure that there is really only a single difference between the instances that we bring into comparison.

The air-pump was invented shortly before the foundation of the Royal Society, and its members made many experiments with this new means of isolating an agent and thus discovering its potentialities.

For example, live animals were put into the receiver, and the air exhausted, with the result that they quickly died. The absence of the air being the sole difference, it was thus proved to be indispensable to life. But air is a composite agent, and when means were contrived of separating its components, the effects of oxygen alone and of carbonic acid alone were experimentally determined.

A good example of the difficulty of excluding agencies other than those we are observing, of making sure that none such intrude, is found in the experiments that have been made in connexion with spontaneous generation. The question to be decided is whether life ever comes into existence without the antecedent presence of living germs. And the method of determining this is to exclude all germs rigorously from a compound of inorganic matter, and observe whether life ever appears. If we could make sure in any one case that no germs were antecedently present, we should have proved that in that case at least life was spontaneously generated.

The difficulty here arises from the subtlety of the agent under observation. The notion that maggots are spontaneously generated in putrid meat, was comparatively easy to explode. It was found that when flies were excluded by fine wire-gauze, the maggots did not appear.

But in the case of microscopic organisms proof is not so easy. The germs are invisible, and it is difficult to make certain of their exclusion. A French experimenter, Pouchet, thought he had obtained indubitable cases of spontaneous generation. He took infusions of vegetable matter, boiled them to a pitch sufficient to destroy all germs of life, and hermetically sealed up the liquid in glass flasks. After an interval, micro-organisms appeared. Doubts as to the conclusion that they had been spontaneously generated turned upon two questions: whether all germs in the liquid had been destroyed by the preliminary boiling, and whether germs could have found access in the course of the interval before life appeared. At a certain stage in Pouchet's process he had occasion to dip the mouths of the flasks in mercury. It occurred to Pasteur in repeating the experiments that germs might have found their way in from the atmospheric dust on the surface of this mercury. That this was so was rendered probable by his finding that when he carefully cleansed the surface of the mercury no life appeared afterwards in his flasks.

The application of the principle in human affairs is rendered uncertain by the immense complication of the phenomena, the difficulty of experiment, and the special liability of our judgments to prejudice. That men and communities of men are influenced by circumstances is not to be denied, and the influence of circumstances, if it is to be traced at all, must be traced through observed facts.

Observation of the succession of phenomena must be part at least of any method of tracing cause and effect. We must watch what follows upon the addition of new agencies to a previously existing sum. But we can seldom or never get a decisive observation from one pair of instances, a clear case of difference of result preceded by a single difference in the antecedents. The simple Method of Experimental Addition or Subtraction is practically inapplicable. We can do nothing with a man analogous to putting him into a hermetically sealed retort.

Any man or any community that is the subject of our observations must be under manifold influences. Each of them probably works some fraction of the total change observable, but how are they to be disentangled? Consider, for example, how impossible it would be to prove in an individual case, on the strict principle of Single Difference, that Evil communications corrupt good manners. Moral deterioration may be observed following upon the introduction of an evil companion, but how can we make sure that no other degrading influence has operated, and that no original depravity has developed itself in the interval? Yet such propositions of moral causation can be proved from experience with reasonable probability. Only it must be by more extended observations than the strict Method of Difference takes into account. The method is to observe repeated coincidences between evil companionship and moral deterioration, and to account for this in accordance with still wider observations of the interaction of human personalities.

For equally obvious reasons the simple Method of Difference is inapplicable to tracing cause and effect in communities. Every new law or repeal of an old law is the introduction of a new agency, but the effects of it are intermixed with the effects of other agencies that operate at the same time. Thus Professor Cairnes remarks, concerning the introduction of a high Protective Tariff into the United States in 1861, that before its results could appear in the trade and manufacture of the States, there occurred (1) The great Civil War, attended with enormous destruction of capital; (2) Consequent upon this the creation of a huge national debt, and a great increase of taxation; (3) The issue of an inconvertible paper currency, deranging prices and wages; (4) The discovery of great mineral resources and oil-springs; (5) A great extension of railway enterprise. Obviously in such circumstances other methods than the Method of Difference must be brought into play before there can be any satisfactory reasoning on the facts observed. Still what investigators aim at is the isolation of the results of single agencies.

[Footnote 1: Prof. Bain, who adopts Mill's Canon, silently drops the words within brackets. They seem to be an inadvertence. The "circumstance," in all the examples that Mill gives, is an antecedent circumstance. Herschel's statement, of which Mill's is an adaptation, runs as follows: "If we can either find produced by nature, or produce designedly for ourselves, two instances which agree exactly in all but one particular and differ in that one, its influence in producing the phenomenon, if it have any, must thereby be rendered apparent".]

