[278] See Hist. Ind. Sc. b. xii. note D, in the second edition.
[279] There are some points in my doctrines on the subject of the Classificatory Sciences to which Mr. Mill objects, (ii. 314, &c.), but there is nothing which I think it necessary to remark here, except one point. After speaking of Classification of organized beings in general, Mr. Mill notices (ii. 321) as an additional subject, the arrangement of natural groups into a Natural Series; and he says, that "all who have attempted a theory of natural arrangement, including among the rest Mr. Whewell, have stopped short of this: all except M. Comte." On this I have to observe, that I stopped short of, or rather passed by, the doctrine of a Series of organized beings, because I thought it bad and narrow philosophy: and that I sufficiently indicated that I did this. In the History (b. xvi. c. vi.) I have spoken of the doctrine of Circular Progression propounded by Mr. Macleay, and have said, "so far as this view negatives a mere linear progression in nature, which would place each genus in contact with the preceding and succeeding ones, and so far as it requires us to attend to the more varied and ramified resemblances, there can be no doubt that it is supported by the result of all the attempts to form natural systems." And with regard to the difference between Cuvier and M. de Blainville, to which Mr. Mill refers (ii. 321), I certainly cannot think that M. Comte's suffrage can add any weight to the opinion of either of those great naturalists.
[280] Hist. Ind. Sc. b. x. note (VA) in the second edition.
[281] B. xi. c. v. art. 11.
[282] I have given elsewhere (see last chapter) reasons why I cannot assign to M. Comte's Philosophie Positive any great value as a contribution to the philosophy of science. In this judgment I conceive that I am supported by the best philosophers of our time. M. Comte owes, I think, much of the notice which has been given to him to his including, as Mr. Mill does, the science of society and of human nature in his scheme, and to his boldness in dealing with these. He appears to have been received with deference as a mathematician: but Sir John Herschel has shown that a supposed astronomical discovery of his is a mere assumption. I conceive that I have shown that his representation of the history of science is erroneous, both in its details and in its generalities. His distinction of the three stages of sciences, the theological, metaphysical, and positive, is not at all supported by the facts of scientific history. Real discoveries always involve what he calls metaphysics; and the doctrine of final causes in physiology, the main element of science which can properly be called theological, is retained at the end, as well as the beginning of the science, by all except a peculiar school.
[283] I have also, in the same place, given the Inductive Pyramid for the science of Optics. These Pyramids are necessarily inverted in their form, in order that, in reading in the ordinary way, we may proceed to the vertex. Phil. Ind. Sc. b. xi. c. vi.
[284] Cosmos, vol. ii. note 35.
[285] The reader will probably recollect that as Induction means the inference of general propositions from particular cases, Deduction means the inference by the application of general propositions to particular cases, and by combining such applications; as when from the most general principles of Geometry or of Mechanics, we prove some less general theorem; for instance, the number of the possible regular solids, or the principle of vis viva.
[286] B. vi. c. v.
[287] c. vi.