On the Philosophy of Discovery, Chapters Historical and Critical

by William Whewell

Mr. Mill would say, I believe, that when we obtain a new inductive law of facts, we find something in which the facts resemble each other; and that the business of making such discoveries is the business of discovering such resemblances. Thus, he says (of me,) (ii. 211), "his Colligation of Facts by means of appropriate Conceptions, is but the ordinary process of finding by a comparison of phenomena, in what consists their agreement or resemblance." And the Methods of experimental Inquiry which he gives (i. 450, &c.), proceed upon the supposition that the business of discovery may be thus more properly described.

37. There is no doubt that when we discover a law of nature by induction, we find some point in which all the particular facts agree. All the orbits of the planets agree in being ellipses, as Kepler discovered; all falling bodies agree in being acted on by a uniform force, as Galileo discovered; all refracted rays agree in having the sines of incidence and refraction in a constant ratio, as Snell discovered; all the bodies in the universe agree in attracting each other, as Newton discovered; all chemical compounds agree in being constituted of elements in definite proportions, as Dalton discovered. But it appears to me a most scanty, vague, and incomplete account of these steps in science, to say that the authors of them discovered something in which the facts in each case agreed. The point in which the cases agree, is of the most diverse kind in the different cases—in some, a relation of space, in others, the action of a force, in others, the mode of composition of a substance;—and the point of agreement, visible to the discoverer alone, does not come even into his sight, till after the facts have been connected by thoughts of his own, and regarded in points of view in which he, by his mental acts, places them. It would seem to me not much more inappropriate to say, that an officer, who disciplines his men till they move together at the word of command, does so by finding something in which they agree. If the power of consentaneous motion did not exist in the individuals, he could not create it: but that power being there, he finds it and uses it. Of course I am aware that the parallel of the two cases is not exact; but in the one case, as in the other, that in which the particular things are found to agree, is something formed in the mind of him who brings the agreement into view.

IV. Mr. Mill's Four Methods of Inquiry.—38. Mr. Mill has not only thus described the business of scientific discovery; he has also given rules for it, founded on this description. It may be expected that we should bestow some attention upon the methods of inquiry which he thus proposes. I presume that they are regarded by his admirers as among the most valuable parts of his book; as certainly they cannot fail to be, if they describe methods of scientific inquiry in such a manner as to be of use to the inquirer.

Mr. Mill enjoins four methods of experimental inquiry, which he calls the Method of Agreement, the Method of Difference, the Method of Residues, and the Method of Concomitant Variations[271]. They are all described by formulæ of this kind:—Let there be, in the observed facts, combinations of antecedents, ABC, BC, ADE, &c. and combinations of corresponding consequents, abc, bc, ade, &c.; and let the object of inquiry be, the consequence of some cause A, or the cause of some consequence a. The Method of Agreement teaches us, that when we find by experiment such facts as abc the consequent of ABC, and ade the consequent of ADE, then a is the consequent of A. The Method of Difference teaches us that when we find such facts as abc the consequent of ABC, and bc the consequent of BC, then a is the consequent of A. The Method of Residues teaches us, that if abc be the consequent of ABC, and if we have already ascertained that the effect of A is a, and the effect of B is b, then we may infer that the effect of C is c. The Method of Concomitant Variations teaches us, that if a phenomenon a varies according as another phenomenon A varies, there is some connexion of causation direct or indirect, between A and a.

39. Upon these methods, the obvious thing to remark is, that they take for granted the very thing which is most difficult to discover, the reduction of the phenomena to formulæ such as are here presented to us. When we have any set of complex facts offered to us; for instance, those which were offered in the cases of discovery which I have mentioned,—the facts of the planetary paths, of falling bodies, of refracted rays, of cosmical motions, of chemical analysis; and when, in any of these cases, we would discover the law of nature which governs them, or, if any one chooses so to term it, the feature in which all the cases agree, where are we to look for our A, B, C and a, b, c? Nature does not present to us the cases in this form; and how are we to reduce them to this form? You say, when we find the combination of ABC with abc and ABD with abd, then we may draw our inference. Granted: but when and where are we to find such combinations? Even now that the discoveries are made, who will point out to us what are the A, B, C and a, b, c elements of the cases which have just been enumerated? Who will tell us which of the methods of inquiry those historically real and successful inquiries exemplify? Who will carry these formulæ through the history of the sciences, as they have really grown up; and show us that these four methods have been operative in their formation; or that any light is thrown upon the steps of their progress by reference to these formulæ?

