[Footnote 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.] [Footnote 284: _Cosmos_, vol. ii. note 35.] [Footnote 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_.] [Footnote 286: B. vi. c. v.] [Footnote 287: c. vi.] [Footnote 288: _Hist._ b. vi. c. vi. sect. 13.] [Footnote 289: _Hist. Ind. Sc._ b. viii.] [Footnote 290: Reprinted in the Appendix to this volume.] CHAPTER XXIII. POLITICAL ECONOMY AS AN INDUCTIVE SCIENCE. (_Moral Sciences._)--1. Both M. Comte and Mr. Mill, in speaking of the methods of advancing science, aim, as I have said, at the extension of their methods to moral subjects, and aspire to suggest means for the augmentation of our knowledge of ethical, political, and social truths. I have not here ventured upon a like extension of my conclusions, because I wished to confine my views of the philosophy of discovery to the cases in which all allow that solid and permanent discoveries have been made. Moreover in the case of moral speculations, we have to consider not only observed external facts and the ideas by which they are colligated, but also internal facts, in which the instrument of observation is consciousness, and in which observations and ideas are mingled together, and act and react in a peculiar manner. It may therefore be doubted whether the methods which have been effectual in the discovery of physical theories will not require to be greatly modified, or replaced by processes altogether different, when we would make advances in ethical, political, or social knowledge. In ethics, at least, it seems plain that we must take our starting-point not without but within us. Our mental powers, our affections, our reason, and any other faculties which we have, must be the basis of our convictions. And in this field of knowledge, the very form of our highest propositions is different from what it is in the physical sciences. In Physics we examine what _is_, in a form more or less general: in Ethics we seek to determine what OUGHT _to be_, as the highest rule, which is supreme over all others. In this case we cannot expect the methods of physical discovery to aid us.