On the Philosophy of Discovery, Chapters Historical and Critical

by William Whewell

I shall now leave the reader to judge whether this feature in the history of science,—that several views which appear at first quite different are yet all true,—which Mr. Mill calls a curious and interesting remark of mine, and which he allows to be "strikingly true" of the Inductions which he calls Descriptions, (i. 364) is, as he says, "unequivocally false" of other Inductions. And I shall confide in having general assent with me, when I continue to speak of Kepler's Induction of the elliptical orbits.

I now proceed to another remark.

III. In Discovery a new Conception is introduced.—

24. There is a difference between Mr. Mill and me in our view of the essential elements of this Induction of Kepler, which affects all other cases of Induction, and which is, I think, the most extensive and important of the differences between us. I must therefore venture to dwell upon it a little in detail.

I conceive that Kepler, in discovering the law of Mars's motion, and in asserting that the planet moved in an ellipse, did this;—he bound together particular observations of separate places of Mars by the notion, or, as I have called it, the conception, of an ellipse, which was supplied by his own mind. Other persons, and he too, before he made this discovery, had present to their minds the facts of such separate successive positions of the planet; but could not bind them together rightly, because they did not apply to them this conception of an ellipse. To supply this conception, required a special preparation, and a special activity in the mind of the discoverer. He, and others before him, tried other ways of connecting the special facts, none of which fully succeeded. To discover such a connexion, the mind must be conversant with certain relations of space, and with certain kinds of figures. To discover the right figure was a matter requiring research, invention, resource. To hit upon the right conception is a difficult step; and when this step is once made, the facts assume a different aspect from what they had before: that done, they are seen in a new point of view; and the catching this point of view, is a special mental operation, requiring special endowments and habits of thought. Before this, the facts are seen as detached, separate, lawless; afterwards, they are seen as connected, simple, regular; as parts of one general fact, and thereby possessing innumerable new relations before unseen. Kepler, then, I say, bound together the facts by superinducing upon them the conception of an ellipse; and this was an essential element in his Induction.

25. And there is the same essential element in all Inductive discoveries. In all cases, facts, before detached and lawless, are bound together by a new thought. They are reduced to law, by being seen in a new point of view. To catch this new point of view, is an act of the mind, springing from its previous preparation and habits. The facts, in other discoveries, are brought together according to other relations, or, as I have called them, Ideas;—the Ideas of Time, of Force, of Number, of Resemblance, of Elementary Composition, of Polarity, and the like. But in all cases, the mind performs the operation by an apprehension of some such relations; by singling out the one true relation; by combining the apprehension of the true relation with the facts; by applying to them the Conception of such a relation.

26. In previous writings, I have not only stated this view generally, but I have followed it into detail, exemplifying it in the greater part of the History of the principal Inductive Sciences in succession. I have pointed out what are the Conceptions which have been introduced in every prominent discovery in those sciences; and have noted to which of the above Ideas, or of the like Ideas, each belongs. The performance of this task is the office of the greater part of my Philosophy of the Inductive Sciences. For that work is, in reality, no less historical than the History which preceded it. The History of the Inductive Sciences is the history of the discoveries, mainly so far as concerns the Facts which were brought together to form sciences. The Philosophy is, in the first ten Books, the history of the Ideas and Conceptions, by means of which the facts were connected, so as to give rise to scientific truths. It would be easy for me to give a long list of the Ideas and Conceptions thus brought into view, but I may refer any reader who wishes to see such a list, to the Tables of Contents of the History, and of the first ten Books of the Philosophy.

27. That these Ideas and Conceptions are really distinct elements of the scientific truths thus obtained, I conceive to be proved beyond doubt, not only by considering that the discoveries never were made, nor could be made, till the right Conception was obtained, and by seeing how difficult it often was to obtain this element; but also, by seeing that the Idea and the Conception itself, as distinct from the Facts, was, in almost every science, the subject of long and obstinate controversies;—controversies which turned upon the possible relations of Ideas, much more than upon the actual relations of Facts. The first ten Books of the Philosophy to which I have referred, contain the history of a great number of these controversies. These controversies make up a large portion of the history of each science; a portion quite as important as the study of the facts; and a portion, at every stage of the science, quite as essential to the progress of truth. Men, in seeking and obtaining scientific knowledge, have always shown that they found the formation of right conceptions in their own minds to be an essential part of the process.

28. Moreover, the presence of a Conception of the mind as a special element of the inductive process, and as the tie by which the particular facts are bound together, is further indicated, by there being some special new term or phrase introduced in every induction; or at least some term or phrase thenceforth steadily applied to the facts, which had not been applied to them before; as when Kepler asserted that Mars moved round the sun in an elliptical orbit, or when Newton asserted that the planets gravitate towards the sun; these new terms, elliptical orbit, and gravitate, mark the new conceptions on which the inductions depend. I have in the Philosophy[270] further illustrated this application of "technical terms," that is, fixed and settled terms, in every inductive discovery; and have spoken of their use in enabling men to proceed from each such discovery to other discoveries more general. But I notice these terms here, for the purpose of showing the existence of a conception in the discoverer's mind, corresponding to the term thus introduced; which conception, the term is intended to convey to the minds of those to whom the discovery is communicated.

29. But this element of discovery,—right conceptions supplied by the mind in order to bind the facts together,—Mr. Mill denies to be an element at all. He says, of Kepler's discovery of the elliptical orbit (i. 363), "It superadded nothing to the particular facts which it served to bind together;" yet he adds, "except indeed the knowledge that a resemblance existed between the planetary orbit and other ellipses;" that is, except the knowledge that it was an ellipse;—precisely the circumstance in which the discovery consisted. Kepler, he says, "asserted as a fact that the planet moved in an ellipse. But this fact, which Kepler did not add to, but found in the motion of the planet ... was the very fact, the separate parts of which had been separately observed; it was the sum of the different observations."