have to content ourselves at last with certain simple laws of chemistry and physics.

When any event is shown to have taken place in accordance with uniform laws, or when some uniformity is reduced to others more simple and more general it is said to be 'explained'. The simplest and most general laws of all must be accepted without explanation on the strength of an Inductio per Enumerationem Simplicem. The most that we can say for the existence of any of them is that they seem to be involved by a vast number of experiences and to be contradicted by none.*

Analysis

thinking.

When we find the causes back of any observed uniformity, the things with which we started become more fully known as well as the relations between them, and the knowledge of both things and relations in becom- and clear ing fuller becomes also clearer. In the example given 'red clover' took a definite character as a plant dependent for its propagation upon cross-fertilization by an insect able to reach its nectar, and if we had asked why the pollen must be carried, why the bumblebee is better able to get at the nectar than other insects, and so on, we should have gained still clearer and fuller ideas about the clover. As the relations with which we begin are not fully analyzed and explained until they are reduced to ultimate laws, so the things with which we start are not completely understood until each of them is analyzed at last into a definite group of various kinds of atoms.

The clearness and definiteness of thought which causal analysis gives is as valuable in itself as the greater certainty of inference that goes along with it. General appearances ob

*The sociologist, for example, cannot get along without assuming certain laws of mind; the psychologist tries to account for mental laws by reference to nerve-physiology; the physiologist tries to reduce his data to laws of chemistry and physics; the chemist tries to explain his data by molecular physics; and the physicist tries to state all his facts in the formulæ of mathematics.

6

scurely apprehended are often sufficient to call forth a fairly definite and appropriate reaction on our part. The lines on a companion's face may be quite indescribable by us and yet suggest the words 'He is angry'. In the same way a number of very indescribable impressions may suggest the word' Iron' or Bewitched' or 'Tyrannizing'. These vague impres sions are valuable because the words and other reactions to which they lead are generally fairly appropriate and useful. And yet real things and relations are never vague, and vague impressions can never represent them. They do not precisely misrepresent them, for vague ideas neither represent nor misrepresent, since they cannot be measured against the facts at all. How can we ever prove that Mother Hubbard does not hoodoo' her dog or 'project' her thoughts in such a way as to impress' the brain of the Czar, until we know precisely what it means to be hoodooed' or what a 'projected' thought is supposed to do to the brain that it 'impresses'? Hence if one's expectations are only vague enough there is no such thing as definite fulfilment or definite disappointment. Definite conceptions, on the other hand, can represent realities; and therefore there is some chance of having one that does. If it does not, its very definiteness makes it possible to prove that it does not. If it does, we can count upon it always. Thus a second reason for seeking to reduce observed uniformities to their causes is the clearness of conception which it gives.

CHAPTER XXVI.

THE METHODS OF DIFFERENCE AND AGREEMENT.

In the preceding chapters we have discussed the general principles involved in inductive reasoning. We must now see how the principles are applied to various kinds

:

Different

ways of exhausting

the uni

verse.

of concrete problems. We have seen already that these problems may be divided roughly into two classes the discovery or verifying of general laws, and the ascertaining of concrete individual facts. Questions of concrete fact will not be discussed until after we come to Chapter XXXIII. At present we shall consider

only questions of general law.

The principles involved in these questions are always the same, yet there are differences in the data to which they are applied which involve corresponding differences in the applications; and if our knowledge of the principles is to have any richness, we ought to know something about these different ways in which they are applied. The most striking applications are to be found in scientific investigations. Many of these are described in Herschel's "Discourse on the Study of Natural Philosophy" (1832) and in Whewell's two large volumes on the "History of the Inductive Sciences" (1837) and his "Philosophy of the Inductive Sciences" (1840), from which subsequent writers have drawn much of their material. With the facts and theories of these writers before him John Stuart Mill set out in his "Logic" (published in 1843) to generalize the modes of investigating truth and

estimating evidence, by which so many important and recondite laws of nature have, in the various sciences, been aggregated to the stock of human knowledge', and Mill's chapter on "The Four Methods of Experimental Inquiry'' contains the classical account of the various ways in which the principle is applied for the discovery of causal relations.* These different ways of applying the principle are called by Mill the Method of Agreement, the Method of Difference (including the Joint Method of Agreement and Difference, or Indirect Method of Difference), the Method of Residues, and the Method of Concomitant Variations. We shall give an account of each of them, beginning with the Method of Difference.

The Method of Difference.

If a baby strikes or pushes a hanging ball and the ball moves, and if the experience happens to be repeated several times, the baby gets in the way after a while of expecting that each new stroke or push will be followed by a new movement of the ball, and years afterwards it learns to say that the stroke of the hand caused the movement of the ball. If a man were to try the same experiment as the child he would reach the same conclusion, but, unlike the child, he might try to explain why the conclusion was reasonable. If he did, his reasoning would be something like this: 'Before I touched the ball it was motionless. I struck it a great many times. Every time I struck it it moved. When I left it alone it gradually stopped moving. If my blows did not move it, what did? I was

*It is hardly necessary to say that inductive inquiry existed long before the theories of these writers, and even a very clear theoretical conception of the principles on which it is founded. Minto's "Logic" (pp. 243-272) gives a good account of the whole matter, including the views and influence of Francis Bacon and of Roger Bacon (1214-1292), whom Minto calls his greater namesake. Minto, however, does not mention Hume and his remarkably clear statement of the canons for the methods of Agreement, Difference, and Concomitant Variations (See the Rules by which to judge of causes and effects' in the "Treatise of Human Nature ").

alone in the room; the house was quiet; there were no sudden draughts of air. It may be that a ball might be moved. before my eyes by some cause that I could not see and do not know about; but if there was any such cause, why did it always wait to move the ball until I struck it?'

The force of this argument lies in the question 'If I did not, what did?' The man assumes that the event must have been caused, and the harder he looks without finding anything that might have caused it except his own activity the surer he feels that that was the real cause; and if he knew for certain that his blow was the only change introduced into the situation before the ball began to move-the only point of difference except the movement itself between the situation in which the ball did not move and that in which it did—then he could be absolutely certain that it was his blow that caused the movement of the ball. It is clear enough that this reasoning is based on our principle of exclusion (one of the forms taken by the wider principle of exhaustion, see p. 225); and the italicized words explain why Mill calls This special application of the principle the Method of Difference.

It makes no difference in the method whether it is used to explain an actual change in one situation or the difference between two. If there are two precisely similar balls suspended in precisely similar manners, except that one is exposed to a steady wind and moving while the other is sheltered and stationary, we can conclude that the wind is the only possible cause of the movement, since it is the only circumstance (except the movement itself) present in one case and not in the other and we cannot suppose that a circumstance present in both cases would move one ball which happens to be here and not move another precisely like it which happens to be there.

The principle of exclusion as used in this method of difference can be stated in the following abstract canon of Mill's: "If an instance in which the phenomenon under in