Chapter XXII: Mr. Mill's Logic264 (2)

Mr. Mill enjoins four methods of experimental inquiry, which he calls _the Method of Agreement_, _the Method of Difference_, _the Method of Residues_, and _the Method of Concomitant Variations_[271]. They are all described by formulæ of this kind:--Let there be, in the observed facts, combinations of antecedents, _ABC_, _BC_, _ADE_, &c. and combinations of corresponding consequents, _abc_, _bc_, _ade_, &c.; and let the object of inquiry be, the consequence of some cause _A_, or the cause of some consequence _a_. The Method of Agreement teaches us, that when we find by experiment such facts as _abc_ the consequent of _ABC_, and _ade_ the consequent of _ADE_, then _a_ is the consequent of _A_. The Method of Difference teaches us that when we find such facts as _abc_ the consequent of _ABC_, and _bc_ the consequent of _BC_, then _a_ is the consequent of _A_. The Method of Residues teaches us, that if _abc_ be the consequent of _ABC_, and if we have already ascertained that the effect of _A_ is _a_, and the effect of _B_ is _b_, then we may infer that the effect of _C_ is _c_. The Method of Concomitant Variations teaches us, that if a phenomenon _a_ varies according as another phenomenon _A_ varies, there is some connexion of causation direct or indirect, between _A_ and _a_.

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

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

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

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

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

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

I confess I am quite at a loss to understand what there is in the doctrine here ascribed to Mr. Bain which was not known to the electricians who, from the time of Franklin, explained the phenomena of the Leyden vial. I may observe also that the mention of an "electrified atmosphere" implies a hypothesis long obsolete. The essential point in all those explanations was, that each electricity produced by induction the opposite electricity in neighbouring bodies, as I have tried to make apparent in the _History_[273]. Faraday has, more recently, illustrated this universal co-existence of opposite electricities with his usual felicity.

But the conjunction of this fact with voltaic phenomena, implies a non-recognition of some of the simplest doctrines of the subject. "Since," it is said (i. 488), "common or machine electricity, and voltaic electricity may be considered for the present purpose to be identical, Faraday wished to know, &c." I think Mr. Faraday would be much astonished to learn that he considered electricity in equilibrium, and electricity in the form of a voltaic current, to be, for any purpose, identical. Nor do I conceive that he would assent to the expression in the next page, that "from the nature of a voltaic charge, the two opposite currents necessary to the existence of each other are both accommodated in one wire." Mr. Faraday has, as it appears to me, studiously avoided assenting to this hypothesis.

44. The next example is the one already so copiously dwelt upon by Sir John Herschel, Dr. Wells's researches on the production of Dew. I have already said[274] that "this investigation, although it has sometimes been praised as an original discovery, was in fact only resolving the phenomenon into principles already discovered namely, the doctrine of a _constituent temperature_ of vapour, the different conducting power of different bodies, and the like. And this agrees in substance with what Mr. Mill says (i. 497); that the discovery, when made, was corroborated by deduction from the known laws of aqueous vapour, of conduction, and the like. Dr. Wells's researches on Dew tended much in this country to draw attention to the general principles of Atmology; and we may see, in this and in other examples which Mr. Mill adduces, that the explanation of special phenomena by means of general principles, already established, has, for common minds, a greater charm, and is more complacently dwelt on, than the discovery of the general principles themselves.

45. The next example, (i. 502) is given in order to illustrate the Method of Residues, and is the discovery by M. Arago that a disk of copper affects the vibrations of the magnetic needle. But this apparently detached fact affords little instruction compared with the singularly sagacious researches by which Mr. Faraday discovered the cause of this effect to reside in the voltaic currents which the motion of the magnetic needle developed in the copper. I have spoken of this discovery in the _History_[275]. Mr. Mill however is quoting Sir John Herschel in thus illustrating the Method of Residues. He rightly gives the Perturbations of the Planets and Satellites as better examples of the method[276].

46. In the next chapter (c. x.) Mr. Mill speaks of Plurality of causes and of the Intermixture of effects, and gives examples of such cases. He here teaches (i. 517) that chemical synthesis and analysis, (as when oxygen and hydrogen compose water, and when water is resolved into oxygen and hydrogen,) is properly _transformation_, but that because we find that the weight of the compound is equal to the sum of the weights of the elements, we take up the notion of chemical _composition_. I have endeavoured to show[277] that the maxim, that the sum of the weights of the elements is equal to the weight of the compound, was, historically, not _proved_ from experiment, but _assumed_ in the reasonings upon experiments.

