CHAPTER V.Of Certain Characteristics of Scientific Induction.Aphorism X.The process of scientific discovery is cautious and rigorous, not by abstaining from hypotheses, but by rigorously comparing hypotheses with facts, and by resolutely rejecting all which the comparison does not confirm.Aphorism XI.Hypotheses may be useful, though involving much that is superfluous, and even erroneous: for they may supply the true bond of connexion of the facts; and the superfluity and errour may afterwards be pared away.Aphorism XII.It is a test of true theories not only to account for, but to predict phenomena.Aphorism XIII.Inductionis a term applied to describe the process of a true Colligation of Facts by means of an exact and appropriate Conception.An Inductionis also employed to denote thepropositionwhich results from this process.Aphorism XIV.The Consilience of Inductionstakes place when an Induction, obtained from one class of facts, coincides with an Induction, obtained from another different class. This71Consilience is a test of the truth of the Theory in which it occurs.Aphorism XV.An Induction is not the meresumof the Facts which are colligated. The Facts are not only brought together, but seen in a new point of view. A new mental Element issuperinduced;and a peculiar constitution and discipline of mind are requisite in order to make this Induction.Aphorism XVI.Although in Every Induction a new conception is superinduced upon the Facts; yet this once effectually done, the novelty of the conception is overlooked, and the conception is considered as a part of the fact.Sect. I.—Invention a part of Induction.1.THE two operations spoken of in the preceding chapters,—the Explication of the Conceptions of our own minds, and the Colligation of observed Facts by the aid of such Conceptions,—are, as we have just said, inseparably connected with each other. When united, and employed in collecting knowledge from the phenomena which the world presents to us, they constitute the mental process ofInduction; which is usually and justly spoken of as the genuine source of all ourreal general knowledgerespecting the external world. And we see, from the preceding analysis of this process into its two constituents, from what origin it derives each of its characters. It isreal, because it arises from the combination of Real Facts, but it isgeneral, because it implies the possession of General Ideas. Without the former, it would not be knowledge of the External World; without the latter, it would not be Knowledge at all. When Ideas and Facts are separated from each other, the neglect of Facts gives rise to empty speculations, idle subtleties, visionary inventions, false opinions concerning the laws of phenomena, disregard of the true aspect of nature:72while the want of Ideas leaves the mind overwhelmed, bewildered, and stupified by particular sensations, with no means of connecting the past with the future, the absent with the present, the example with the rule; open to the impression of all appearances, but capable of appropriating none. Ideas are theForm, facts theMaterial, of our structure. Knowledge does not consist in the empty mould, or in the brute mass of matter, but in the rightly-moulded substance. Induction gathers general truths from particular facts;—and in her harvest, the corn and the reaper, the solid ears and the binding band, are alike requisite. All our knowledge of nature is obtained by Induction; the term being understood according to the explanation we have now given. And our knowledge is then most complete, then most truly deserves the name of Science, when both its elements are most perfect;—when the Ideas which have been concerned in its formation have, at every step, been clear and consistent; and when they have, at every step also, been employed in binding together real and certain Facts. Of such Induction, I have already given so many examples and illustrations in the two preceding chapters, that I need not now dwell further upon the subject.2. Induction is familiarly spoken of as the process by which we collect aGeneral Propositionfrom a number ofParticular Cases: and it appears to be frequently imagined that the general proposition results from a mere juxta-position of the cases, or at most, from merely conjoining and extending them. But if we consider the process more closely, as exhibited in the cases lately spoken of, we shall perceive that this is an inadequate account of the matter. The particular facts are not merely brought together, but there is a New Element added to the combination by the very act of thought by which they are combined. There is a Conception of the mind introduced in the general proposition, which did not exist in any of the observed facts. When the Greeks, after long observing the motions of the planets, saw that these motions might be rightly considered as produced by the motion of one73wheel revolving in the inside of another wheel, these Wheels were Creations of their minds, added to the Facts which they perceived by sense. And even if the wheels were no longer supposed to be material, but were reduced to mere geometrical spheres or circles, they were not the less products of the mind alone,—something additional to the facts observed. The same is the case in all other discoveries. The facts are known, but they are insulated and unconnected, till the discoverer supplies from his own stores a Principle of Connexion. The pearls are there, but they will not hang together till some one provides the String. The distances and periods of the planets were all so many separate facts; by Kepler’s Third Law they are connected into a single truth: but the Conceptions which this law involves were supplied by Kepler’s mind, and without these, the facts were of no avail. The planets described ellipses round the sun, in the contemplation of others as well as of Newton; but Newton conceived the deflection from the tangent in these elliptical motions in a new light,—as the effect of a Central Force following a certain law; and then it was, that such a force was discovered truly to exist.Thus5in each inference made by Induction, there is introduced some General Conception, which is given, not by the phenomena, but by the mind. The conclusion is not contained in the premises, but includes them by the introduction of a New Generality. In order to obtain our inference, we travel beyond the cases which we have before us; we consider them as mere exemplifications of some Ideal Case in which the relations are complete and intelligible. We take a Standard, and measure the facts by it; and this Standard is constructed by us, not offered by Nature. We assert, for example, that a body left to itself will move on with unaltered velocity; not because our senses ever disclosed to us a body doing this, but because (taking this as our Ideal Case) we find that all74actual cases are intelligible and explicable by means of the Conception ofForces, causing change and motion, and exerted by surrounding bodies. In like manner, we see bodies striking each other, and thus moving and stopping, accelerating and retarding each other: but in all this, we do not perceive by our senses that abstract quantity,Momentum, which is always lost by one body as it is gained by another. This Momentum is a creation of the mind, brought in among the facts, in order to convert their apparent confusion into order, their seeming chance into certainty, their perplexing variety into simplicity. This the Conception ofMomentum gained and lostdoes: and in like manner, in any other case in which a truth is established by Induction, some Conception is introduced, some Idea is applied, as the means of binding together the facts, and thus producing the truth.5I repeat here remarks made at the end of theMechanical Euclid, p. 178.3. Hence in every inference by Induction, there is some Conceptionsuperinducedupon the Facts: and we may henceforth conceive this to be the peculiar import of the termInduction. I am not to be understood as asserting that the term was originally or anciently employed with this notion of its meaning; for the peculiar feature just pointed out in Induction has generally been overlooked. This appears by the accounts generally given of Induction. ‘Induction,’ says Aristotle6, ‘is when by means of one extreme term7we infer the other extreme term to be true of the middle term.’ Thus, (to take such exemplifications as belong to our subject,) from knowing that Mercury, Venus, Mars, describe ellipses about the Sun, we infer that all Planets describe ellipses about the Sun. In making this inference syllogistically, we assume that the evident proposition, ‘Mercury, Venus, Mars, do what all Planets do,’ may be takenconversely, ‘All75Planets do what Mercury, Venus, Mars, do.’ But we may remark that, in this passage, Aristotle (as was natural in his line of discussion) turns his attention entirely to theevidenceof the inference; and overlooks a step which is of far more importance to our knowledge, namely, theinventionof the second extreme term. In the above instance, the particular luminaries, Mercury, Venus, Mars, are one logicalExtreme; the general designation Planets is theMiddle Term; but having these before us, how do we come to think ofdescription of ellipses, which is the other Extreme of the syllogism? When we have once invented this ‘second Extreme Term,’ we may, or may not, be satisfied with the evidence of the syllogism; we may, or may not, be convinced that, so far as this property goes, the extremes are co-extensive with the middle term8; but thestatementof the syllogism is the important step in science. We know how long Kepler laboured, how hard he fought, how many devices he tried, before he hit upon thisTerm, the Elliptical Motion. He rejected, as we know, many other ‘second extreme Terms,’ for example, various combinations of epicyclical constructions, because they did not represent with sufficient accuracy the special facts of observation. When he had established his premiss, that ‘Mars does describe an Ellipse about the Sun,’ he does not hesitate toguessat least that, in this respect, he mightconvertthe other premiss, and assert that ‘All the Planets do what Mars does.’ But the main business was, the inventing and verifying the proposition respecting the Ellipse. The Invention of the Conception was the great step in thediscovery; the Verification of the Proposition was the great step in theproofof the discovery. If Logic consists in pointing out the conditions of proof, the Logic of Induction must consist in showing what are the conditions of proof, in such inferences as this: but this subject must be pursued in the next chapter; I now speak principally of the act of76Invention, which is requisite in every inductive inference.6Analyt. Prior.lib. ii. c. xxiii.ΠεÏὶ τῆς á¼Ï€Î±Î³Ï‰Î³á¿†Ï‚.7The syllogism here alluded to would be this:—Mercury, Venus, Mars, describe ellipses about the Sun;All Planets do what Mercury, Venus, Mars, do;Therefore all Planets describe ellipses about the Sun.8Εἰ οὖν ἀντιστÏÎφει τὸ Γ Ï„á¿· Î’ καὶ μὴ ὑπεÏτείνει τὸ μÎσον.—Aristot.Ibid.4. Although in every inductive inference, an act of invention is requisite, the act soon slips out of notice. Although we bind together facts by superinducing upon them a new Conception, this Conception, once introduced and applied, is looked upon as inseparably connected with the facts, and necessarily implied in them. Having once had the phenomena bound together in their minds in virtue of the Conception, men can no longer easily restore them back to the detached and incoherent condition in which they were before they were thus combined. The pearls once strung, they seem to form a chain by their nature. Induction has given them a unity which it is so far from costing us an effort to preserve, that it requires an effort to imagine it dissolved. For instance, we usually represent to ourselves the Earth asround, the Earth and the Planets asrevolvingabout the Sun, and asdrawnto the Sun by a Central Force; we can hardly understand how it could cost the Greeks, and Copernicus, and Newton, so much pains and trouble to arrive at a view which to us is so familiar. These are no longer to us Conceptions caught hold of and kept hold of by a severe struggle; they are the simplest modes of conceiving the facts: they are really Facts. We are willing toownour obligation to those discoverers, but we hardlyfeelit: for in what other manner (we ask in our thoughts) could we represent the facts to ourselves?Thus we see why it is that this step of which we now speak, the Invention of a new Conception in every inductive inference, is so generally overlooked that it has hardly been noticed by preceding philosophers. When once performed by the discoverer, it takes a fixed and permanent place in the understanding of every one. It is a thought which, once breathed forth, permeates all men’s minds. All fancy they nearly or quite knew it before. It oft was thought, or almost thought, though never till now expressed. Men accept it and retain it, and know it cannot be taken77from them, and look upon it as their own. They will not and cannot part with it, even though they may deem it trivial and obvious. It is a secret, which once uttered, cannot be recalled, even though it be despised by those to whom it is imparted. As soon as the leading term of a new theory has been pronounced and understood, all the phenomena change their aspect. There is a standard to which we cannot help referring them. We cannot fall back into the helpless and bewildered state in which we gazed at them when we possessed no principle which gave them unity. Eclipses arrive in mysterious confusion: the notion of aCycledispels the mystery. The Planets perform a tangled and mazy dance; butEpicyclesreduce the maze to order. The Epicycles themselves run into confusion; the conception of anEllipsemakes all clear and simple. And thus from stage to stage, new elements of intelligible order are introduced. But this intelligible order is so completely adopted by the human understanding, as to seem part of its texture. Men ask Whether Eclipses follow a Cycle; Whether the Planets describe Ellipses; and they imagine that so long as they do notanswersuch questions rashly, they take nothing for granted. They do not recollect how much they assume inaskingthe question:—how far the conceptions of Cycles and of Ellipses are beyond the visible surface of the celestial phenomena:—how many ages elapsed, how much thought, how much observation, were needed, before men’s thoughts were fashioned into the words which they now so familiarly use. And thus they treat the subject, as we have seen Aristotle treating it; as if it were a question, not of invention, but of proof; not of substance, but of form: as if the main thing were notwhatwe assert, buthowwe assert it. But for our purpose, it is requisite to bear in mind the feature which we have thus attempted to mark; and to recollect that, in every inference by induction, there is a Conception supplied by the mind and superinduced upon the Facts.5. In collecting scientific truths by Induction, we often find (as has already been observed) a Definition78and a Proposition established at the same time,—introduced together, and mutually dependent on each other. The combination of the two constitutes the Inductive act; and we may consider the Definition as representing the superinduced Conception, and the Proposition as exhibiting the Colligation of Facts.Sect. II.—Use of Hypotheses.6. To discover a Conception of the mind which will justly represent a train of observed facts is, in some measure, a process of conjecture, as I have stated already; and as I then observed, the business of conjecture is commonly conducted by calling up before our minds several suppositions, and selecting that one which most agrees with what we know of the observed facts. Hence he who has to discover the laws of nature may have to invent many suppositions before he hits upon the right one; and among the endowments which lead to his success, we must reckon that fertility of invention which ministers to him such imaginary schemes, till at last he finds the one which conforms to the true order of nature. A facility in devising hypotheses, therefore, is so far from being a fault in the intellectual character of a discoverer, that it is, in truth, a faculty indispensable to his task. It is, for his purposes, much better that he should be too ready in contriving, too eager in pursuing systems which promise to introduce law and order among a mass of unarranged facts, than that he should be barren of such inventions and hopeless of such success. Accordingly, as we have already noticed, great discoverers have often invented hypotheses which would not answer to all the facts, as well as those which would; and have fancied themselves to have discovered laws, which a more careful examination of the facts overturned.The tendencies of our speculative nature9, carrying79us onwards in pursuit of symmetry and rule, and thus producing all true theories, perpetually show their vigour by overshooting the mark. They obtain something, by aiming at much more. They detect the order and connexion which exist, by conceiving imaginary relations of order and connexion which have no existence. Real discoveries are thus mixed with baseless assumptions; profound sagacity is combined with fanciful conjecture; not rarely, or in peculiar instances, but commonly, and in most cases; probably in all, if we could read the thoughts of discoverers as we read the books of Kepler. To try wrong guesses is, with most persons, the only way to hit upon right ones. The character of the true philosopher is, not that he never conjectures hazardously, but that his conjectures are clearly conceived, and brought into rigid contact with facts. He sees and compares distinctly the Ideas and the Things;—the relations of his notions to each other and to phenomena. Under these conditions, it is not only excusable, but necessary for him, to snatch at every semblance of general rule,—to try all promising forms of simplicity and symmetry.9I here take the liberty of characterizing inventive minds in general in the same phraseology which, in the History of Science, I have employed in reference to particular examples. These expressions are what I have used in speaking of the discoveries of Copernicus.—Hist. Ind. Sc.b. v. c. ii.Hence advances in knowledge10are not commonly made without the previous exercise of some boldness and license in guessing. The discovery of new truths requires, undoubtedly, minds careful and scrupulous in examining what is suggested; but it requires, no less, such as are quick and fertile in suggesting. What is Invention, except the talent of rapidly calling before us the many possibilities, and selecting the appropriate one? It is true, that when we have rejected all the inadmissible suppositions, they are often quickly forgotten; and few think it necessary to dwell on these discarded hypotheses, and on the process by which they were condemned. But all who discover truths, must have reasoned upon many errours to obtain each truth;80every accepted doctrine must have been one chosen out of many candidates. If many of the guesses of philosophers of bygone times now appear fanciful and absurd, because time and observation have refuted them, others, which were at the time equally gratuitous, have been conformed in a manner which makes them appear marvellously sagacious. To form hypotheses, and then to employ much labour and skill in refuting them, if they do not succeed in establishing them, is a part of the usual process of inventive minds. Such a proceeding belongs to theruleof the genius of discovery, rather than (as has often been taught in modern times) to theexception.10These observations are made on occasion of Kepler’s speculations, and are illustrated by reference to his discoveries.