circumstance in which alone the two sets of instances differ is the effect, or the cause, or an indispensable part of the cause, of the phenomenon.” (3) The Method of Residues:  “Subduct from any phenomenon such part as is known by previous inductions to be the effect of certain antecedents, and the residue of the phenomenon is the effect of the remaining antecedents.” (4) 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.”  When the phenomena are complex the deductive method must be called in to aid:  from the inductively ascertained laws of the action of single causes this deduces the laws of their combined action; and, as a final step, the results of such ratiocination are verified by the proof of their agreement with empirical facts.  To explain a phenomenon means to point out its cause; the explanation of a law is its reduction to other, more general laws.  In all this, however, we remain within the sphere of phenomena; the essence of nature always eludes our knowledge.

In the chapter “Of Liberty and Necessity” (book vi. chap, ii.) Mill emphasizes the position that the necessity to which human actions are subject must not be conceived, as is commonly done, as irresistible compulsion, for it denotes nothing more than the uniform order of our actions and the possibility of predicting them.  This does not destroy the element in the idea of freedom which is legitimate and practically valuable:  we have the power to alter our character; it is formed by us as well as for us; the desire to mould it is one of the most influential circumstances in its formation.  The principle of morality is the promotion of the happiness of all sentient beings.  Mill differs from Bentham, however, from whom he derives the principle of utility, in several important particulars—­by his recognition of qualitative as well as of quantitative differences in pleasures, of the value of the ordinary rules of morality as intermediate principles, of the social feelings, and of the disinterested love of virtue.  Opponents of the utilitarian theory have not been slow in availing themselves of the opportunities for attack thus afforded.[1] A third distinguished representative of the same general movement is Alexander Bain, the psychologist (born 1818; The Senses and the Intellect, 3d ed., 1868; The Emotions and the Will, 3d ed., 1875; Mental and Moral Science, 1868, 3d ed., 1872, part ii., 1872; Mind and Body, 3d ed., 1874).

[Footnote 1:  On the relation of Bentham and Mill cf.  Hoeffding, p. 68:  Sidgwick’s Outlines, chap. iv.  Sec. 16; and John Grote’s Examination of the Utilitarian Philosophy, 1870, chap. i.]