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 thePhilosophy[281], of theConsilience of Inductions, as one of theTests 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 wordfact—unexplained in any permanent and definite opposition to theory. As I have said, the Newtonian theoryisa 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 freepassage 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 vibrationscanbe 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 toalltheories which suppose amedium. 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 voltaiccurrents, about which Mr. Mill appears to have no doubt; or of electricatmospheres, which, though generally obsolete, Mr. Mill appears to favour; for though it had been said that wefeelsuch 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 avera 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 tothe samecause, such a coincidence gives areality 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 theTests of Hypotheses, to which I have just referred,—that I have given various methods of Induction, as theMethod of Gradation, theMethod of Natural Classification, theMethod of Curves, theMethod of Means, theMethod of Least Squares, theMethod 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 ofhis 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, ascendingcontinuously and by degrees, so that in the end it arrives at the most general axioms:" meaning byaxioms, 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), "thesubsumptionof 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 thesumof 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 amountin a new point ofview. 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 thehighest 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 ofnaturalandviolentmotions, and ofterrestrialandcelestialmotions. 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 theHistory[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 successiveascent 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 thepeculiarityof 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 theknowledge of new causes, and the generalization of the laws of those already known, can only be obtained by newinductivediscoveries. 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 destinedto 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 hereafterarrive 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 termedInduction; and that in those sciences, what may be calledDeductionsfrom 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'sLogic, so far as it bears upon the doctrines contained in myHistoryandPhilosophy. And yet thereremains 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,allaxioms,) 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 aretwodistinct elements in our knowledge, Experience, without, and the Mind, within. Mr. Mill derives all our knowledge from Experiencealone. 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,seemsto benecessary. I cannot deny that our knowledge, axiomatic as well as other,never isacquiredwithout 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 myPhilosophy, 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 myHistoryandPhilosophywhich appeared in theQuarterly Reviewin 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 uponFallacies, 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 "thereductio ad absurdumof 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 necessaryprinciples 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 byallminds 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 thelast pointof space or thelast instantof time. He holds (ii. 360) that it is strange that any one should rely upon theà priorievidence that space or extension is infinite, or that nothing can be made of nothing. He holds (i. 304) that the first law ofmotionisrigorously true, but that the axioms respecting theleverare onlyapproximatelytrue. 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 nowherehave a world in which events werecasual. 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 perpetuallyfoundtrue and never false. He holds (i. 338) that "In allpropositions concerning numbers, a condition is implied, without which none of them would be true; and that condition is an assumption whichmay be false.The condition is that1 = 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 appearhowwe can compare ourideaswith therealities, since we know the realities onlybyour ideas; or why this property of their resemblance should be confined toone classof ideas alone.74. I have now made such remarks as appear to me to be necessary, on the most important parts of Mr. Mill's criticism of myPhilosophy. I hope I have avoided urging any thing in a contentious manner; as I have certainly written with no desire of controversy, but only with a view to offer to those who may be willing to receive it, some explanation of portions of my previous writings. I have already said, that if this had not have been my especial object, I could with pleasure have noted the passages of Mr. Mill'sLogicwhich I admire, rather than the points in which we differ. I will in a very few words refer to some of these points, as the most agreeable way of taking leave of the dispute.I say then that Mr. Mill appears to me especially instructive in his discussion of the nature of the proof which is conveyed by the syllogism; and that his doctrine, that the force of the syllogism consists in aninductive assertion, with an interpretation added to it, solves very happily the difficulties which baffle theother theories of this subject. I think that this doctrine of his is made still more instructive, by his excepting from it the cases of Scriptural Theology and of Positive Law (i. 260), as cases in which general propositions, not particular facts, are our original data. I consider also that the recognition ofKinds(i. 166) as classes in which we have, not a finite but aninexhaustiblebody of resemblances among individuals, and as groups made by nature, not by mere definition, is very valuable, as stopping the inroad to an endless train of false philosophy. I conceive that he takes the right ground in his answer to Hume's argument against miracles (ii. 183): and I admire the acuteness with which he has criticized Laplace's tenets on the Doctrine of Chances, and the candour with which he has, in the second edition, acknowledged oversights on this subject made in the first. I think that much, I may almost say all, which he says on the subject of Language, is very philosophical; for instance, what he says (ii. 238) of the way in which words acquire their meaning in common use. I especially admire the acuteness and force with which he has shown (ii. 255) how moral principles expressed in words degenerate into formulas, and yet how the formula cannot be rejected without a moral loss. This "perpetual oscillation in spiritual truths," as he happily terms it, has never, I think, been noted in the same broad manner, and is a subject of most instructive contemplation. And though I have myself refrained from associating moral and political with physical science in my study of the subject, I see a great deal which is full of promise for the future progress of moral and political knowledge in Mr. Mill's sixth Book, "On the Logic of the Moral and Political Sciences." Even his arrangement of the various methods which have been or may be followed in "the Social Science,"—"the Chemical or Experimental Method," "the Geometrical or Abstract Method," "the Physical or Concrete Deductive Method," "the Inverse Deductive or Historical Method," though in some degree fanciful and forced, abounds with valuable suggestions; and his estimate of "theinteresting philosophy of the Bentham school," the main example of "the geometrical method," is interesting and philosophical. On some future occasion, I may, perhaps, venture into the region of which Mr. Mill has thus essayed to map the highways: for it is from no despair either of the great progress to be made in such truth as that here referred to, or of the effect of philosophical method in arriving at such truth, that I have, in what I have now written, confined myself to the less captivating but more definite part of the subject.
