that genius borders very closely on savage coarseness, that it is a light which shines readily in the midst of darkness, and which, therefore, often argues against, rather than in favor of, the taste of the time. When the golden age of art appears under Pericles and Alexander, and the sway of taste becomes more general, strength and liberty have abandoned Greece; eloquence corrupts the truth, wisdom offends it on the lips of Socrates, and virtue in the life of Phocion. It is well known that the Romans had to exhaust their energies in civil wars, and, corrupted by Oriental luxury, to bow their heads under the yoke of a foreign despot, before Grecian art triumphed over the stiffness of their character. The same was the case with the Arabs: civilization only dawned upon them when the vigor of their military spirit became softened under the Abbassides. Art did not appear in modern Italy till the glorious Lombard league was dissolved, Florence submitting to the Medici, and all those brave cities gave up the spirit of independence for an inglorious resignation. It is almost superfluous to call to mind the example of modern nations, with whom refinement has increased in direct proportion to the decline of their liberties. Wherever we direct our eyes in past times, we see taste and freedom mutually avoiding each other. Everywhere we see that the beautiful only founds its sway on the ruins of heroic virtues." 1

Under this canon three cases may arise, represented by symbols as follows:

In the first case there is one common event and one common circumstance. In the second case there is a group of common events and a group of common circumstances. In the third case there is a single common circumstance but a group of common events.

This third case suggests a remark, which should be. made also regarding the others. A serious element of

1 Bohn's Trans., p. 55.

uncertainty weakens the test of agreement, and that is what is called the Plurality of Causes. What is apparently the same event may be caused by different things. Light may be made by electricity or by combustion. The canon asserts no more than that the common circumstances probably include the cause. Even in Case 1, A, the only common circumstance, may not be the cause of d, the only common event; for B may be the cause of d in the first instance and D may be the cause of d in the second. A may be wholly inert in both instances. It is only when a number of instances have been observed that confidence finds much basis. Ebullition may occur in hydrochloric acid, and yet all the common circumstances may be irrelevant, for marble may be the cause in one instance and zinc may be the cause in the second. In Case 3, A may be the cause of d and some other circumstance may each time cause e.

CHAPTER XII.

MR. MILL'S FOUR EXPERIMENTAL METHODS.

To Mr. Mill is due the credit of first distinctly formulating and elaborately discussing the methods of isolating facts of causation. His treatment of the subject has powerfully influenced all subsequent writers, and his terminology has entered into the general vocabulary of philosophy. It is, therefore, necessary for the student to understand these, if he would understand the current literature of inductive logic.

Mr. Mill treats of the tests which we have discussed in the last chapter, under the heading, "The Four Experimental Methods." He recognizes, indeed, that fundamentally there are but two, and says:

"The simplest and most obvious modes of singling out from among the circumstances which precede or follow a phenomenon, those with which it is really connected by an invariable law, are two in number. One is, by comparing together different instances in which the phenomenon occurs. The other is, by comparing instances in which the phenomenon does occur, with instances in other respects similar in which it does not. These two methods may respectively be denominated the Method of Agreement and the Method of Difference." 1

For the application of these methods Mr. Mill proceeds to formulate five canons, as follows:

1 Logic, p. 278.

FIRST CANON.

For the Method of Agreement.

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.

SECOND CANON.

For the Method of Difference.

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 the cause, or an indispensable part of the cause, of the phenomenon.

THIRD CANON.

For the Joint Method of Agreement and Difference; or the Indirect Method of Difference.

If two or more instances in which the phenomenon occurs have only one circumstance in common, while two or more instances in which it does not occur have nothing in common save the absence of that circumstance; the circumstance in which alone the two sets of instances differ, is the effect, or cause, or an indispensable part of the cause, of the phenomenon.

FOURTH CANON.

For the Method of Residues.

Subduct from any phenomenon such part as is known by previ ous inductions to be the effect of certain antecedents, and the residue of the phenomenon is the effect of the remaining antecedents.

FIFTH CANON.

For the Method of Concomitant Variations.

Whatever phenomenon varies in any manner whenever another phenomenon varies in some particular manner, is either a cause or an effect of that phenomenon, or is connected with it through some fact of causation.

Upon these methods we remark :

1. The name "The Four Experimental Methods" is of doubtful propriety. The methods are confessedly in principle but two; and the canons are five. But Mr. Mill fixed upon the number four because he did not regard the method of Residues as strictly inductive. The method of Residues provides for those instances. of the application of the method of Difference which we have discussed under Case I of our Canon I, on page 98, in which, instead of subtracting a single instance, we subtract the sum of several instances, in order to make the isolation. The fact that in such cases the subtrahend is composite, made by an addition of simpler instances, leads Mr. Mill to formulate a special canon and to declare it deductive. He is not always of the same mind regarding the method of Residues; since he says, "By previous inductions we have ascertained the causes of some of these effects," meaning those which are added together to make the compound subtrahend; but he says later, "It concludes not from a comparison of instances, but from the comparison of an instance with the result of a previous deduction." 2

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