16. But yet the opinions which such persons may entertain, will not lead us to doubt concerning the value of the attempts to analyse and methodize the process of discovery. Who would attend to Kepler if he had maintained that the speculations of Francis Bacon were worthless? Notwithstanding what has been said, we may venture to assert that the Maxim which points out the necessity of Ideas appropriate as well as clear, for the purpose of discovering truth, is not without its use. It may, at least, have a value as a caution or prohibition, and may thus turn us away from labours certain to be fruitless. We have already seen, in the History of Ideas, that this maxim, if duly attended to, would have at once condemned, as wrongly directed, the speculations of physiologists of the mathematical, mechanical, chemical, and vital-fluid schools; since the Ideas which the teachers of these schools introduce, cannot suffice for the purposes of physiology, which seeks truths respecting the vital powers. Again, 45 it is clear from similar considerations that no definition of a mineralogical species by chemical characters alone can answer the end of science, since we seek to make mineralogy, not an analytical but a classificatory science[1]. Even before the appropriate conception is matured in men’s minds so that they see clearly what it is, they may still have light enough to see what it is not.
[1] This agrees with what M. Necker has well observed in his Règne Mineral, that those who have treated mineralogy as a merely chemical science, have substituted the analysis of substances for the classification of individuals. See History of Ideas, b. viii. chap. iii.
17. Another result of this view of the necessity of appropriate Ideas, combined with a survey of the history of science is, that though for the most part, as we shall see, the progress of science consists in accumulating and combining Facts rather than in debating concerning Definitions; there are still certain periods when the discussion of Definitions may be the most useful mode of cultivating some special branch of science. This discussion is of course always to be conducted by the light of facts; and, as has already been said, along with the settlement of every good Definition will occur the corresponding establishment of some Proposition. But still at particular periods, the want of a Definition, or of the clear conceptions which Definition supposes, may be peculiarly felt. A good and tenable Definition of Species in Mineralogy would at present be perhaps the most important step which the science could make. A just conception of the nature of Life, (and if expressed by means of a Definition, so much the better,) can hardly fail to give its possessor an immense advantage in the speculations which now come under the considerations of physiologists. And controversies respecting Definitions, in these cases, and such as these, may be very far from idle and unprofitable.
Thus the knowledge that Clear and Appropriate Ideas are requisite for discovery, although it does not lead to any very precise precepts, or supersede the value of natural sagacity and inventiveness, may still 46 be of use to us in our pursuit after truth. It may show us what course of research is, in each stage of science, recommended by the general analogy of the history of knowledge; and it may both save us from hopeless and barren paths of speculation, and make us advance with more courage and confidence, to know that we are looking for discoveries in the manner in which they have always hitherto been made.
Sect. V.—Accidental Discoveries.
18. Another consequence follows from the views presented in this Chapter, and it is the last I shall at present mention. No scientific discovery can, with any justice, be considered due to accident. In whatever manner facts may be presented to the notice of a discoverer, they can never become the materials of exact knowledge, except they find his mind already provided with precise and suitable conceptions by which they may be analysed and connected. Indeed, as we have already seen, facts cannot be observed as Facts, except in virtue of the Conceptions which the observer[2] himself unconsciously supplies; and they are not Facts of Observation for any purpose of Discovery, except these familiar and unconscious acts of thought be themselves of a just and precise kind. But supposing the Facts to be adequately observed, they can never be combined into any new Truth, except by means of some new Conceptions, clear and appropriate, such as I have endeavoured to characterize. When the observer’s mind is prepared with such instruments, a very few facts, or it may be a single one, may bring the process of discovery into action. But in such cases, this previous condition of the intellect, and not the single fact, is really the main and peculiar cause of the success. The fact is merely the occasion by which the engine of discovery is brought into play sooner or later. It is, as I have elsewhere said, only the spark which discharges a gun already loaded and pointed; and there 47 is little propriety in speaking of such an accident as the cause why the bullet hits the mark. If it were true that the fall of an apple was the occasion of Newton’s pursuing the train of thought which led to the doctrine of universal gravitation, the habits and constitution of Newton’s intellect, and not the apple, were the real source of this great event in the progress of knowledge. The common love of the marvellous, and the vulgar desire to bring down the greatest achievements of genius to our own level, may lead men to ascribe such results to any casual circumstances which accompany them; but no one who fairly considers the real nature of great discoveries, and the intellectual processes which they involve, can seriously hold the opinion of their being the effect of accident.