47. I have now made my remarks upon nearly all the examples which Mr. Mill gives of scientific inquiry, so far as they consist of knowledge which has really been obtained. I may mention, as points which appear to me to interfere with the value of Mr. Mill's references to examples, expressions which I cannot reconcile with just conceptions of scientific truth; as when he says (i. 523), "some other force which _impinges on_ the first force;" and very frequently indeed, of the "tangential _force_," as co-ordinate with the centripetal force.

When he speaks (ii. 20, Note) of "the doctrine now universally received that the earth is a great natural magnet with two poles," he does not recognize the recent theory of Gauss, so remarkably coincident with a vast body of facts[278]. Indeed in his statement, he rejects no less the earlier views proposed by Halley, theorized by Euler, and confirmed by Hansteen, which show that we are compelled to assume at least _four_ poles of terrestrial magnetism; which I had given an account of in the first edition of the _History_.

There are several other cases which he puts, in which, the knowledge spoken of not having been yet acquired, he tells us how he would set about acquiring it; for instance, if the question were (i. 526) whether mercury be a cure for a given disease; or whether the brain be a voltaic pile (ii. 21); or whether the moon be inhabited (ii. 100); or whether all crows are black (ii. 124); I confess that I have no expectation of any advantage to philosophy from discussions of this kind.

48. I will add also, that I do not think any light can be thrown upon scientific methods, at present, by grouping along with such physical inquiries as I have been speaking of, speculations concerning the human mind, its qualities and operations. Thus he speaks (i. 508) of human characters, as exemplifying the effect of plurality of causes; of (i. 518) the phenomena of our mental nature, which are analogous to chemical rather than to dynamical phenomena; of (i. 518) the reason why susceptible persons are imaginative; to which I may add, the passage where he says (i. 444), "let us take as an example of a phenomenon which we have no means of fabricating artificially, a human mind." These, and other like examples, occur in the part of his work in which he is speaking of scientific inquiry in general, not in the Book on the Logic of the Moral Sciences; and are, I think, examples more likely to lead us astray than to help our progress, in discovering the laws of Scientific Inquiry, in the ordinary sense of the term.

VI. _Mr. Mill against Hypothesis._--49. I will now pass from Mr. Mill's methods, illustrated by such examples as those which I have been considering, to the views respecting the conditions of Scientific Induction to which I have been led, by such a survey as I could make, of the whole history of the principal Inductive Sciences; and especially, to those views to which Mr. Mill offers his objections[279].

Mr. Mill thinks that I have been too favourable to the employment of hypotheses, as means of discovering scientific truth; and that I have countenanced a laxness of method, in allowing hypotheses to be established, merely in virtue of the accordance of their results with the phenomena. I believe I should be as cautious as Mr. Mill, in accepting mere hypothetical explanations of phenomena, in any case in which we had the phenomena, and their relations, placed before both of us in an equally clear light. I have not accepted the Undulatory theory of Heat, though recommended by so many coincidences and analogies[280]. But I see some grave reasons for not giving any great weight to Mr. Mill's admonitions;--reasons drawn from the language which he uses on the subject, and which appears to me inconsistent with the conditions of the cases to which he applies it. Thus, when he says (ii. 22) that the condition of a hypothesis accounting for all the known phenomena is "often fulfilled equally well by two conflicting hypotheses," I can only say that I know of no such case in the history of Science, where the phenomena are at all numerous and complicated; and that if such a case were to occur, one of the hypotheses might always be resolved into the other. When he says, that "this evidence (the agreement of the results of the hypothesis with the phenomena) cannot be of the smallest value, because we cannot have in the case of such an hypothesis the assurance that if the hypothesis be false it must lead to results at variance with the true facts," we must reply, with due submission, that we have, in the case spoken of, the most complete evidence of this; for any change in the hypothesis would make it incapable of accounting for the facts. When he says that "if we give ourselves the license of inventing the causes as well as their laws, a person of fertile imagination might devise a hundred modes of accounting for any given fact;" I reply, that the question is about accounting for a large and complex series of facts, of which the laws have been ascertained: and as a test of Mr. Mill's assertion, I would propose as a challenge to any person of fertile imagination to devise any _one_ other hypothesis to account for the perturbations of the moon, or the coloured fringes of shadows, besides the hypothesis by which they have actually been explained with such curious completeness. This challenge has been repeatedly offered, but never in any degree accepted; and I entertain no apprehension that Mr. Mill's supposition will ever be verified by such a performance.

