The Making of Arguments

by J. H. Gardiner

The method of agreement has been defined as follows:

If 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.[³⁴][!--Note--]

A few examples, which might easily be multiplied, will show how constantly we use this method in everyday life. Suppose that a teacher is annoyed at somewhat irregular intervals by whispering and laughing in the back of the schoolroom, for which he can find no cause, but that presently he notices that whenever a certain pair of boys sit together there the trouble begins; he infers that these two boys are the cause of the trouble.

In the old days before it had been discovered that the germs of malaria are carried by mosquitoes, the disease was ascribed to a miasma which floated over low ground at night; and the innkeepers of the Roman Campagna, where malaria had almost driven out the population, urged their guests never to leave their windows open at night, for fear of letting in the miasma. In the lights of those days this was good reasoning by the method of agreement, for it was common observation that of all the many kinds of people who slept with their windows open most had malaria. We are constantly using this method in cases of this sort, where from observation we are sure that a single cause is at work under diverse circumstances. If the cases are numerous enough and diverse enough, we arrive at a safe degree of certainty for practical purposes. As the case just cited shows, however, the method does not establish a cause with great certainty. No matter how many cases we gather, if a whole new field related to the subject happens to be opened up, the agreement may be shattered.

The method of difference, which in some cases does establish causes with as great certainty as is possible for human fallibility, works in the opposite way: instead of collecting a large number of cases and noting the single point of agreement, it takes a single case and varies a single one of its elements. The method has been stated as follows:

If an instance in which the phenomenon 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 the cause, or an indispensable part of the cause, of the phenomenon.[³⁵][!--Note--]

The principle is clearer and more apprehensible in the concrete example than in the abstract statement; as a matter of fact it is applied in every experimental search for a cause. The Agricultural College of New York, for example, in the course of certain experiments on apple orchards, bought an orchard which had not been yielding well, and divided it into halves; one half was then kept plowed and cultivated, the other half was left in grass; otherwise the treatment was the same. When the half which was kept cultivated gave a much larger yield than the other, it was safe to infer that the cultivation was the cause of the heavier yield. Dr. Ehrlich, the great German pathologist, is said to have tried six hundred and five different substances before he found one which would kill the germ of a certain disease; in each experiment he was using the method of difference, keeping the conditions the same in all except a single point, which was the addition of the substance used in that particular experiment. Wherever the conditions of an experiment can be thus controlled, the method of difference gives a very accurate way of discovering causes. With advancing knowledge a supposed cause may be in turn analyzed in such a way that each of its parts can be separately varied, in order to come more closely to the actual sequence involved.

It has been pointed out[³⁶][!--Note--] that the two methods are really statements of what is required for the verification of a theory at two stages of its growth: when we are first getting a glimpse of a causal connection between two facts we collect all the cases in which they occur in as much variety as possible, to see if the connection is really universal; then, having established the universal sequence, we come to close quarters with it in a single critical instance, varying the conditions singly until we run down the one without which the effect cannot take place.

No neater and more illuminating example of this relation between the two methods and the successful working of them can be found than that in the article by General Steinberg, "Yellow Fever and Mosquitoes" (p. 251). In that case first Dr. Carlos Finlay of Havana, and then Dr. Sternberg himself, had become convinced by comparing many cases of yellow fever that there was some intermediate host for the bacillus that caused the disease. This conclusion they reached through the method of agreement. Dr. Finlay's experiments by the method of difference had failed, however, indisputably to establish the cause, since he did not see that it was necessary to allow the bacillus at least twelve days for incubation in the body of the mosquito. The final and definitive proof, which came through the splendid self-devotion of the surgeons in charge of the experiment and of certain enlisted men who volunteered to be made the subject of the experiment, was by the method of difference. These brave men allowed themselves to be exposed to mosquitoes which had already bitten patients suffering from the fever, and they promptly came down with the disease; one of them, Dr. Lazear, gave his life for his devotion to the cause of his fellow men. Then other men were exposed in a mosquito-proof room to clothes and other articles brought directly from yellow-fever patients, and showed no ill effects. Thus it was absolutely proved, though the bacillus itself had not been found, that yellow fever is carried by mosquitoes, and is not carried by ordinary contagion.

The unsuccessful experiments of Dr. Finlay and the later success of Major Reed show how science advances by refinement of analysis in the use of the method. The hypothesis on which the former worked was that all mosquitoes who had bitten a yellow-fever patient can carry the disease. Dr. Reed and his associates analyzed the phenomenon more closely and tried their experiments on the hypothesis that only mosquitoes who have lived twelve days after biting the patient are capable of passing on the disease. This refinement of analysis and observation is the chief mode of advance in the sciences which depend on experiment.