[2] B. i. of this vol. Aphorism [III.]
19. Such accidents never happen to common men. Thousands of men, even of the most inquiring and speculative men, had seen bodies fall; but who, except Newton, ever followed the accident to such consequences? And in fact, how little of his train of thought was contained in, or even directly suggested by, the fall of the apple! If the apple fall, said the discoverer, ‘why should not the moon, the planets, the satellites, fall?’ But how much previous thought,—what a steady conception of the universality of the laws of motion gathered from other sources,—were requisite, that the inquirer should see any connexion in these cases! Was it by accident that he saw in the apple an image of the moon, and of every body in the solar system?
20. The same observations may be made with regard to the other cases which are sometimes adduced as examples of accidental discovery. It has been said, ‘By the accidental placing of a rhomb of calcareous spar upon a book or line Bartholinus discovered the property of the Double Refraction of light.’ But Bartholinus could have seen no such consequence in the accident if he had not previously had a clear conception of single refraction. A lady, in describing an optical experiment which had been shown her, said of her teacher, ‘He told me to increase and diminish 48 the angle of refraction, and at last I found that he only meant me to move my head up and down.’ At any rate, till the lady had acquired the notions which the technical terms convey, she could not have made Bartholinus’s discovery by means of his accident. ‘By accidentally combining two rhombs in different positions,’ it is added, ‘Huyghens discovered the Polarization of Light.’ Supposing that this experiment had been made without design, what Huyghens really observed was, that the images appeared and disappeared alternately as he turned one of the rhombs round. But was it an easy or an obvious business to analyze this curious alternation into the circumstances of the rays of light having sides, as Newton expressed it, and into the additional hypotheses which are implied in the term ‘polarization’? Those will be able to answer this question, who have found how far from easy it is to understand clearly what is meant by ‘polarization’ in this case, now that the property is fully established. Huyghens’s success depended on his clearness of thought, for this enabled him to perform the intellectual analysis, which never would have occurred to most men, however often they had ‘accidentally combined two rhombs in different positions.’ ‘By accidentally looking through a prism of the same substance, and turning it round, Malus discovered the polarization of light by reflection.’ Malus saw that, in some positions of the prism, the light reflected from the windows of the Louvre thus seen through the prism, became dim. A common man would have supposed this dimness the result of accident; but Malus’s mind was differently constituted and disciplined. He considered the position of the window, and of the prism; repeated the experiment over and over; and in virtue of the eminently distinct conceptions of space which he possessed, resolved the phenomena into its geometrical conditions. A believer in accident would not have sought them; a person of less clear ideas would not have found them. A person must have a strange confidence in the virtue of chance, and the worthlessness of intellect, who can say that 49 ‘in all these fundamental discoveries appropriate ideas had no share,’ and that the discoveries ‘might have been made by the most ordinary observers.’
21. I have now, I trust, shown in various ways, how the Explication of Conceptions, including in this term their clear development from Fundamental Ideas in the discoverer’s mind, as well as their precise expression in the form of Definitions or Axioms, when that can be done, is an essential part in the establishment of all exact and general physical truths. In doing this, I have endeavoured to explain in what sense the possession of clear and appropriate ideas is a main requisite for every step in scientific discovery. That it is far from being the only step, I shall soon have to show; and if any obscurity remain on the subject treated of in the present chapter, it will, I hope, be removed when we have examined the other elements which enter into the constitution of our knowledge.