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 thePhilosophy[281], of theConsilience of Inductions, as one of theTests 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 wordfact—unexplained in any permanent and definite opposition to theory. As I have said, the Newtonian theoryisa 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 freepassage 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 vibrationscanbe 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 toalltheories which suppose amedium. 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 voltaiccurrents, about which Mr. Mill appears to have no doubt; or of electricatmospheres, which, though generally obsolete, Mr. Mill appears to favour; for though it had been said that wefeelsuch 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 avera 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 tothe samecause, such a coincidence gives areality 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 theTests of Hypotheses, to which I have just referred,—that I have given various methods of Induction, as theMethod of Gradation, theMethod of Natural Classification, theMethod of Curves, theMethod of Means, theMethod of Least Squares, theMethod 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 ofhis 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, ascendingcontinuously and by degrees, so that in the end it arrives at the most general axioms:" meaning byaxioms, 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), "thesubsumptionof 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 thesumof 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 amountin a new point ofview. 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 thehighest 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 ofnaturalandviolentmotions, and ofterrestrialandcelestialmotions. 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 theHistory[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 successiveascent 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 thepeculiarityof 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 theknowledge of new causes, and the generalization of the laws of those already known, can only be obtained by newinductivediscoveries. 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 destinedto 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 hereafterarrive 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 termedInduction; and that in those sciences, what may be calledDeductionsfrom 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'sLogic, so far as it bears upon the doctrines contained in myHistoryandPhilosophy. And yet thereremains 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,allaxioms,) 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 aretwodistinct elements in our knowledge, Experience, without, and the Mind, within. Mr. Mill derives all our knowledge from Experiencealone. 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,seemsto benecessary. I cannot deny that our knowledge, axiomatic as well as other,never isacquiredwithout 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 myPhilosophy, 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 myHistoryandPhilosophywhich appeared in theQuarterly Reviewin 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 uponFallacies, 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 "thereductio ad absurdumof 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 necessaryprinciples 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 byallminds 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 thelast pointof space or thelast instantof time. He holds (ii. 360) that it is strange that any one should rely upon theà priorievidence that space or extension is infinite, or that nothing can be made of nothing. He holds (i. 304) that the first law ofmotionisrigorously true, but that the axioms respecting theleverare onlyapproximatelytrue. 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 nowherehave a world in which events werecasual. 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 perpetuallyfoundtrue and never false. He holds (i. 338) that "In allpropositions concerning numbers, a condition is implied, without which none of them would be true; and that condition is an assumption whichmay be false.The condition is that1 = 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 appearhowwe can compare ourideaswith therealities, since we know the realities onlybyour ideas; or why this property of their resemblance should be confined toone classof ideas alone.
74. I have now made such remarks as appear to me to be necessary, on the most important parts of Mr. Mill's criticism of myPhilosophy. I hope I have avoided urging any thing in a contentious manner; as I have certainly written with no desire of controversy, but only with a view to offer to those who may be willing to receive it, some explanation of portions of my previous writings. I have already said, that if this had not have been my especial object, I could with pleasure have noted the passages of Mr. Mill'sLogicwhich I admire, rather than the points in which we differ. I will in a very few words refer to some of these points, as the most agreeable way of taking leave of the dispute.
I say then that Mr. Mill appears to me especially instructive in his discussion of the nature of the proof which is conveyed by the syllogism; and that his doctrine, that the force of the syllogism consists in aninductive assertion, with an interpretation added to it, solves very happily the difficulties which baffle theother theories of this subject. I think that this doctrine of his is made still more instructive, by his excepting from it the cases of Scriptural Theology and of Positive Law (i. 260), as cases in which general propositions, not particular facts, are our original data. I consider also that the recognition ofKinds(i. 166) as classes in which we have, not a finite but aninexhaustiblebody of resemblances among individuals, and as groups made by nature, not by mere definition, is very valuable, as stopping the inroad to an endless train of false philosophy. I conceive that he takes the right ground in his answer to Hume's argument against miracles (ii. 183): and I admire the acuteness with which he has criticized Laplace's tenets on the Doctrine of Chances, and the candour with which he has, in the second edition, acknowledged oversights on this subject made in the first. I think that much, I may almost say all, which he says on the subject of Language, is very philosophical; for instance, what he says (ii. 238) of the way in which words acquire their meaning in common use. I especially admire the acuteness and force with which he has shown (ii. 255) how moral principles expressed in words degenerate into formulas, and yet how the formula cannot be rejected without a moral loss. This "perpetual oscillation in spiritual truths," as he happily terms it, has never, I think, been noted in the same broad manner, and is a subject of most instructive contemplation. And though I have myself refrained from associating moral and political with physical science in my study of the subject, I see a great deal which is full of promise for the future progress of moral and political knowledge in Mr. Mill's sixth Book, "On the Logic of the Moral and Political Sciences." Even his arrangement of the various methods which have been or may be followed in "the Social Science,"—"the Chemical or Experimental Method," "the Geometrical or Abstract Method," "the Physical or Concrete Deductive Method," "the Inverse Deductive or Historical Method," though in some degree fanciful and forced, abounds with valuable suggestions; and his estimate of "theinteresting philosophy of the Bentham school," the main example of "the geometrical method," is interesting and philosophical. On some future occasion, I may, perhaps, venture into the region of which Mr. Mill has thus essayed to map the highways: for it is from no despair either of the great progress to be made in such truth as that here referred to, or of the effect of philosophical method in arriving at such truth, that I have, in what I have now written, confined myself to the less captivating but more definite part of the subject.