—Hist. Ind. Sc.b. v. c. iv. sect. 1.7. But if it be an advantage for the discoverer of truth that he be ingenious and fertile in inventing hypotheses which may connect the phenomena of nature, it is indispensably requisite that he be diligent and careful in comparing his hypotheses with the facts, and ready to abandon his invention as soon as it appears that it does not agree with the course of actual occurrences. This constant comparison of his own conceptions and supposition with observed facts under all aspects, forms the leading employment of the discoverer: this candid and simple love of truth, which makes him willing to suppress the most favourite production of his own ingenuity as soon as it appears to be at variance with realities, constitutes the first characteristic of his temper. He must have neither the blindness which cannot, nor the obstinacy which will not, perceive the discrepancy of his fancies and his facts. He must allow no indolence, or partial views, or self-complacency, or delight in seeming demonstration, to make him tenacious of the schemes which he devises, any further than they are confirmed by their accordance with nature. The framing of hypotheses is, for the inquirer after truth, not the end, but the beginning of his work. Each of his systems is invented, not that he may admire it and follow it into all its consistent consequences, but that he may make it the occasion of a course of active experiment and observation. And if the results of this process81contradict his fundamental assumptions, however ingenious, however symmetrical, however elegant his system may be, he rejects it without hesitation. He allows no natural yearning for the offspring of his own mind to draw him aside from the higher duty of loyalty to his sovereign, Truth: to her he not only gives his affections and his wishes, but strenuous labour and scrupulous minuteness of attention.We may refer to what we have said of Kepler, Newton, and other eminent philosophers, for illustrations of this character. In Kepler we have remarked11the courage and perseverance with which he undertook and executed the task of computing his own hypotheses: and, as a still more admirable characteristic, that he never allowed the labour he had spent upon any conjecture to produce any reluctance in abandoning the hypothesis, as soon as he had evidence of its inaccuracy. And in the history of Newton’s discovery that the moon is retained in her orbit by the force of gravity, we have noticed the same moderation in maintaining the hypothesis, after it had once occurred to the author’s mind. The hypothesis required that the moon should fall from the tangent of her orbit every second through a space of sixteen feet; but according to his first calculations it appeared that in fact she only fell through a space of thirteen feet in that time. The difference seems small, the approximation encouraging, the theory plausible; a man in love with his own fancies would readily have discovered or invented some probable cause of the difference. But Newton acquiesced in it as a disproof of his conjecture, and ‘laid aside at that time any further thoughts of this matter12.’11Hist. Ind. Sc.b. v. c. iv. sect. 1.12Hist. Ind. Sc.b. vii. c. ii. sect. 3.8. It has often happened that those who have undertaken to instruct mankind have not possessed this pure love of truth and comparative indifference to the maintenance of their own inventions. Men have frequently adhered with great tenacity and vehemence to the hypotheses which they have once framed; and in their82affection for these, have been prone to overlook, to distort, and to misinterpret facts. In this manner,Hypotheseshave so often been prejudicial to the genuine pursuit of truth, that they have fallen into a kind of obloquy; and have been considered as dangerous temptations and fallacious guides. Many warnings have been uttered against the fabrication of hypotheses, by those who profess to teach philosophy; many disclaimers of such a course by those who cultivate science.Thus we shall find Bacon frequently discommending this habit, under the name of ‘anticipation of the mind,’ and Newton thinks it necessary to say emphatically ‘hypotheses non fingo.’ It has been constantly urged that the inductions by which sciences are formed must becautiousandrigorous; and the various imaginations which passed through Kepler’s brain, and to which he has given utterance, have been blamed or pitied, as lamentable instances of an unphilosophical frame of mind. Yet it has appeared in the preceding remarks that hypotheses rightly used are among the helps, far more than the dangers, of science;—that scientific induction is not a ‘cautious’ or a ‘rigorous’ process in the sense ofabstaining fromsuch suppositions, but innot adheringto them till they are confirmed by fact, and in carefully seeking from facts confirmation or refutation. Kepler’s distinctive character was, not that he was peculiarly given to the construction of hypotheses, but that he narrated with extraordinary copiousness and candour the course of his thoughts, his labours, and his feelings. In the minds of most persons, as we have said, the inadmissible suppositions, when rejected, are soon forgotten: and thus the trace of them vanishes from the thoughts, and the successful hypothesis alone holds its place in our memory. But in reality, many other transient suppositions must have been made by all discoverers;—hypotheses which are not afterwards asserted as true systems, but entertained for an instant;—‘tentative hypotheses,’ as they have been called. Each of these hypotheses is followed by its corresponding train of observations, from which it derives its power of leading to truth. The hypothesis is83like the captain, and the observations like the soldiers of an army: while he appears to command them, and in this way to work his own will, he does in fact derive all his power of conquest from their obedience, and becomes helpless and useless if they mutiny.Since the discoverer has thus constantly to work his way onwards by means of hypotheses, false and true, it is highly important for him to possess talents and means for rapidlytestingeach supposition as it offers itself. In this as in other parts of the work of discovery, success has in general been mainly owing to the native ingenuity and sagacity of the discoverer’s mind. Yet some Rules tending to further this object have been delivered by eminent philosophers, and some others may perhaps be suggested. Of these we shall here notice only some of the most general, leaving for a future chapter the consideration of some more limited and detailed processes by which, in certain cases, the discovery of the laws of nature may be materially assisted.Sect. III.—Tests of Hypotheses.9. A maxim which it may be useful to recollect is this;—thathypotheses may often be of service to science, when they involve a certain portion of incompleteness, and even of errour. The object of such inventions is to bind together facts which without them are loose and detached; and if they do this, they may lead the way to a perception of the true rule by which the phenomena are associated together, even if they themselves somewhat misstate the matter. The imagined arrangement enables us to contemplate, as a whole, a collection of special cases which perplex and overload our minds when they are considered in succession; and if our scheme has so much of truth in it as to conjoin what is really connected, we may afterwards duly correct or limit the mechanism of this connexion. If our hypothesis renders a reason for the agreement of cases really similar, we may afterwards find this reason to be84false, but we shall be able to translate it into the language of truth.A conspicuous example of such an hypothesis,—one which was of the highest value to science, though very incomplete, and as a representation of nature altogether false,—is seen in theDoctrine of epicyclesby which the ancient astronomers explained the motions of the sun, moon, and planets. This doctrine connected the places and velocities of these bodies at particular times in a manner which was, in its general features, agreeable to nature. Yet this doctrine was erroneous in its assertion of thecircularnature of all the celestial motions, and in making the heavenly bodies revolveround the earth. It was, however, of immense value to the progress of astronomical science; for it enabled men to express and reason upon many important truths which they discovered respecting the motion of the stars, up to the time of Kepler. Indeed we can hardly imagine that astronomy could, in its outset, have made so great a progress under any other form, as it did in consequence of being cultivated in this shape of the incomplete and falseepicyclical hypothesis.We may notice another instance of an exploded hypothesis, which is generally mentioned only to be ridiculed, and which undoubtedly is both false in the extent of its assertion, and unphilosophical in its expression; but which still, in its day, was not without merit. I mean the doctrine ofNature’s horrour of a vacuum(fuga vacui), by which the action of siphons and pumps and many other phenomena were explained, till Mersenne and Pascal taught a truer doctrine. This hypothesis was of real service; for it brought together many facts which really belong to the same class, although they are very different in their first aspect. A scientific writer of modern times13appears to wonder that men did not at once divine the weight of the air, from which the phenomena formerly ascribed to thefuga vacuireally result. ‘Loaded,85compressed by the atmosphere,’ he says, ‘they did not recognize its action. In vain all nature testified that air was elastic and heavy; they shut their eyes to her testimony. The water rose in pumps and flowed in siphons at that time, as it does at this day. They could not separate the boards of a pair of bellows of which the holes were stopped; and they could not bring together the same boards without difficulty, if they were at first separated. Infants sucked the milk of their mothers; air entered rapidly into the lungs of animals at every inspiration; cupping-glasses produced tumours on the skin; and in spite of all these striking proofs of the weight and elasticity of the air, the ancient philosophers maintained resolutely that air was light, and explained all these phenomena by the horrour which they said nature had for a vacuum.’ It is curious that it should not have occurred to the author while writing this, that if these facts, so numerous and various, can all be accounted for byoneprinciple, there is a strong presumption that the principle is not altogether baseless. And in reality is it not true that naturedoesabhor a vacuum, and does all she can to avoid it? No doubt this power is not unlimited; and moreover we can trace it to a mechanical cause, the pressure of the circumambient air. But the tendency, arising from this pressure, which the bodies surrounding a space void of air have to rush into it, may be expressed, in no extravagant or unintelligible manner, by saying that nature has a repugnance to a vacuum.13Deluc,Modifications de l’Atmosphère, Partie 1.That imperfect and false hypotheses, though they may thus explainsomephenomena, and may be useful in the progress of science, cannot explainallphenomena;—and that we are never to rest in our labours or acquiesce in our results, till we have found some view of the subject whichisconsistent withallthe observed facts;—will of course be understood. We shall afterwards have to speak of the other steps of such a progress.10. Thus the hypotheses which we accept ought to explain phenomena which we have observed. But they86ought to do more than this: our hypotheses ought toforetelphenomena which have not yet been observed; at least all phenomena of the same kind as those which the hypothesis was invented to explain. For our assent to the hypothesis implies that it is held to be true of all particular instances. That these cases belong to past or to future times, that they have or have not already occurred, makes no difference in the applicability of the rule to them. Because the rule prevails, it includes all cases; and will determine them all, if we can only calculate its real consequences. Hence it will predict the results of new combinations, as well as explain the appearances which have occurred in old ones. And that it does this with certainty and correctness, is one mode in which the hypothesis is to be verified as right and useful.The scientific doctrines which have at various periods been established have been verified in this manner. For example, theEpicyclical Theoryof the heavens was confirmed by itspredictingtruly eclipses of the sun and moon, configurations of the planets, and other celestial phenomena; and by its leading to the construction of Tables by which the places of the heavenly bodies were given at every moment of time. The truth and accuracy of these predictions were a proof that the hypothesis was valuable, and, at least to a great extent, true; although, as was afterwards found, it involved a false representation of the structure of the heavens. In like manner, the discovery of theLaws of Refractionenabled mathematicians topredict, by calculation, what would be the effect of any new form or combination of transparent lenses. Newton’s hypothesis ofFits of Easy Transmission and Easy Reflectionin the particles of light, although not confirmed by other kinds of facts, involved a true statement of the law of the phenomena which it was framed to include, and served topredictthe forms and colours of thin plates for a wide range of given cases. The hypothesis that Light operates byUndulationsandInterferences, afforded the means ofpredictingresults under a still larger extent of conditions. In like manner in the87progress of chemical knowledge, the doctrine ofPhlogistonsupplied the means offoreseeingthe consequence of many combinations of elements, even before they were tried; but theOxygen Theory, besides affording predictions, at least equally exact, with regard to the general results of chemical operations, included all the facts concerning the relations of weight of the elements and their compounds, and enabled chemists toforeseesuch facts in untried cases. And the Theory ofElectromagnetic Forces, as soon as it was rightly understood, enabled those who had mastered it topredictmotions such as had not been before observed, which were accordingly found to take place.Men cannot help believing that the laws laid down by discoverers must be in a great measure identical with the real laws of nature, when the discoverers thus determine effects beforehand in the same manner in which nature herself determines them when the occasion occurs. Those who can do this, must, to a considerable extent, have detected nature’s secret;—must have fixed upon the conditions to which she attends, and must have seized the rules by which she applies them. Such a coincidence of untried facts with speculative assertions cannot be the work of chance, but implies some large portion of truth in the principles on which the reasoning is founded. To trace order and law in that which has been observed, may be considered as interpreting what nature has written down for us, and will commonly prove that we understand her alphabet. But to predict what has not been observed, is to attempt ourselves to use the legislative phrases of nature; and when she responds plainly and precisely to that which we thus utter, we cannot but suppose that we have in a great measure made ourselves masters of the meaning and structure of her language. The prediction of results, even of the same kind as those which have been observed, in new cases, is a proof of real success in our inductive processes.11. We have here spoken of the prediction of factsof the same kindas those from which our rule was collected. But the evidence in favour of our88induction is of a much higher and more forcible character when it enables us to explain and determine cases of akind differentfrom those which were contemplated in the formation of our hypothesis. The instances in which this has occurred, indeed, impress us with a conviction that the truth of our hypothesis is certain. No accident could give rise to such an extraordinary coincidence. No false supposition could, after being adjusted to one class of phenomena, exactly represent a different class, where the agreement was unforeseen and uncontemplated. That rules springing from remote and unconnected quarters should thus leap to the same point, can only arise fromthatbeing the point where truth resides.Accordingly the cases in which inductions from classes of facts altogether different have thusjumped together, belong only to the best established theories which the history of science contains. And as I shall have occasion to refer to this peculiar feature in their evidence, I will take the liberty of describing it by a particular phrase; and will term it theConsilience of Inductions.It is exemplified principally in some of the greatest discoveries. Thus it was found by Newton that the doctrine of the Attraction of the Sun varying according to the Inverse Square of this distance, which explained Kepler’sThird Law, of the proportionality of the cubes of the distances to the squares of the periodic times of the planets, explained also hisFirstandSecond Laws, of the elliptical motion of each planet; although no connexion of these laws had been visible before. Again, it appeared that the force of universal Gravitation, which had been inferred from thePerturbationsof the moon and planets by the sun and by each other, also accounted for the fact, apparently altogether dissimilar and remote, of thePrecession of the equinoxes. Here was a most striking and surprising coincidence, which gave to the theory a stamp of truth beyond the power of ingenuity to counterfeit. In like manner in Optics; the hypothesis of alternate Fits of easy Transmission and Reflection would explain89the colours of thin plates, and indeed was devised and adjusted for that very purpose; but it could give no account of the phenomena of the fringes of shadows. But the doctrine of Interferences, constructed at first with reference to phenomena of the nature of theFringes, explained also theColours of thin platesbetter than the supposition of the Fits invented for that very purpose. And we have in Physical Optics another example of the same kind, which is quite as striking as the explanation of Precession by inferences from the facts of Perturbation. The doctrine of Undulations propagated in a Spheroidal Form was contrived at first by Huyghens, with a view to explain the laws ofDouble Refractionin calc-spar; and was pursued with the same view by Fresnel. But in the course of the investigation it appeared, in a most unexpected and wonderful manner, that this same doctrine of spheroidal undulations, when it was so modified as to account for thedirectionsof the two refracted rays, accounted also for the positions of theirPlanes of Polarization14, a phenomenon which, taken by itself, it had perplexed previous mathematicians, even to represent.14Hist. Ind. Sc.b. ix. c. xi. sect. 4.The Theory of Universal Gravitation, and of the Undulatory Theory of Light, are, indeed, full of examples of this Consilience of Inductions. With regard to the latter, it has been justly asserted by Herschel, that the history of the undulatory theory was a succession offelicities15. And it is precisely the unexpected coincidences of results drawn from distant parts of the subject which are properly thus described. Thus the Laws of theModification of polarizationto which Fresnel was led by his general views, accounted for the Rule respecting theAngle at which light is polarized, discovered by Sir D. Brewster16. The conceptions of the theory pointed out peculiarModificationsof the phenomena whenNewton’s ringswere produced by polarised light, which modifications were90ascertained to take place in fact, by Arago and Airy17. When the beautiful phenomena ofDipolarized lightwere discovered by Arago and Biot, Young was able to declare that they were reducible to the general laws ofInterferencewhich he had already established18. And what was no less striking a confirmation of the truth of the theory,Measuresof the same element deduced from various classes of facts were found to coincide. Thus theLengthof a luminiferous undulation, calculated by Young from the measurement ofFringesof shadows, was found to agree very nearly with the previous calculation from the colours ofThin plates19.15SeeHist. Ind. Sc.b. ix. c. xii.16Ib.c. xi. sect. 4.17SeeHist. Ind. Sc.b. ix. c. xiii. sect. 6.
CHAPTER V.Of Certain Characteristics of Scientific Induction.
