  [First published in The Fortnightly Review for November and December 1873.] When made by a competent reader, an objection usually implies one of two things. Either the statement to which he demurs is wholly or partially untrue; or, if true, it is presented in such a way as to permit misapprehension. A need for some change or addition is in any case shown. Not recognizing the errors alleged, but thinking rather that misapprehensions cause the dissent of those who have attacked the metaphysico-theological doctrines held by me, I propose here to meet, by explanations and arguments, the chief objections urged: partly with the view of justifying these doctrines, and partly with the view of guarding against the wrong interpretations which it appears are apt to be made. The pages of a periodical intended for general reading may be thought scarcely fitted for the treatment of these highly abstract questions. There is now, however, so considerable a class interested in them, and they are so deeply involved with the great changes of opinion in progress, that I have ventured to hope for readers outside the circle of those who occupy themselves with philosophy. Of course the criticisms to be noticed I have selected, {219} either because of their intrinsic force, or because they come from men whose positions or reputations give them weight. To meet more than a few of my opponents is out of the question. Let me begin with a criticism contained in the sermon preached by the Rev. Principal Caird before the British Association, on the occasion of its meeting in Edinburgh, in August, 1871. Expressed with a courtesy which, happily, is now less rare than of yore in theological controversy, Dr. Caird’s objection might, I think, be admitted without involving essential change in the conclusion demurred to; while it might be shown to tell with greater force against the conclusions of thinkers classed as orthodox, Sir W. Hamilton and Dean Mansel, than against my own. Describing this as set forth by me, Dr. Caird says:—
That this objection is one I am not disinclined to recognize, will be inferred when I state that it is one I have myself raised. While preparing the second edition of the {220} Principles of Psychology, I found, among my memoranda, a note which still bore the wafers by which it had been attached to the original manuscript (unless, indeed, it had been transferred from the MS. of First Principles, which its allusion seems to imply). It was this:—
Why I omitted this note I cannot now remember. Possibly it was because re-consideration disclosed a reply to the contained objection. For while it is true that the intellect cannot prove its own competence, since it must postulate its own competence in the course of the proof, and so beg the question; yet it does not follow that it cannot prove its own incompetence respecting questions of certain kinds. Its inability in respect of such questions has two conceivable causes. It may be that the deliverances of Reason in general are invalid, in which case the incompetence of Reason to solve questions of a certain class is implied by its general incompetence; or it may be that the deliverances of Reason, valid within a certain range, themselves end in the conclusion that Reason is incapable beyond that range. So that while there can be no proof of competence, because competence is postulated in each step of the demonstration, there may be proof of incompetence either (1) if the successive deliverances forming the steps of the demonstration, by severally evolving contradictions, show their untrustworthiness, or (2) if, being trustworthy, {221} they lead to the result that on certain questions Reason cannot give any deliverance. Reason leads both inductively and deductively to the conclusion that the sphere of Reason is limited. Inductively, this conclusion expresses the result of countless futile attempts to transcend this sphere—attempts to understand Matter, Motion, Space, Time, Force, in their ultimate natures—attempts which, bringing us always to alternative impossibilities of thought, warrant the inference that such attempts will continue to fail, as they have hitherto failed. Deductively, this conclusion expresses the result of mental analysis, which shows us that the product of thought is in all cases a relation, identified as such or such; that the process of thought is the identification and classing of relations; that therefore Being in itself, out of relation, is unthinkable, as not admitting of being brought within the form of thought. That is to say, deduction explains that failure of Reason established as an induction from many experiments. And to call in question the ability of Reason to give this verdict against itself in respect of these transcendent problems, is to call in question its ability to draw valid conclusions from premises; which is to assert a general incompetence necessarily inclusive of the special incompetence. Closely connected with the foregoing, is a criticism from Dr. Mansel, on which I may here make some comments. In a note to his Philosophy of the Conditioned p. 39, he says:—
Putting these statements in the order most convenient for discussion, I will deal first with the last of them. Instead of saying what he does, Dr. Mansel should have said that I decline to follow Sir W. Hamilton in confounding two distinct, and indeed radically-opposed, meanings of the word belief. This word “is habitually applied to dicta of consciousness for which no proof can be assigned: both those which are unprovable because they underlie all proof, and those which are unprovable because of the absence of evidence.”
