[Footnote 1:  Cf. on Mill.  Taine, Le Positivisme Anglais, 1864 [English, by Haye]; the objections of Jevons (Contemporary Review, December, 1877 seq., reprinted in Pure Logic and other Minor Works, 1890; cf. Mind, vol. xvi. pp. 106-110) to Mill’s doctrine of the inductive character of geometry, his treatment of the relation of resemblance, and his exposition of the four methods of experimental inquiry in their relation to the law of causation; and the finely conceived essay on utilitarianism, by C. Hebler, Philosophische Aufsatze, 1869, pp. 35-66. [Also Mill’s own Autobiography, 1873:  Bain’s John Stuart Mill, a Criticism, 1882; and T.H.  Green, Lectures on the Logic, Works, vol. ii.—­TR.]]

When I assert the major premise the inference proper is already made, and in the conclusion the comprehensive formula for a number of particular truths which was given in the premise is merely explicated, interpreted.  Because universal judgments are for him merely brief expressions for aggregates of particular truths, Mill is able to say that all knowledge is generalization, and at the same time to argue that all inference is from particulars to particulars.  Inference through a general proposition is not necessary, yet useful as a collateral security, inasmuch as the syllogistic forms enable us more easily to discover errors committed.  The ground of induction, the uniformity of nature in reference both to the coexistence and the succession of phenomena, since it wholly depends on induction, is not unconditionally certain; but it may be accepted as very highly probable, until some instance of lawless action (in itself conceivable) shall have been actually proved.  Like the law of causation, the principles of logic are also not a priori, but only the highest generalizations from all previous experience.

Mill’s most brilliant achievement is his theory of experimental inquiry, for which he advances four methods:  (1) 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.” (2) 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,” These two methods (the method of observation, and the method of artificial experiment) may also be employed in combination, and the Canon of the Joint Method of Agreement and Difference runs:  “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