Aphorism X.
The process of scientific discovery is cautious and rigorous, not by abstaining from hypotheses, but by rigorously comparing hypotheses with facts, and by resolutely rejecting all which the comparison does not confirm.
Aphorism XI.
Hypotheses may be useful, though involving much that is superfluous, and even erroneous: for they may supply the true bond of connexion of the facts; and the superfluity and errour may afterwards be pared away.
Aphorism XII.
It is a test of true theories not only to account for, but to predict phenomena.
Aphorism XIII.
Inductionis a term applied to describe the process of a true Colligation of Facts by means of an exact and appropriate Conception.An Inductionis also employed to denote thepropositionwhich results from this process.
Aphorism XIV.
The Consilience of Inductionstakes place when an Induction, obtained from one class of facts, coincides with an Induction, obtained from another different class. This71Consilience is a test of the truth of the Theory in which it occurs.
Aphorism XV.
An Induction is not the meresumof the Facts which are colligated. The Facts are not only brought together, but seen in a new point of view. A new mental Element issuperinduced;and a peculiar constitution and discipline of mind are requisite in order to make this Induction.
Aphorism XVI.
Although in Every Induction a new conception is superinduced upon the Facts; yet this once effectually done, the novelty of the conception is overlooked, and the conception is considered as a part of the fact.
Sect. I.—Invention a part of Induction.
1.THE two operations spoken of in the preceding chapters,—the Explication of the Conceptions of our own minds, and the Colligation of observed Facts by the aid of such Conceptions,—are, as we have just said, inseparably connected with each other. When united, and employed in collecting knowledge from the phenomena which the world presents to us, they constitute the mental process ofInduction; which is usually and justly spoken of as the genuine source of all ourreal general knowledgerespecting the external world. And we see, from the preceding analysis of this process into its two constituents, from what origin it derives each of its characters. It isreal, because it arises from the combination of Real Facts, but it isgeneral, because it implies the possession of General Ideas. Without the former, it would not be knowledge of the External World; without the latter, it would not be Knowledge at all. When Ideas and Facts are separated from each other, the neglect of Facts gives rise to empty speculations, idle subtleties, visionary inventions, false opinions concerning the laws of phenomena, disregard of the true aspect of nature:72while the want of Ideas leaves the mind overwhelmed, bewildered, and stupified by particular sensations, with no means of connecting the past with the future, the absent with the present, the example with the rule; open to the impression of all appearances, but capable of appropriating none. Ideas are theForm, facts theMaterial, of our structure. Knowledge does not consist in the empty mould, or in the brute mass of matter, but in the rightly-moulded substance. Induction gathers general truths from particular facts;—and in her harvest, the corn and the reaper, the solid ears and the binding band, are alike requisite. All our knowledge of nature is obtained by Induction; the term being understood according to the explanation we have now given. And our knowledge is then most complete, then most truly deserves the name of Science, when both its elements are most perfect;—when the Ideas which have been concerned in its formation have, at every step, been clear and consistent; and when they have, at every step also, been employed in binding together real and certain Facts. Of such Induction, I have already given so many examples and illustrations in the two preceding chapters, that I need not now dwell further upon the subject.
2. Induction is familiarly spoken of as the process by which we collect aGeneral Propositionfrom a number ofParticular Cases: and it appears to be frequently imagined that the general proposition results from a mere juxta-position of the cases, or at most, from merely conjoining and extending them. But if we consider the process more closely, as exhibited in the cases lately spoken of, we shall perceive that this is an inadequate account of the matter. The particular facts are not merely brought together, but there is a New Element added to the combination by the very act of thought by which they are combined. There is a Conception of the mind introduced in the general proposition, which did not exist in any of the observed facts. When the Greeks, after long observing the motions of the planets, saw that these motions might be rightly considered as produced by the motion of one73wheel revolving in the inside of another wheel, these Wheels were Creations of their minds, added to the Facts which they perceived by sense. And even if the wheels were no longer supposed to be material, but were reduced to mere geometrical spheres or circles, they were not the less products of the mind alone,—something additional to the facts observed. The same is the case in all other discoveries. The facts are known, but they are insulated and unconnected, till the discoverer supplies from his own stores a Principle of Connexion. The pearls are there, but they will not hang together till some one provides the String. The distances and periods of the planets were all so many separate facts; by Kepler’s Third Law they are connected into a single truth: but the Conceptions which this law involves were supplied by Kepler’s mind, and without these, the facts were of no avail. The planets described ellipses round the sun, in the contemplation of others as well as of Newton; but Newton conceived the deflection from the tangent in these elliptical motions in a new light,—as the effect of a Central Force following a certain law; and then it was, that such a force was discovered truly to exist.
Thus5in each inference made by Induction, there is introduced some General Conception, which is given, not by the phenomena, but by the mind. The conclusion is not contained in the premises, but includes them by the introduction of a New Generality. In order to obtain our inference, we travel beyond the cases which we have before us; we consider them as mere exemplifications of some Ideal Case in which the relations are complete and intelligible. We take a Standard, and measure the facts by it; and this Standard is constructed by us, not offered by Nature. We assert, for example, that a body left to itself will move on with unaltered velocity; not because our senses ever disclosed to us a body doing this, but because (taking this as our Ideal Case) we find that all74actual cases are intelligible and explicable by means of the Conception ofForces, causing change and motion, and exerted by surrounding bodies. In like manner, we see bodies striking each other, and thus moving and stopping, accelerating and retarding each other: but in all this, we do not perceive by our senses that abstract quantity,Momentum, which is always lost by one body as it is gained by another. This Momentum is a creation of the mind, brought in among the facts, in order to convert their apparent confusion into order, their seeming chance into certainty, their perplexing variety into simplicity. This the Conception ofMomentum gained and lostdoes: and in like manner, in any other case in which a truth is established by Induction, some Conception is introduced, some Idea is applied, as the means of binding together the facts, and thus producing the truth.
5I repeat here remarks made at the end of theMechanical Euclid, p. 178.
3. Hence in every inference by Induction, there is some Conceptionsuperinducedupon the Facts: and we may henceforth conceive this to be the peculiar import of the termInduction. I am not to be understood as asserting that the term was originally or anciently employed with this notion of its meaning; for the peculiar feature just pointed out in Induction has generally been overlooked. This appears by the accounts generally given of Induction. ‘Induction,’ says Aristotle6, ‘is when by means of one extreme term7we infer the other extreme term to be true of the middle term.’ Thus, (to take such exemplifications as belong to our subject,) from knowing that Mercury, Venus, Mars, describe ellipses about the Sun, we infer that all Planets describe ellipses about the Sun. In making this inference syllogistically, we assume that the evident proposition, ‘Mercury, Venus, Mars, do what all Planets do,’ may be takenconversely, ‘All75Planets do what Mercury, Venus, Mars, do.’ But we may remark that, in this passage, Aristotle (as was natural in his line of discussion) turns his attention entirely to theevidenceof the inference; and overlooks a step which is of far more importance to our knowledge, namely, theinventionof the second extreme term. In the above instance, the particular luminaries, Mercury, Venus, Mars, are one logicalExtreme; the general designation Planets is theMiddle Term; but having these before us, how do we come to think ofdescription of ellipses, which is the other Extreme of the syllogism? When we have once invented this ‘second Extreme Term,’ we may, or may not, be satisfied with the evidence of the syllogism; we may, or may not, be convinced that, so far as this property goes, the extremes are co-extensive with the middle term8; but thestatementof the syllogism is the important step in science. We know how long Kepler laboured, how hard he fought, how many devices he tried, before he hit upon thisTerm, the Elliptical Motion. He rejected, as we know, many other ‘second extreme Terms,’ for example, various combinations of epicyclical constructions, because they did not represent with sufficient accuracy the special facts of observation. When he had established his premiss, that ‘Mars does describe an Ellipse about the Sun,’ he does not hesitate toguessat least that, in this respect, he mightconvertthe other premiss, and assert that ‘All the Planets do what Mars does.’ But the main business was, the inventing and verifying the proposition respecting the Ellipse. The Invention of the Conception was the great step in thediscovery; the Verification of the Proposition was the great step in theproofof the discovery. If Logic consists in pointing out the conditions of proof, the Logic of Induction must consist in showing what are the conditions of proof, in such inferences as this: but this subject must be pursued in the next chapter; I now speak principally of the act of76Invention, which is requisite in every inductive inference.