50. I see additional reason for mistrusting the precision of Mr. Mill's views of that accordance of phenomena with the results of a hypothesis, in several others of the expressions which he uses (ii. 23). He speaks of a hypothesis being a "_plausible_ explanation of all or most of the phenomena;" but the case which we have to consider is where it gives an _exact_ representation of all the phenomena in which its results can be traced. He speaks of its being certain that the laws of the phenomena are "_in some measure analogous_" to those given by the hypothesis; the case to be dealt with being, that they are in every way identical. He speaks of this analogy being certain, from the fact that the hypothesis can be "for a moment _tenable_;" as if any one had recommended a hypothesis which is tenable only while a small part of the facts are considered, when it is inconsistent with others which a fuller examination of the case discloses. I have nothing to say, and have said nothing, in favour of hypotheses which are _not_ tenable. He says there are many such "_harmonies_ running through the laws of phenomena in other respects radically distinct;" and he gives as an instance, the laws of light and heat. I have never alleged such harmonies as grounds of theory, unless they should amount to identities; and if they should do this, I have no doubt that the most sober thinkers will suppose the causes to be of the same kind in the two harmonizing instances. If chlorine, iodine and brome, or sulphur and phosphorus, have, as Mr. Mill says, analogous properties, I should call these substances _analogous_: but I can see no temptation to frame an hypothesis that they are _identical_ (which he seems to fear), so long as Chemistry proves them distinct. But any hypothesis of an analogy in the constitution of these elements (suppose, for instance, a resemblance in their atomic form or composition) would seem to me to have a fair claim to trial; and to be capable of being elevated from one degree of probability to another by the number, variety, and exactitude of the explanations of phenomena which it should furnish.

VII. _Against prediction of Facts._--51. These expressions of Mr. Mill have reference to a way in which hypotheses may be corroborated, in estimating the value of which, it appears that he and I differ. "It seems to be thought," he says (ii. 23), "that an hypothesis of the sort in question is entitled to a more favourable reception, if, besides accounting for the facts previously known, it has led to the anticipation and prediction of others which experience afterwards verified." And he adds, "Such predictions and their fulfilment are indeed well calculated to strike the ignorant vulgar;" but it is strange, he says, that any considerable stress should be laid upon such a coincidence by scientific thinkers. However strange it may seem to him, there is no doubt that the most scientific thinkers, far more than the ignorant vulgar, have allowed the coincidence of results predicted by theory with fact afterwards observed, to produce the strongest effects upon their conviction; and that all the best-established theories have obtained their permanent place in general acceptance in virtue of such coincidences, more than of any other evidence. It was not the ignorant vulgar alone, who were struck by the return of Halley's comet, as an evidence of the Newtonian theory. Nor was it the ignorant vulgar, who were struck with those facts which did so much strike men of science, as curiously felicitous proofs of the undulatory theory of light,--the production of darkness by two luminous rays interfering in a special manner; the refraction of a single ray of light into a conical pencil; and other complex yet precise results, predicted by the theory and verified by experiment. It must, one would think, strike all persons in proportion to their thoughtfulness, that when Nature thus does our bidding, she acknowledges that we have learnt her true language. If we can predict new facts which we have not seen, as well as explain those which we have seen, it must be because our explanation is not a mere formula of observed facts, but a truth of a deeper kind. Mr. Mill says, "If the laws of the propagation of light agree with those of the vibrations of an elastic fluid in so many respects as is necessary to make the hypothesis a plausible explanation of all or most of the phenomena known at the time, it is nothing strange that they should accord with each other in one respect more." Nothing strange, if the theory be true; but quite unaccountable, if it be not. If I copy a long series of letters of which the last half-dozen are concealed, and if I guess those aright, as is found to be the case when they are afterwards uncovered, this must be because I have made out the import of the inscription. To say, that because I have copied all that I could see, it is nothing strange that I should guess those which I cannot see, would be absurd, without supposing such a ground for guessing. The notion that the discovery of the laws and causes of phenomena is a loose haphazard sort of guessing, which gives "plausible" explanations, accidental coincidences, casual "harmonies," laws, "in some measure analogous" to the true ones, suppositions "tenable" for a time, appears to me to be a misapprehension of the whole nature of science; as it certainly is inapplicable to the case to which it is principally applied by Mr. Mill.