Now that the belief which the moral and religious {223} feelings are said to yield of a personal God, is not one of the beliefs which are unprovable because they underlie all proof, is obvious. It needs but to remember that in works on Natural Theology, the existence of a personal God is inferred from these moral and religious feelings, to show that it is not contained in these feelings themselves, or joined with them as an inseparable intuition. It is not a belief like the beliefs which I now have that this is daylight, and that there is open space before me—beliefs which cannot be proved because they are of equal simplicity with, and of no less certainty than, each step in a demonstration. Were it a belief of this most certain kind, argument would be superfluous: all races of men and every individual would have the belief in an inexpugnable form. Hence it is manifest that, confusing the two very different states of consciousness called beliefs, Sir W. Hamilton ascribes to the second a certainty that belongs only to the first. Again, neither Sir W. Hamilton nor Dr. Mansel has enabled us to distinguish those “facts of our moral and emotional consciousness” which imperatively demand the belief in a personal God, from those facts of our (or of men’s) “moral and emotional consciousness” which, in those having them, imperatively demand beliefs that Sir W. Hamilton would regard as untrue. A New Zealand chief, discovering his wife in an infidelity, killed the man; the wife then killed herself that she might join her lover in the other world; and the chief thereupon killed himself that he might go after them to defeat this intention. These two acts of suicide furnish tolerably strong evidence that these New Zealanders believed in another world to which, they could go at will, and fulfil their desires as they did here. If they were asked the justification for this belief, and if the arguments by which they sought to establish it were not admitted, they might still fall back on emotional {224} consciousness as yielding them an unshakeable foundation for it. I do not see why a Fiji Islander, adopting the Hamiltonian argument, should not justify by it his conviction that after being buried alive, his life in the other world, forthwith commencing at the age he has reached in this, will similarly supply him with the joys of conquest and the gratifications of cannibalism. That he has a conviction to this effect stronger than the religious convictions current among civilized people, is proved by the fact that he goes to be buried alive quite willingly. And as we may presume that his conviction is not the outcome of a demonstration, it must be the outcome of some state of feeling—some “emotional consciousness.” Why, then, should he not assign the “facts” of his “emotional consciousness” as “imperatively demanding” this belief? Manifestly, this principle that “consciousness must be accepted entire,” either obliges us to accept as true the superstitions of all mankind, or else obliges us to say that the consciousness of a certain limited class of cultivated people is alone meant. If things are to be believed simply because the facts of emotional consciousness imperatively demand the beliefs, I do not see why the actual existence of a ghost in a house, is not inevitably implied by the intense fear of it that is aroused in the child or the servant. Lastly, and chiefly, I have to deal with Dr. Mansel’s statement that “Mr. Spencer, on the other hand, takes these negative inferences as the only basis of religion.” This statement is exactly the reverse of the truth; since I have contended, against Hamilton and against him, that the consciousness of that which is manifested to us through phenomena is positive, and not negative, as they allege, and that this positive consciousness supplies an indestructible basis for the religious sentiment (First Principles, § 26). Instead of giving here passages to show this, I may fitly quote the statement and opinion of a {225} foreign theologian. M. le pasteur Grotz, of the Reformed Church at Nismes, writes thus:—
I turn next to what has been said by Dr. Shadworth H. Hodgson, in his essay on “The Future of Metaphysic,” published in the Contemporary Review for November, 1872. Remarking only, with respect to the agreements he expresses in certain views of mine, that I value them as coming from a thinker of subtlety and independence, I will confine myself here to his disagreements. Dr. Hodgson, before giving his own view, briefly describes and criticizes the views of Hegel and Comte, with both of whom he partly agrees and partly disagrees, and then {226} proceeds to criticize the view set forth by me. After a preliminary brief statement of my position, to the wording of which I demur, he goes on to say:—