6Analyt. Prior.lib. ii. c. xxiii.ΠεÏὶ τῆς á¼Ï€Î±Î³Ï‰Î³á¿†Ï‚.
7The syllogism here alluded to would be this:—Mercury, Venus, Mars, describe ellipses about the Sun;All Planets do what Mercury, Venus, Mars, do;Therefore all Planets describe ellipses about the Sun.
8Εἰ οὖν ἀντιστÏÎφει τὸ Γ Ï„á¿· Î’ καὶ μὴ ὑπεÏτείνει τὸ μÎσον.—Aristot.Ibid.
4. Although in every inductive inference, an act of invention is requisite, the act soon slips out of notice. Although we bind together facts by superinducing upon them a new Conception, this Conception, once introduced and applied, is looked upon as inseparably connected with the facts, and necessarily implied in them. Having once had the phenomena bound together in their minds in virtue of the Conception, men can no longer easily restore them back to the detached and incoherent condition in which they were before they were thus combined. The pearls once strung, they seem to form a chain by their nature. Induction has given them a unity which it is so far from costing us an effort to preserve, that it requires an effort to imagine it dissolved. For instance, we usually represent to ourselves the Earth asround, the Earth and the Planets asrevolvingabout the Sun, and asdrawnto the Sun by a Central Force; we can hardly understand how it could cost the Greeks, and Copernicus, and Newton, so much pains and trouble to arrive at a view which to us is so familiar. These are no longer to us Conceptions caught hold of and kept hold of by a severe struggle; they are the simplest modes of conceiving the facts: they are really Facts. We are willing toownour obligation to those discoverers, but we hardlyfeelit: for in what other manner (we ask in our thoughts) could we represent the facts to ourselves?
Thus we see why it is that this step of which we now speak, the Invention of a new Conception in every inductive inference, is so generally overlooked that it has hardly been noticed by preceding philosophers. When once performed by the discoverer, it takes a fixed and permanent place in the understanding of every one. It is a thought which, once breathed forth, permeates all men’s minds. All fancy they nearly or quite knew it before. It oft was thought, or almost thought, though never till now expressed. Men accept it and retain it, and know it cannot be taken77from them, and look upon it as their own. They will not and cannot part with it, even though they may deem it trivial and obvious. It is a secret, which once uttered, cannot be recalled, even though it be despised by those to whom it is imparted. As soon as the leading term of a new theory has been pronounced and understood, all the phenomena change their aspect. There is a standard to which we cannot help referring them. We cannot fall back into the helpless and bewildered state in which we gazed at them when we possessed no principle which gave them unity. Eclipses arrive in mysterious confusion: the notion of aCycledispels the mystery. The Planets perform a tangled and mazy dance; butEpicyclesreduce the maze to order. The Epicycles themselves run into confusion; the conception of anEllipsemakes all clear and simple. And thus from stage to stage, new elements of intelligible order are introduced. But this intelligible order is so completely adopted by the human understanding, as to seem part of its texture. Men ask Whether Eclipses follow a Cycle; Whether the Planets describe Ellipses; and they imagine that so long as they do notanswersuch questions rashly, they take nothing for granted. They do not recollect how much they assume inaskingthe question:—how far the conceptions of Cycles and of Ellipses are beyond the visible surface of the celestial phenomena:—how many ages elapsed, how much thought, how much observation, were needed, before men’s thoughts were fashioned into the words which they now so familiarly use. And thus they treat the subject, as we have seen Aristotle treating it; as if it were a question, not of invention, but of proof; not of substance, but of form: as if the main thing were notwhatwe assert, buthowwe assert it. But for our purpose, it is requisite to bear in mind the feature which we have thus attempted to mark; and to recollect that, in every inference by induction, there is a Conception supplied by the mind and superinduced upon the Facts.
5. In collecting scientific truths by Induction, we often find (as has already been observed) a Definition78and a Proposition established at the same time,—introduced together, and mutually dependent on each other. The combination of the two constitutes the Inductive act; and we may consider the Definition as representing the superinduced Conception, and the Proposition as exhibiting the Colligation of Facts.
Sect. II.—Use of Hypotheses.
6. To discover a Conception of the mind which will justly represent a train of observed facts is, in some measure, a process of conjecture, as I have stated already; and as I then observed, the business of conjecture is commonly conducted by calling up before our minds several suppositions, and selecting that one which most agrees with what we know of the observed facts. Hence he who has to discover the laws of nature may have to invent many suppositions before he hits upon the right one; and among the endowments which lead to his success, we must reckon that fertility of invention which ministers to him such imaginary schemes, till at last he finds the one which conforms to the true order of nature. A facility in devising hypotheses, therefore, is so far from being a fault in the intellectual character of a discoverer, that it is, in truth, a faculty indispensable to his task. It is, for his purposes, much better that he should be too ready in contriving, too eager in pursuing systems which promise to introduce law and order among a mass of unarranged facts, than that he should be barren of such inventions and hopeless of such success. Accordingly, as we have already noticed, great discoverers have often invented hypotheses which would not answer to all the facts, as well as those which would; and have fancied themselves to have discovered laws, which a more careful examination of the facts overturned.
The tendencies of our speculative nature9, carrying79us onwards in pursuit of symmetry and rule, and thus producing all true theories, perpetually show their vigour by overshooting the mark. They obtain something, by aiming at much more. They detect the order and connexion which exist, by conceiving imaginary relations of order and connexion which have no existence. Real discoveries are thus mixed with baseless assumptions; profound sagacity is combined with fanciful conjecture; not rarely, or in peculiar instances, but commonly, and in most cases; probably in all, if we could read the thoughts of discoverers as we read the books of Kepler. To try wrong guesses is, with most persons, the only way to hit upon right ones. The character of the true philosopher is, not that he never conjectures hazardously, but that his conjectures are clearly conceived, and brought into rigid contact with facts. He sees and compares distinctly the Ideas and the Things;—the relations of his notions to each other and to phenomena. Under these conditions, it is not only excusable, but necessary for him, to snatch at every semblance of general rule,—to try all promising forms of simplicity and symmetry.
9I here take the liberty of characterizing inventive minds in general in the same phraseology which, in the History of Science, I have employed in reference to particular examples. These expressions are what I have used in speaking of the discoveries of Copernicus.—Hist. Ind. Sc.b. v. c. ii.
Hence advances in knowledge10are not commonly made without the previous exercise of some boldness and license in guessing. The discovery of new truths requires, undoubtedly, minds careful and scrupulous in examining what is suggested; but it requires, no less, such as are quick and fertile in suggesting. What is Invention, except the talent of rapidly calling before us the many possibilities, and selecting the appropriate one? It is true, that when we have rejected all the inadmissible suppositions, they are often quickly forgotten; and few think it necessary to dwell on these discarded hypotheses, and on the process by which they were condemned. But all who discover truths, must have reasoned upon many errours to obtain each truth;80every accepted doctrine must have been one chosen out of many candidates. If many of the guesses of philosophers of bygone times now appear fanciful and absurd, because time and observation have refuted them, others, which were at the time equally gratuitous, have been conformed in a manner which makes them appear marvellously sagacious. To form hypotheses, and then to employ much labour and skill in refuting them, if they do not succeed in establishing them, is a part of the usual process of inventive minds. Such a proceeding belongs to theruleof the genius of discovery, rather than (as has often been taught in modern times) to theexception.
10These observations are made on occasion of Kepler’s speculations, and are illustrated by reference to his discoveries.—Hist. Ind. Sc.b. v. c. iv. sect. 1.