52. There is another kind of evidence of theories, very closely approaching to the verification of untried predictions, and to which, apparently, Mr. Mill does not attach much importance, since he has borrowed the term by which I have described it, _Consilience_, but has applied it in a different manner (ii. 530, 563, 590). I have spoken, in the _Philosophy_[281], of the _Consilience of Inductions_, as one of the _Tests of Hypotheses_, and have exemplified it by many instances; for example, the theory of universal gravitation, obtained by induction from the motions of the planets, was found to explain also that peculiar motion of the spheroidal earth which produces the Precession of the Equinoxes. This, I have said, was a striking and surprising coincidence which gave the theory a stamp of truth beyond the power of ingenuity to counterfeit. I may compare such occurrences to a case of interpreting an unknown character, in which two different inscriptions, deciphered by different persons, had given the same alphabet. We should, in such a case, believe with great confidence that the alphabet was the true one; and I will add, that I believe the history of science offers no example in which a theory supported by such consiliences, had been afterwards proved to be false.

53. Mr. Mill accepts (ii. 21) a rule of M. Comte's, that we may apply hypotheses, provided they are capable of being afterwards verified as facts. I have a much higher respect for Mr. Mill's opinion than for M. Comte's[282]; but I do not think that this rule will be found of any value. It appears to me to be tainted with the vice which I have already noted, of throwing the whole burthen of explanation upon the unexplained word _fact_--unexplained in any permanent and definite opposition to theory. As I have said, the Newtonian theory _is_ a fact. Every true theory is a fact. Nor does the distinction become more clear by Mr. Mill's examples. "The vortices of Descartes would have been," he says, "a perfectly legitimate hypothesis, if it had been possible by any mode of explanation which we could entertain the hope of possessing, to bring the question whether such vortices exist or not, within the reach of our observing faculties." But this was possible, and was done. The free passage of comets through the spaces in which these vortices should have been, convinced men that these vortices did not exist. In like manner Mr. Mill rejects the hypothesis of a luminiferous ether, "because it can neither be seen, heard, smelt, tasted, or touched." It is a strange complaint to make of the vehicle of light, that it cannot be heard, smelt, or tasted. Its vibrations _can_ be seen. The fringes of shadows for instance, show its vibrations, just as the visible lines of waves near the shore show the undulations of the sea. Whether this can be touched, that is, whether it resists motion, is hardly yet clear. I am far from saying there are not difficulties on this point, with regard to _all_ theories which suppose a _medium_. But there are no more difficulties of this kind in the undulatory theory of light, than there are in Fourier's theory of heat, which M. Comte adopts as a model of scientific investigation; or in the theory of voltaic _currents_, about which Mr. Mill appears to have no doubt; or of electric _atmospheres_, which, though generally obsolete, Mr. Mill appears to favour; for though it had been said that we _feel_ such atmospheres, no one had said that they have the other attributes of matter.

VIII. _Newton's Vera Causa._--54. Mr. Mill conceives (ii. 17) that his own rule concerning hypotheses coincides with Newton's Rule, that the cause assumed must be a _vera causa_. But he allows that "Mr. Whewell ... has had little difficulty in showing that his (Newton's) conception was neither precise nor consistent with itself." He also allows that "Mr. Whewell is clearly right in denying it to be necessary that the cause assigned should be a cause already known; else how could we ever become acquainted with new causes?" These points being agreed upon, I think that a little further consideration will lead to the conviction that Newton's Rule of philosophizing will best become a valuable guide, if we understand it as asserting that when the explanation of two or more different kinds of phenomena (as the revolutions of the planets, the fall of a stone, and the precession of the equinoxes,) lead us to _the same_ cause, such a coincidence gives a reality to the cause. We have, in fact, in such a case, a Consilience of Inductions.

55. When Mr. Mill condemns me (ii. 24) (using, however, expressions of civility which I gladly acknowledge,) for having recognized no mode of Induction except that of trying hypothesis after hypothesis until one is found which fits the phenomena, I must beg to remind the readers of our works, that Mr. Mill himself allows (i. 363) that the process of finding a conception which binds together observed facts "is tentative, that it consists of a succession of guesses, many being rejected until one at last occurs fit to be chosen." I must remind them also that I have given a Section upon the _Tests of Hypotheses_, to which I have just referred,--that I have given various methods of Induction, as the _Method of Gradation_, the _Method of Natural Classification_, the _Method of Curves_, the _Method of Means_, the _Method of Least Squares_, the _Method of Residues_: all which I have illustrated by conspicuous examples from the History of Science; besides which, I conceive that what I have said of the Ideas belonging to each science, and of the construction and explication of conceptions, will point out in each case, in what region we are to look for the Inductive Element in order to make new discoveries. I have already ventured to say, elsewhere, that the methods which I have given, are as definite and practical as any others which have been proposed, with the great additional advantage of being the methods by which all great discoveries in science have really been made.

