But in this point also, our speculations are far from being barren of practical results. The examination to which we have subjected each science, gives us the means of discerning whether what is needed for the further progress of the science, has its place in the Observations, or in the Ideas, or in the union of the two. If observations be wanted, the Methods of Observation, given in [b. iii. c. ii.] may be referred to. If those who are to make the next discoveries need, for that purpose, a developement of their Ideas, the modes in which such a developement has usually taken vii place are treated of in Chapters [iii.] and [iv.] of that Book.
No one who has well studied the history of science can fail to see how important a part of that history is the explication, or as I might call it, the clarification of men’s Ideas. This, the metaphysical aspect of each of the physical sciences, is very far from being, as some have tried to teach, an aspect which it passes through at an early period of progress, and previously to the stage of positive knowledge. On the contrary, the metaphysical movement is a necessary part of the inductive movement. This, which is evidently so by the nature of the case, was proved by a copious collection of historical evidences, in the History of Scientific Ideas. The ten Books of that History contain an account of the principal philosophical controversies which have taken place in all the physical sciences, from Mathematics to Physiology. These controversies, which must be called metaphysical if anything be so called, have been conducted by the greatest discoverers in each science, and have been an essential part of the discoveries made. Physical discoverers have differed from barren speculators, not by having no metaphysics in their heads, but by having good metaphysics in their heads while their adversaries had bad; and by binding their metaphysics to their physics, instead of keeping the two asunder. I trust that the History of Scientific Ideas is of some value, even as a record of a number of remarkable controversies; but I conceive that it also contains an indisputable proof that there viii is, in progressive science, a metaphysical as well as a physical element;—ideas as well as facts;—thoughts as well as things. Metaphysics is the process of ascertaining that thought is consistent with itself: and if it be not so, our supposed knowledge is not knowledge.
In [Chapter vi.] of the Second Book, I have spoken of the Logic of Induction. Several writers[3] have quoted very emphatically my assertion that the Logic of Induction does not exist in previous writers: using it as an introduction to Logical Schemes of their own. They seem to have overlooked the fact that at the same time that I noted the deficiency, I offered a scheme which I think fitted to supply this want. And I am obliged to say that I do not regard the schemes proposed by any of those gentlemen as at all satisfactory for the purpose. But I must defer to a future occasion any criticism of authors who have written on the subjects here treated. A critical notice of such authors formed the Twelfth Book of the former edition of the Philosophy of the Sciences. I have there examined the opinions concerning the Nature of Real Knowledge and the mode of acquiring it, which have been promulgated in all ages, from Plato and Aristotle, to Roger Bacon, to Francis Bacon, to Newton, to Herschel. Such a survey, with the additions which I should now have to make to it, may hereafter be put forth as a separate book: but I ix have endeavoured to confine the present volume to such positive teaching regarding Knowledge and Science as results from the investigations pursued in the other works of this series. But with regard to this matter, of the Logic of Induction, I may venture to say, that we shall not find anything deserving the name explained in the common writers on Logic, or exhibited under the ordinary Logical Forms. That in previous writers which comes the nearest to the notice of such a Logic as the history of science has suggested and verified, is the striking declaration of Bacon in two of his Aphorisms (b. i. aph. civ. cv.).
[3] Apelt Die Theorie der Induction: Gratry Logique.
“There will be good hopes for the Sciences then, and not till then, when by a true scale or Ladder, and by successive steps, following continuously without gaps or breaks, men shall ascend from particulars to the narrower Propositions, from those to intermediate ones, rising in order one above another, and at last to the most general.
“But in establishing such propositions, we must devise some other Form of Induction than has hitherto been in use; and this must be one which serves not only to prove and discover Principles, (as very general Propositions are called,) but also the narrower and the intermediate, and in short, all true Propositions.”
And he elsewhere speaks of successive Floors of Induction.
All the truths of an extensive science form a Series of such Floors, connected by such Scales or Ladders; and a part of the Logic of Induction consists, as I x conceive, in the construction of a Scheme of such Floors. Converging from a wide basis of various classes of particulars, at last to one or a few general truths, these schemes necessarily take the shape of a Pyramid. I have constructed such Pyramids for Astronomy and for Optics[4]; and the illustrious Von Humboldt in speaking of the former subject, does me the honour to say that my attempt in that department is perfectly successful[5]. The Logic of Induction contains other portions, which may be seen in the following work, [b. ii. c. vi.]
[4] See the Tables at the end of book ii.
[5] Cosmos, vol. ii. n. 35.