7. But if it be an advantage for the discoverer of truth that he be ingenious and fertile in inventing hypotheses which may connect the phenomena of nature, it is indispensably requisite that he be diligent and careful in comparing his hypotheses with the facts, and ready to abandon his invention as soon as it appears that it does not agree with the course of actual occurrences. This constant comparison of his own conceptions and supposition with observed facts under all aspects, forms the leading employment of the discoverer: this candid and simple love of truth, which makes him willing to suppress the most favourite production of his own ingenuity as soon as it appears to be at variance with realities, constitutes the first characteristic of his temper. He must have neither the blindness which cannot, nor the obstinacy which will not, perceive the discrepancy of his fancies and his facts. He must allow no indolence, or partial views, or self-complacency, or delight in seeming demonstration, to make him tenacious of the schemes which he devises, any further than they are confirmed by their accordance with nature. The framing of hypotheses is, for the inquirer after truth, not the end, but the beginning of his work. Each of his systems is invented, not that he may admire it and follow it into all its consistent consequences, but that he may make it the occasion of a course of active experiment and observation. And if the results of this process81contradict his fundamental assumptions, however ingenious, however symmetrical, however elegant his system may be, he rejects it without hesitation. He allows no natural yearning for the offspring of his own mind to draw him aside from the higher duty of loyalty to his sovereign, Truth: to her he not only gives his affections and his wishes, but strenuous labour and scrupulous minuteness of attention.
We may refer to what we have said of Kepler, Newton, and other eminent philosophers, for illustrations of this character. In Kepler we have remarked11the courage and perseverance with which he undertook and executed the task of computing his own hypotheses: and, as a still more admirable characteristic, that he never allowed the labour he had spent upon any conjecture to produce any reluctance in abandoning the hypothesis, as soon as he had evidence of its inaccuracy. And in the history of Newton’s discovery that the moon is retained in her orbit by the force of gravity, we have noticed the same moderation in maintaining the hypothesis, after it had once occurred to the author’s mind. The hypothesis required that the moon should fall from the tangent of her orbit every second through a space of sixteen feet; but according to his first calculations it appeared that in fact she only fell through a space of thirteen feet in that time. The difference seems small, the approximation encouraging, the theory plausible; a man in love with his own fancies would readily have discovered or invented some probable cause of the difference. But Newton acquiesced in it as a disproof of his conjecture, and ‘laid aside at that time any further thoughts of this matter12.’
11Hist. Ind. Sc.b. v. c. iv. sect. 1.
12Hist. Ind. Sc.b. vii. c. ii. sect. 3.
8. It has often happened that those who have undertaken to instruct mankind have not possessed this pure love of truth and comparative indifference to the maintenance of their own inventions. Men have frequently adhered with great tenacity and vehemence to the hypotheses which they have once framed; and in their82affection for these, have been prone to overlook, to distort, and to misinterpret facts. In this manner,Hypotheseshave so often been prejudicial to the genuine pursuit of truth, that they have fallen into a kind of obloquy; and have been considered as dangerous temptations and fallacious guides. Many warnings have been uttered against the fabrication of hypotheses, by those who profess to teach philosophy; many disclaimers of such a course by those who cultivate science.
Thus we shall find Bacon frequently discommending this habit, under the name of ‘anticipation of the mind,’ and Newton thinks it necessary to say emphatically ‘hypotheses non fingo.’ It has been constantly urged that the inductions by which sciences are formed must becautiousandrigorous; and the various imaginations which passed through Kepler’s brain, and to which he has given utterance, have been blamed or pitied, as lamentable instances of an unphilosophical frame of mind. Yet it has appeared in the preceding remarks that hypotheses rightly used are among the helps, far more than the dangers, of science;—that scientific induction is not a ‘cautious’ or a ‘rigorous’ process in the sense ofabstaining fromsuch suppositions, but innot adheringto them till they are confirmed by fact, and in carefully seeking from facts confirmation or refutation. Kepler’s distinctive character was, not that he was peculiarly given to the construction of hypotheses, but that he narrated with extraordinary copiousness and candour the course of his thoughts, his labours, and his feelings. In the minds of most persons, as we have said, the inadmissible suppositions, when rejected, are soon forgotten: and thus the trace of them vanishes from the thoughts, and the successful hypothesis alone holds its place in our memory. But in reality, many other transient suppositions must have been made by all discoverers;—hypotheses which are not afterwards asserted as true systems, but entertained for an instant;—‘tentative hypotheses,’ as they have been called. Each of these hypotheses is followed by its corresponding train of observations, from which it derives its power of leading to truth. The hypothesis is83like the captain, and the observations like the soldiers of an army: while he appears to command them, and in this way to work his own will, he does in fact derive all his power of conquest from their obedience, and becomes helpless and useless if they mutiny.
Since the discoverer has thus constantly to work his way onwards by means of hypotheses, false and true, it is highly important for him to possess talents and means for rapidlytestingeach supposition as it offers itself. In this as in other parts of the work of discovery, success has in general been mainly owing to the native ingenuity and sagacity of the discoverer’s mind. Yet some Rules tending to further this object have been delivered by eminent philosophers, and some others may perhaps be suggested. Of these we shall here notice only some of the most general, leaving for a future chapter the consideration of some more limited and detailed processes by which, in certain cases, the discovery of the laws of nature may be materially assisted.
Sect. III.—Tests of Hypotheses.
9. A maxim which it may be useful to recollect is this;—thathypotheses may often be of service to science, when they involve a certain portion of incompleteness, and even of errour. The object of such inventions is to bind together facts which without them are loose and detached; and if they do this, they may lead the way to a perception of the true rule by which the phenomena are associated together, even if they themselves somewhat misstate the matter. The imagined arrangement enables us to contemplate, as a whole, a collection of special cases which perplex and overload our minds when they are considered in succession; and if our scheme has so much of truth in it as to conjoin what is really connected, we may afterwards duly correct or limit the mechanism of this connexion. If our hypothesis renders a reason for the agreement of cases really similar, we may afterwards find this reason to be84false, but we shall be able to translate it into the language of truth.
A conspicuous example of such an hypothesis,—one which was of the highest value to science, though very incomplete, and as a representation of nature altogether false,—is seen in theDoctrine of epicyclesby which the ancient astronomers explained the motions of the sun, moon, and planets. This doctrine connected the places and velocities of these bodies at particular times in a manner which was, in its general features, agreeable to nature. Yet this doctrine was erroneous in its assertion of thecircularnature of all the celestial motions, and in making the heavenly bodies revolveround the earth. It was, however, of immense value to the progress of astronomical science; for it enabled men to express and reason upon many important truths which they discovered respecting the motion of the stars, up to the time of Kepler. Indeed we can hardly imagine that astronomy could, in its outset, have made so great a progress under any other form, as it did in consequence of being cultivated in this shape of the incomplete and falseepicyclical hypothesis.
We may notice another instance of an exploded hypothesis, which is generally mentioned only to be ridiculed, and which undoubtedly is both false in the extent of its assertion, and unphilosophical in its expression; but which still, in its day, was not without merit. I mean the doctrine ofNature’s horrour of a vacuum(fuga vacui), by which the action of siphons and pumps and many other phenomena were explained, till Mersenne and Pascal taught a truer doctrine. This hypothesis was of real service; for it brought together many facts which really belong to the same class, although they are very different in their first aspect. A scientific writer of modern times13appears to wonder that men did not at once divine the weight of the air, from which the phenomena formerly ascribed to thefuga vacuireally result. ‘Loaded,85compressed by the atmosphere,’ he says, ‘they did not recognize its action. In vain all nature testified that air was elastic and heavy; they shut their eyes to her testimony. The water rose in pumps and flowed in siphons at that time, as it does at this day. They could not separate the boards of a pair of bellows of which the holes were stopped; and they could not bring together the same boards without difficulty, if they were at first separated. Infants sucked the milk of their mothers; air entered rapidly into the lungs of animals at every inspiration; cupping-glasses produced tumours on the skin; and in spite of all these striking proofs of the weight and elasticity of the air, the ancient philosophers maintained resolutely that air was light, and explained all these phenomena by the horrour which they said nature had for a vacuum.’ It is curious that it should not have occurred to the author while writing this, that if these facts, so numerous and various, can all be accounted for byoneprinciple, there is a strong presumption that the principle is not altogether baseless. And in reality is it not true that naturedoesabhor a vacuum, and does all she can to avoid it? No doubt this power is not unlimited; and moreover we can trace it to a mechanical cause, the pressure of the circumambient air. But the tendency, arising from this pressure, which the bodies surrounding a space void of air have to rush into it, may be expressed, in no extravagant or unintelligible manner, by saying that nature has a repugnance to a vacuum.