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:--

When two or more instances of the phenomenon under investigation have only one circumstance in common, the circumstance in which alone all the instances agree is the cause (or effect) of the given phenomenon.

Herschel's statement, on which this canon is founded, runs as follows: "Any circumstance in which all the facts without exception agree, may be the cause in question, or if not, at least a collateral effect of the same cause: if there be but one such point of agreement, the possibility becomes a certainty".

All the instances examined must agree in one circumstance--hence the title Method of Agreement. But it is not in the agreement merely that the proof consists, but the agreement in one circumstance combined with difference in all the other circumstances, when we are certain that every circumstance has come within our observation. It is the singleness of the agreement that constitutes the proof just as it is the singleness of the difference in the Method of Difference.[3]

It has been said that Mill's Method of Agreement amounts after all only to an uncontradicted _Inductio per enumerationem simplicem_, which he himself stigmatised as Induction improperly so called. But this is not strictly correct. It is a misunderstanding probably caused by calling the method that of agreement simply, instead of calling it the Method of Single Agreement, so as to lay stress upon the process of elimination by which the singleness is established. It is true that in the course of our observations we do perform an induction by simple enumeration. In eliminating, we at the same time generalise. That is to say, in multiplying instances for the elimination of non-causes, we necessarily at the same time multiply instances where the true causal antecedent, if there is only one possible, is present. An antecedent containing the true cause must always be there when the phenomenon appears, and thus we may establish by our eliminating observations a uniformity of connexion between two facts.

Take, for example, Roger Bacon's inquiry into the cause of the colours of the rainbow. His first notion seems to have been to connect the phenomenon with the substance crystal, probably from his thinking of the crystal firmament then supposed to encircle the universe. He found the rainbow colours produced by the passage of light through hexagonal crystals. But on extending his observations, he found that the passage of light through other transparent mediums was also attended by the phenomenon. He found it in dewdrops, in the spray of waterfalls, in drops shaken from the oar in rowing. He thus eliminated the substance crystal, and at the same time established the empirical law that the passage of light through transparent mediums of a globular or prismatic shape was a causal antecedent of the rainbow colours.[4]

Ascertainment of invariable antecedents may thus proceed side by side with that of variable antecedents, the use of the elimination being simply to narrow the scope of the inquiry. But the proof set forth in Mill's Canon does not depend merely on one antecedent or concomitant being invariably present, but also on the assumption that all the influential circumstances have been within our observation. Then only can we be sure that the instances have _only one_ circumstance in common.

The truth is that owing to the difficulty of fulfilling this condition, proof of causation in accordance with Mill's Canon is practically all but impossible. It is not attained in any of the examples commonly given. The want of conclusiveness is disguised by the fact that both elimination and positive observation of mere agreement or uniform concomitance are useful and suggestive in the search for causes, though they do not amount to complete proof such as the Canon describes. Thus in the inquiry into the cause of goitre, the elimination serves some purpose though the result is purely negative.

When the inquirer is satisfied that goitre is not originated by any directly observable local conditions, altitude, temperature, climate, soil, water, social circumstances, habits of exertion, his search is profitably limited. And mere frequency, much more constancy of concomitance, raises a presumption of causal connexion, and looking out for it is valuable as a mode of reconnoitring. The first thing that an inquirer naturally asks when confronted by numerous instances of a phenomenon is, What have they in common? And if he finds that they have some one circumstance invariably or even frequently present, although he cannot prove that they have no other circumstance in common as the Cannon of Single Agreement requires, the presumption of causal connexion is strong enough to furnish good ground for further inquiry. If an inquirer finds an illness with marked symptoms in a number of different households, and finds also that all the households get their milk supply from the same source, this is not conclusive proof of causation, but it is a sufficient presumption to warrant him in examining whether there is any virulent ingredient in the milk.

Thus varying the circumstances so as to bring out a common antecedent, though it does not end in exact proof, may indicate causal connexion though it does not prove what the nature of the connexion is. Roger Bacon's observations indicated that the production of rainbow colours was connected with the passage of light through a transparent globe or prism. It was reserved for Newton to prove by other methods that white light was composed of rays, and that those rays were differently refracted in passing through the transparent medium. We have another example of how far mere agreement, revealed by varying the circumstances, carries us towards discovery of the cause, in Wells's investigation of the cause of dew. Comparing the numerous instances of dew appearing without visible fall of moisture, Wells found that they all agreed in the comparative coldness of the surface dewed. This was all the agreement that he established by observation; he did not carry observation to the point of determining that there was absolutely no other common circumstance: when he had simply discovered dewed surfaces, he tried next to show by reasoning from other knows facts how the coldness of the surface affected the aqueous vapour of the neighbouring air. He did not establish his Theory of Dew by the Method of Agreement: but the observation of an agreement or common feature in a number of instances was a stage in the process by which he reached his theory.