40. Mr. Mill's four methods have a great resemblance to Bacon's "Prerogatives of Instances;" for example, the Method of Agreement to the Instantiæ Ostensivæ; the Method of Differences to the Instantiæ Absentiæ in Proximo, and the Instantiæ Crucis; the Method of Concomitant Variations to the Instantiæ Migrantes. And with regard to the value of such methods, I believe all study of science will convince us more and more of the wisdom of the remarks which Sir John Herschel has made upon them[272].

"It has always appeared to us, we must confess, that the help which the classification of instances under their different titles of prerogative, affords to inductions, however just such classification may be in itself, is yet more apparent than real. The force of the instance must be felt in the mind before it can be referred to its place in the system; and before it can be either referred or appreciated it must be known; and when it is appreciated, we are ready enough to weave our web of induction, without greatly troubling ourselves whence it derives the weight we acknowledge it to have in our decisions.... No doubt such instances as these are highly instructive; but the difficulty in physics is to find such, not to perceive their force when found."

V. His Examples.—41. If Mr. Mill's four methods had been applied by him in his book to a large body of conspicuous and undoubted examples of discovery, well selected and well analysed, extending along the whole history of science, we should have been better able to estimate the value of these methods. Mr. Mill has certainly offered a number of examples of his methods; but I hope I may say, without offence, that they appear to me to be wanting in the conditions which I have mentioned. As I have to justify myself for rejecting Mr. Mill's criticism of doctrines which I have put forward, and examples which I have adduced, I may, I trust, be allowed to offer some critical remarks in return, bearing upon the examples which he has given, in order to illustrate his doctrines and precepts.

42. The first remark which I have to make is, that a large proportion of his examples (i. 480, &c.) is taken from one favourite author; who, however great his merit may be, is too recent a writer to have had his discoveries confirmed by the corresponding investigations and searching criticisms of other labourers in the same field, and placed in their proper and permanent relation to established truths; these alleged discoveries being, at the same time, principally such as deal with the most complex and slippery portions of science, the laws of vital action. Thus Mr. Mill has adduced, as examples of discoveries, Prof. Liebig's doctrine—that death is produced by certain metallic poisons through their forming indecomposable compounds; that the effect of respiration upon the blood consists in the conversion of peroxide of iron into protoxide—that the antiseptic power of salt arises from its attraction for moisture—that chemical action is contagious; and others. Now supposing that we have no doubt of the truth of these discoveries, we must still observe that they cannot wisely be cited, in order to exemplify the nature of the progress of knowledge, till they have been verified by other chemists, and worked into their places in the general scheme of chemistry; especially, since it is tolerably certain that in the process of verification, they will be modified and more precisely defined. Nor can I think it judicious to take so large a proportion of our examples from a region of science in which, of all parts of our material knowledge, the conceptions both of ordinary persons, and even of men of science themselves, are most loose and obscure, and the genuine principles most contested; which is the case in physiology. It would be easy, I think, to point out the vague and indeterminate character of many of the expressions in which the above examples are propounded, as well as their doubtful position in the scale of chemical generalization; but I have said enough to show why I cannot give much weight to these, as cardinal examples of the method of discovery; and therefore I shall not examine in detail how far they support Mr. Mill's methods of inquiry.

43. Mr. Liebig supplies the first and the majority of Mr. Mill's examples in chapter IX. of his Book on Induction. The second is an example for which Mr. Mill states himself to be indebted to Mr. Alexander Bain; the law established being this, that (i. 487) electricity cannot exist in one body without the simultaneous excitement of the opposite electricity in some neighbouring body, which Mr. Mill also confirms by reference to Mr. Faraday's experiments on voltaic wires.