IX. _Successive Generalizations._--56. There is one feature in the construction of science which Mr. Mill notices, but to which he does not ascribe, as I conceive, its due importance: I mean, that process by which we not only ascend from particular facts to a general law, but when this is done, ascend from the first general law to others more general; and so on, proceeding to the highest point of generalization. This character of the scientific process was first clearly pointed out by Bacon, and is one of the most noticeable instances of his philosophical sagacity. "There are," he says, "two ways, and can be only two, of seeking and finding truth. The one from sense and particulars, takes a flight to the most general axioms, and from these principles and their truth, settled once for all, invents and judges of intermediate axioms. The other method collects axioms from sense and particulars, ascending _continuously and by degrees_, so that in the end it arrives at the most general axioms:" meaning by _axioms_, laws or principles. The structure of the most complete sciences consists of several such steps,--_floors_, as Bacon calls them, of successive generalization; and thus this structure may be exhibited as a kind of scientific pyramid. I have constructed this pyramid in the case of the science of Astronomy[283]: and I am gratified to find that the illustrious Humboldt approves of the design, and speaks of it as executed with complete success[284]. The capability of being exhibited in this form of successive generalizations, arising from particulars upward to some very general law, is the condition of all tolerably perfect sciences; and the steps of the successive generalizations are commonly the most important events in the history of the science.

57. Mr. Mill does not reject this process of generalization; but he gives it no conspicuous place, making it only one of three modes of reducing a law of causation into other laws. "There is," he says (i. 555), "the _subsumption_ of one law under another; ... the gathering up of several laws into one more general law which includes them all. He adds afterwards, that the general law is the _sum_ of the partial ones (i. 557), an expression which appears to me inadequate, for reasons which I have already stated. The general law is not the mere sum of the particular laws. It is, as I have already said, their amount _in a new point of view_. A new conception is introduced; thus, Newton did not merely add together the laws of the motions of the moon and of the planets, and of the satellites, and of the earth; he looked at them altogether as the result of a universal force of mutual gravitation; and therein consisted his generalization. And the like might be pointed out in other cases.

58. I am the more led to speak of Mr. Mill as not having given due importance to this process of successive generalization, by the way in which he speaks in another place (ii. 525) of this doctrine of Bacon. He conceives Bacon "to have been radically wrong when he enunciates, as a universal rule, that induction should proceed from the lowest to the middle principles, and from those to the highest, never reversing that order, and consequently, leaving no room for the discovery of new principles by way of deduction[285] at all."

59. I conceive that the Inductive Table of Astronomy, to which I have already referred, shows that in that science,--the most complete which has yet existed,--the history of the science has gone on, as to its general movement, in accordance with the view which Bacon's sagacity enjoined. The successive generalizations, _so far as they were true_, were made by successive generations. I conceive also that the Inductive Table of Optics shows the same thing; and this, without taking for granted the truth of the Undulatory Theory; for with regard to all the steps of the progress of the science, lower than that highest one, there is, I conceive, no controversy.

60. Also, the Science of Mechanics, although Mr. Mill more especially refers to it, as a case in which the highest generalizations (for example the Laws of Motion) were those earliest ascertained with any scientific exactness, will, I think, on a more careful examination of its history, be found remarkably to confirm Bacon's view. For, in that science, we have, in the first place, very conspicuous examples of the vice of the method pursued by the ancients in flying to the highest generalizations first; as when they made their false distinctions of the laws of _natural_ and _violent_ motions, and of _terrestrial_ and _celestial_ motions. Many erroneous laws of motion were asserted through neglect of facts or want of experiments. And when Galileo and his school had in some measure succeeded in discovering some of the true laws of the motions of terrestrial bodies, they did not at once assert them as general: for they did not at all apply those laws to the celestial motions. As I have remarked, all Kepler's speculations respecting the causes of the motions of the planets, went upon the supposition that the First Law of terrestrial Motion did not apply to celestial bodies; but that, on the contrary, some continual force was requisite to keep up, as well as to originate, the planetary motions. Nor did Descartes, though he enunciated the Laws of Motion with more generality than his predecessors, (but not with exactness,) venture to trust the planets to those laws; on the contrary, he invented his machinery of Vortices in order to keep up the motions of the heavenly bodies. Newton was the first who extended the laws of terrestrial motion to the celestial spaces; and in doing so, he used all the laws of the celestial motions which had previously been discovered by more limited inductions. To these instances, I may add the gradual generalization of the Third Law of motion by Huyghens, the Bernoullis, and Herman, which I have described in the _History_[286] as preceding that Period of Deduction, to which the succeeding narrative[287] is appropriated. In Mechanics, then, we have a cardinal example of the historically gradual and successive ascent of science from particulars to the most general laws.