13Deluc,Modifications de l’Atmosphère, Partie 1.
That imperfect and false hypotheses, though they may thus explainsomephenomena, and may be useful in the progress of science, cannot explainallphenomena;—and that we are never to rest in our labours or acquiesce in our results, till we have found some view of the subject whichisconsistent withallthe observed facts;—will of course be understood. We shall afterwards have to speak of the other steps of such a progress.
10. Thus the hypotheses which we accept ought to explain phenomena which we have observed. But they86ought to do more than this: our hypotheses ought toforetelphenomena which have not yet been observed; at least all phenomena of the same kind as those which the hypothesis was invented to explain. For our assent to the hypothesis implies that it is held to be true of all particular instances. That these cases belong to past or to future times, that they have or have not already occurred, makes no difference in the applicability of the rule to them. Because the rule prevails, it includes all cases; and will determine them all, if we can only calculate its real consequences. Hence it will predict the results of new combinations, as well as explain the appearances which have occurred in old ones. And that it does this with certainty and correctness, is one mode in which the hypothesis is to be verified as right and useful.
The scientific doctrines which have at various periods been established have been verified in this manner. For example, theEpicyclical Theoryof the heavens was confirmed by itspredictingtruly eclipses of the sun and moon, configurations of the planets, and other celestial phenomena; and by its leading to the construction of Tables by which the places of the heavenly bodies were given at every moment of time. The truth and accuracy of these predictions were a proof that the hypothesis was valuable, and, at least to a great extent, true; although, as was afterwards found, it involved a false representation of the structure of the heavens. In like manner, the discovery of theLaws of Refractionenabled mathematicians topredict, by calculation, what would be the effect of any new form or combination of transparent lenses. Newton’s hypothesis ofFits of Easy Transmission and Easy Reflectionin the particles of light, although not confirmed by other kinds of facts, involved a true statement of the law of the phenomena which it was framed to include, and served topredictthe forms and colours of thin plates for a wide range of given cases. The hypothesis that Light operates byUndulationsandInterferences, afforded the means ofpredictingresults under a still larger extent of conditions. In like manner in the87progress of chemical knowledge, the doctrine ofPhlogistonsupplied the means offoreseeingthe consequence of many combinations of elements, even before they were tried; but theOxygen Theory, besides affording predictions, at least equally exact, with regard to the general results of chemical operations, included all the facts concerning the relations of weight of the elements and their compounds, and enabled chemists toforeseesuch facts in untried cases. And the Theory ofElectromagnetic Forces, as soon as it was rightly understood, enabled those who had mastered it topredictmotions such as had not been before observed, which were accordingly found to take place.
Men cannot help believing that the laws laid down by discoverers must be in a great measure identical with the real laws of nature, when the discoverers thus determine effects beforehand in the same manner in which nature herself determines them when the occasion occurs. Those who can do this, must, to a considerable extent, have detected nature’s secret;—must have fixed upon the conditions to which she attends, and must have seized the rules by which she applies them. Such a coincidence of untried facts with speculative assertions cannot be the work of chance, but implies some large portion of truth in the principles on which the reasoning is founded. To trace order and law in that which has been observed, may be considered as interpreting what nature has written down for us, and will commonly prove that we understand her alphabet. But to predict what has not been observed, is to attempt ourselves to use the legislative phrases of nature; and when she responds plainly and precisely to that which we thus utter, we cannot but suppose that we have in a great measure made ourselves masters of the meaning and structure of her language. The prediction of results, even of the same kind as those which have been observed, in new cases, is a proof of real success in our inductive processes.
11. We have here spoken of the prediction of factsof the same kindas those from which our rule was collected. But the evidence in favour of our88induction is of a much higher and more forcible character when it enables us to explain and determine cases of akind differentfrom those which were contemplated in the formation of our hypothesis. The instances in which this has occurred, indeed, impress us with a conviction that the truth of our hypothesis is certain. No accident could give rise to such an extraordinary coincidence. No false supposition could, after being adjusted to one class of phenomena, exactly represent a different class, where the agreement was unforeseen and uncontemplated. That rules springing from remote and unconnected quarters should thus leap to the same point, can only arise fromthatbeing the point where truth resides.
Accordingly the cases in which inductions from classes of facts altogether different have thusjumped together, belong only to the best established theories which the history of science contains. And as I shall have occasion to refer to this peculiar feature in their evidence, I will take the liberty of describing it by a particular phrase; and will term it theConsilience of Inductions.
It is exemplified principally in some of the greatest discoveries. Thus it was found by Newton that the doctrine of the Attraction of the Sun varying according to the Inverse Square of this distance, which explained Kepler’sThird Law, of the proportionality of the cubes of the distances to the squares of the periodic times of the planets, explained also hisFirstandSecond Laws, of the elliptical motion of each planet; although no connexion of these laws had been visible before. Again, it appeared that the force of universal Gravitation, which had been inferred from thePerturbationsof the moon and planets by the sun and by each other, also accounted for the fact, apparently altogether dissimilar and remote, of thePrecession of the equinoxes. Here was a most striking and surprising coincidence, which gave to the theory a stamp of truth beyond the power of ingenuity to counterfeit. In like manner in Optics; the hypothesis of alternate Fits of easy Transmission and Reflection would explain89the colours of thin plates, and indeed was devised and adjusted for that very purpose; but it could give no account of the phenomena of the fringes of shadows. But the doctrine of Interferences, constructed at first with reference to phenomena of the nature of theFringes, explained also theColours of thin platesbetter than the supposition of the Fits invented for that very purpose. And we have in Physical Optics another example of the same kind, which is quite as striking as the explanation of Precession by inferences from the facts of Perturbation. The doctrine of Undulations propagated in a Spheroidal Form was contrived at first by Huyghens, with a view to explain the laws ofDouble Refractionin calc-spar; and was pursued with the same view by Fresnel. But in the course of the investigation it appeared, in a most unexpected and wonderful manner, that this same doctrine of spheroidal undulations, when it was so modified as to account for thedirectionsof the two refracted rays, accounted also for the positions of theirPlanes of Polarization14, a phenomenon which, taken by itself, it had perplexed previous mathematicians, even to represent.
14Hist. Ind. Sc.b. ix. c. xi. sect. 4.
The Theory of Universal Gravitation, and of the Undulatory Theory of Light, are, indeed, full of examples of this Consilience of Inductions. With regard to the latter, it has been justly asserted by Herschel, that the history of the undulatory theory was a succession offelicities15. And it is precisely the unexpected coincidences of results drawn from distant parts of the subject which are properly thus described. Thus the Laws of theModification of polarizationto which Fresnel was led by his general views, accounted for the Rule respecting theAngle at which light is polarized, discovered by Sir D. Brewster16. The conceptions of the theory pointed out peculiarModificationsof the phenomena whenNewton’s ringswere produced by polarised light, which modifications were90ascertained to take place in fact, by Arago and Airy17. When the beautiful phenomena ofDipolarized lightwere discovered by Arago and Biot, Young was able to declare that they were reducible to the general laws ofInterferencewhich he had already established18. And what was no less striking a confirmation of the truth of the theory,Measuresof the same element deduced from various classes of facts were found to coincide. Thus theLengthof a luminiferous undulation, calculated by Young from the measurement ofFringesof shadows, was found to agree very nearly with the previous calculation from the colours ofThin plates19.
15SeeHist. Ind. Sc.b. ix. c. xii.
16Ib.c. xi. sect. 4.
17SeeHist. Ind. Sc.b. ix. c. xiii. sect. 6.