61. The Science of Hydrostatics may appear to offer a more favourable example of the ascent to the most general laws, without going through the intermediate particular laws; and it is true, with reference to this science, as I have observed[288], that it does exhibit the _peculiarity_ of our possessing the most general principles on which the phenomena depend, and from which many cases of special facts are explained by deduction; while other cases cannot be so explained, from the want of principles intermediate between the highest and the lowest. And I have assigned, as the reason of this peculiarity, that the general principles of the Mechanics of Fluids were not obtained with reference to the science itself, but by extension from the sister science of the Mechanics of Solids. The two sciences are parts of the same Inductive Pyramid; and having reached the summit of this Pyramid on one side, we are tempted to descend on the other from the highest generality to more narrow laws. Yet even in this science, the best part of our knowledge is mainly composed of inductive laws, obtained by inductive examination of particular classes of facts. The mere mathematical investigations of the laws of waves, for instance, have not led to any results so valuable as the experimental researches of Bremontier, Emy, the Webers, and Mr. Scott Russell. And in like manner in Acoustics, the Mechanics of Elastic Fluids[289], the deductions of mathematicians made on general principles have not done so much for our knowledge, as the cases of vibrations of plates and pipes examined experimentally by Chladni, Savart, Mr. Wheatstone and Mr. Willis. We see therefore, even in these sciences, no reason to slight the wisdom which exhorts us to ascend from particulars to intermediate laws, rather than to hope to deduce these latter better from the more general laws obtained once for all.

62. Mr. Mill himself indeed, notwithstanding that he slights Bacon's injunction to seek knowledge by proceeding from less general to more general laws, has given a very good reason why this is commonly necessary and wise. He says (ii. 526), "Before we attempt to explain deductively, from more general laws, any new class of phenomena, it is desirable to have gone as far as is practicable in ascertaining the empirical laws of these phenomena; so as to compare the results of deduction, not with one individual instance after another, but with general propositions expressive of the points of agreement which have been found among many instances. For," he adds with great justice, "if Newton had been obliged to verify the theory of gravitation, not by deducing from it Kepler's laws, but by deducing all the observed planetary positions which had served Kepler to establish those laws, the Newtonian theory would probably never have emerged from the state of an hypothesis." To which we may add, that it is certain, from the history of the subject, that in that case the hypothesis would never have been framed at all.

X. _Mr. Mill's Hope from Deduction._--63. Mr. Mill expresses a hope of the efficacy of Deduction, rather than Induction, in promoting the future progress of Science; which hope, so far as the physical sciences are concerned, appears to me at variance with all the lessons of the history of those sciences. He says (i. 579), "that the advances henceforth to be expected even in physical, and still more in mental and social science, will be chiefly the result of deduction, is evident from the general considerations already adduced:" these considerations being, that the phenomena to be considered are very complex, and are the result of many known causes, of which we have to disentangle the results.

64. I cannot but take a very different view from this. I think that any one, looking at the state of physical science, will see that there are still a vast mass of cases, in which we do not at all know the causes, at least, in their full generality; and that the knowledge of new causes, and the generalization of the laws of those already known, can only be obtained by new _inductive_ discoveries. Except by new Inductions, equal, in their efficacy for grouping together phenomena in new points of view, to any which have yet been performed in the history of science, how are we to solve such questions as those which, in the survey of what we already know, force themselves upon our minds? Such as, to take only a few of the most obvious examples--What is the nature of the connexion of heat and light? How does heat produce the expansion, liquefaction and vaporization of bodies? What is the nature of the connexion between the optical and the chemical properties of light? What is the relation between optical, crystalline and chemical polarity? What is the connexion between the atomic constitution and the physical qualities of bodies? What is the tenable definition of a mineral species? What is the true relation of the apparently different types of vegetable life (monocotyledons, dicotyledons, and cryptogamous plants)? What is the relation of the various types of animal life (vertebrates, articulates, radiates, &c.)? What is the number, and what are the distinctions of the Vital Powers? What is the internal constitution of the earth? These, and many other questions of equal interest, no one, I suppose, expects to see solved by deduction from principles already known. But we can, in many of them, see good hope of progress by a large use of induction; including, of course, copious and careful experiments and observations.

65. With such questions before us, as have now been suggested, I can see nothing but a most mischievous narrowing of the field and enfeebling of the spirit of scientific exertion, in the doctrine that "Deduction is the great scientific work of the present and of future ages;" and that "A revolution is peaceably and progressively effecting itself in philosophy the reverse of that to which Bacon has attached his name." I trust, on the contrary, that we have many new laws of nature still to discover; and that our race is destined to obtain a sight of wider truths than any we yet discern, including, as cases, the general laws we now know, and obtained from these known laws as they must be, by Induction.

66. I can see, however, reasons for the comparatively greater favour with which Mr. Mill looks upon Deduction, in the views to which he has mainly directed his attention. The explanation of remarkable phenomena by known laws of Nature, has, as I have already said, a greater charm for many minds than the discovery of the laws themselves. In the case of such explanations, the problem proposed is more definite, and the solution more obviously complete. For the process of induction includes a mysterious step, by which we pass from particulars to generals, of which step the reason always seems to be inadequately rendered by any words which we can use; and this step to most minds is not demonstrative, as to few is it given to perform it on a great scale. But the process of explanation of facts by known laws is deductive, and has at every step a force like that of demonstration, producing a feeling peculiarly gratifying to the clear intellects which are most capable of following the process. We may often see instances in which this admiration for deductive skill appears in an extravagant measure; as when men compare Laplace with Newton. Nor should I think it my business to argue against such a preference, unless it were likely to leave us too well satisfied with what we know already, to chill our hope of scientific progress, and to prevent our making any further strenuous efforts to ascend, higher than we have yet done, the mountain-chain which limits human knowledge.

67. But there is another reason which, I conceive, operates in leading Mr. Mill to look to Deduction as the principal means of future progress in knowledge, and which is a reason of considerable weight in the subjects of research which, as I conceive, he mainly has in view. In the study of our own minds and of the laws which govern the history of society, I do not think that it is very likely that we shall hereafter arrive at any wider principles than those of which we already possess some considerable knowledge; and this, for a special reason; namely, that our knowledge in such cases is not gathered by mere external observation of a collection of external facts; but acquired by attention to internal facts, our own emotions, thoughts, and springs of action; facts are connected by ties existing in our own consciousness, and not in mere observed juxtaposition, succession, or similitude. How the character, for instance, is influenced by various causes, (an example to which Mr. Mill repeatedly refers, ii. 518, &c.), is an inquiry which may perhaps be best conducted by considering what we know of the influence of education and habit, government and occupation, hope and fear, vanity and pride, and the like, upon men's characters, and by tracing the various effects of the intermixture of such influences. Yet even here, there seems to be room for the discovery of laws in the way of experimental inquiry: for instance, what share race or family has in the formation of character; a question which can hardly be solved to any purpose in any other way than by collecting and classing instances. And in the same way, many of the principles which regulate the material wealth of states, are obtained, if not exclusively, at least most clearly and securely, by induction from large surveys of facts. Still, however, I am quite ready to admit that in Mental and Social Science, we are much less likely than in Physical Science, to obtain new truths by any process which can be distinctively termed _Induction_; and that in those sciences, what may be called _Deductions_ from principles of thought and action of which we are already conscious, or to which we assent when they are felicitously picked out of our thoughts and put into words, must have a large share; and I may add, that this observation of Mr. Mill appears to me to be important, and, in its present connexion, new.

XI. _Fundamental opposition of our doctrines._--68. I have made nearly all the remarks which I now think it of any consequence to make upon Mr. Mill's _Logic_, so far as it bears upon the doctrines contained in my _History_ and _Philosophy_. And yet there remains still untouched one great question, involving probably the widest of all the differences between him and me. I mean the question whether geometrical axioms, (and, as similar in their evidence to these, _all_ axioms,) be truths derived from experience, or be necessary truths in some deeper sense. This is one of the fundamental questions of philosophy; and all persons who take an interest in metaphysical discussions, know that the two opposite opinions have been maintained with great zeal in all ages of speculation. To me it appears that there are _two_ distinct elements in our knowledge, Experience, without, and the Mind, within. Mr. Mill derives all our knowledge from Experience _alone_. In a question thus going to the root of all knowledge, the opposite arguments must needs cut deep on both sides. Mr. Mill cannot deny that our knowledge of geometrical axioms and the like, _seems_ to be _necessary_. I cannot deny that our knowledge, axiomatic as well as other, _never is_ acquired _without experience_.

69. Perhaps ordinary readers may despair of following our reasonings, when they find that they can only be made intelligible by supposing, on the one hand, a person who thinks distinctly and yet has never seen or felt any external object; and on the other hand, a person who is transferred, as Mr. Mill supposes (ii. 117), to "distant parts of the stellar regions where the phenomena may be entirely unlike those with which we are acquainted," and where even the axiom, that every effect must have a cause, does not hold good. Nor, in truth, do I think it necessary here to spend many words on this subject. Probably, for those who take an interest in this discussion, most of the arguments on each side have already been put forwards with sufficient repetition. I have, in an "Essay on the Fundamental Antithesis of Philosophy," and in some accompanying "Remarks," printed[290] at the end of the second edition of my _Philosophy_, given my reply to what has been said on this subject, both by Mr. Mill, and by the author of a very able critique on my _History_ and _Philosophy_ which appeared in the _Quarterly Review_ in 1841: and I will not here attempt to revive the general discussion.

70. Perhaps I may be allowed to notice, that in one part of Mr. Mill's work where this subject is treated, there is the appearance of one of the parties to the controversy pronouncing judgment in his own cause. This indeed is a temptation which it is especially difficult for an author to resist, who writes a treatise upon _Fallacies_, the subject of Mr. Mill's fifth Book. In such a treatise, the writer has an easy way of disposing of adverse opinions by classing them as "Fallacies," and putting them side by side with opinions universally acknowledged to be false. In this way, Mr. Mill has dealt with several points which are still, as I conceive, matters of controversy (ii. 357, &c.).

71. But undoubtedly, Mr. Mill has given his argument against my opinions with great distinctness in another place (i. 319). In order to show that it is merely habitual association which gives to an experimental truth the character of a necessary truth, he quotes the case of the laws of motion, which were really discovered from experiment, but are now looked upon as the only conceivable laws; and especially, what he conceives as "the _reductio ad absurdum_ of the theory of inconceivableness," an opinion which I had ventured to throw out, that if we could conceive the Composition of bodies distinctly, we might be able to see that it is necessary that the modes of their composition should be definite. I do not think that readers in general will see anything absurd in the opinion, that the laws of Mechanics, and even the laws of the Chemical Composition of bodies, may depend upon principles as necessary as the properties of space and number; and that this necessity, though not at all perceived by persons who have only the ordinary obscure and confused notions on such subjects, may be evident to a mind which has, by effort and discipline, rendered its ideas of Mechanical Causation, Elementary Composition and Difference of Kind, clear and precise. It may easily be, I conceive, that while such necessary principles are perceived to be necessary only by a few minds of highly cultivated insight, such principles as the axioms of Geometry and Arithmetic may be perceived to be necessary by _all_ minds which have any habit of abstract thought at all: and I conceive also, that though these axioms are brought into distinct view by a certain degree of intellectual cultivation, they may still be much better described as conditions of experience, than as results of experience:--as laws of the mind and of its activity, rather than as facts impressed upon a mind merely passive.

XII. _Absurdities in Mr. Mill's Logic._--72. I will not pursue the subject further: only, as the question has arisen respecting the absurdities to which each of the opposite doctrines leads, I will point out opinions connected with this subject, which Mr. Mill has stated in various parts of his book.

He holds (i. 317) that it is merely from habit that we are unable to conceive the _last point_ of space or the _last instant_ of time. He holds (ii. 360) that it is strange that any one should rely upon the _à priori_ evidence that space or extension is infinite, or that nothing can be made of nothing. He holds (i. 304) that the first law of _motion_ is _rigorously true_, but that the axioms respecting the _lever_ are only _approximately_ true. He holds (ii. 110) that there may be sidereal firmaments in which events succeed each other at random, without obeying any laws of causation; although one might suppose that even if space and cause are both to have their limits, still they might terminate together: and then, even on this bold supposition, we should no _where_ have a world in which events were _casual_. He holds (ii. 111) that the axiom, that every event must have a cause, is established by means of an "induction by simple enumeration:" and in like manner, that the principles of number and of geometry are proved by this method of simple enumeration alone. He ascribes the proof (i. 162) of the axiom, "things which are equal to the same are equal to each other," to the fact that this proposition has been perpetually _found_ true and never false. He holds (i. 338) that "In all propositions concerning numbers, a condition is implied, without which none of them would be true; and that condition is an assumption which _may be false_. _The condition is that_ 1 = 1."

73. Mr. Mill further holds (i. 309), that it is a characteristic property of geometrical forms, that they are capable of being painted in the imagination with a distinctness equal to reality:--that our ideas of forms exactly resemble our sensations: which, it is implied, is not the case with regard to any other class of our ideas;--that we thus may have mental pictures of all possible combinations of lines and angles, which are as fit subjects of geometrical experimentation as the realities themselves. He says, that "we know that the imaginary lines exactly resemble real ones;" and that we obtain this knowledge respecting the characteristic property of the idea of space by experience; though it does not appear _how_ we can compare our _ideas_ with the _realities_, since we know the realities only _by_ our ideas; or why this property of their resemblance should be confined to _one class_ of ideas alone.