I willingly join issue with Dr. Hodgson on these terms; and proceed to examine, one by one, the several arguments he uses to show the invalidity of my conclusions. Following his criticisms in the order he has chosen, I begin with the sentence following that which I have just quoted. The first part of it runs thus:—“The metaphysical view of Space and Time is, that they are elements in all phenomena, whether the phenomena are presentations or representations.” Whether, by “the metaphysical view,” is here meant the view of Kant, whether it means Dr. Hodgson’s own view, or whether the expression has a more general meaning, I have simply to reply that the metaphysical view is incorrect. Dealing with the Kantian version of this doctrine, that Space is a form of intuition, I have pointed out that only with certain classes of phenomena is Space united indissolubly; that Kant habitually considers phenomena belonging to the visual and tactual groups, with which the consciousness of space is inseparably joined, and overlooks groups with which it is not inseparably joined. Though in the adult, perception of sound has certain space-implications, mostly, if not wholly, acquired by individual experience; and though it would seem from the instructive experiments of Mr. Spalding, that in creatures born with nervous systems much more organized than our own are at birth, {227} there is some innate perception of the side from which a sound comes; yet it is demonstrable that the space-implications of sound are not originally given with the sensation as its form of intuition. Bearing in mind the Kantian doctrine, that Space is the form of sensuous intuitions not only as presented but also as represented, let us examine critically our musical ideas. As I have elsewhere suggested to the reader—
As I thus dissent, not I think without good reason, from “the metaphysical view of Space and Time” as “elements in all phenomena,” it will naturally be expected that I dissent from the first criticism which Dr. Hodgson proceeds to deduce from it. Dealing first with the arguments I have used to show the incomprehensibility of Space and Time, if we consider them as objective, and stating in other words the conclusion I draw, that “as Space and Time cannot be either nonentities nor the attributes of entities, we have no choice but to consider them as entities.” Dr. Hodgson continues:—
Whether the fault is in me or not I cannot say, but I fail to see that my argument is thus rebutted. On the contrary, it appears to me substantially conceded. What kind of entity is that which can exist only when occupied by something else? Dr. Hodgson’s own argument is a tacit assertion that Space by itself cannot be conceived as an existence; and this is all that I have alleged. Dr. Hodgson deals next with the further argument, familiar to all readers, which I have added as showing the insurmountable difficulty in the way of conceiving Space and Time as objective entities; namely, that “all entities which we actually know as such are limited. ... But of Space and Time we cannot assert either limitation, or the absence of limitation.” Without quoting at length the reasons Dr. Hodgson gives for distinguishing between Space as perceived and Space as conceived, it will suffice if I quote his own statement of the result to which they bring him: “So that Space and Time as perceived are not finite, but infinite, as conceived are not infinite, but finite.” Most readers will, I think, be startled by the assertion that conception is less extensive in range than perception; but, without dwelling on this, I will content myself by asking in what case Space is perceived as infinite? Surely Dr. Hodgson does not mean to say that he can perceive the whole surrounding Space at once—that the Space behind is united in perception with the Space in front. Yet this is the necessary implication of his words. Taking his statement less literally, however, and not dwelling on the fact that in perception Space is habitually bounded by objects more or less distant, let us test his {229} assertion under the most favourable conditions. Supposing the eye directed upwards towards a clear sky; is not the space then perceived, laterally limited? The visual area, restricted by the visual apertures, cannot include in perception even 180° from side to side, and is still more confined in a direction at right angles to this. Even in the third direction, to which alone Dr. Hodgson evidently refers, it cannot properly be said that it is infinite in perception. Look at a position in the sky a thousand miles off. Now look at a position a million miles off. What is the difference in perception? Nothing. How then can an infinite distance be perceived when these immensely-unlike finite distances cannot be perceived as differing from one another, or from an infinite distance? Dr. Hodgson has used the wrong word. Instead of saying that Space as perceived is infinite, he should have said that, in perception, Space is finite in two dimensions, and becomes indefinite in the third when this becomes great. I now come to the paragraph beginning “Mr. Spencer then turns to the second or subjective hypothesis, that of Kant.” This paragraph is somewhat difficult to deal with, because in it my reasoning is criticized both from the Kantian point of view and from Dr. Hodgson’s own point of view. Dissenting from Kant’s view, Dr. Hodgson says, “I hold that both Space and Time and Feeling, or the material element, are equally and alike subjective, equally and alike objective.” As I cannot understand this, I am unable to deal with those arguments against me which Dr. Hodgson bases upon it, and must limit myself to that which he urges on behalf of Kant. He says:—
If I have misunderstood Kant, as thus alleged, then my comment must be that I credited him with an hypothesis less objectionable than that which he held. I supposed his view to be that Space, as a form of intuition belonging to the ego, is imposed by it on the non-ego (by which I understood the thing in itself) in the act of intuition. But now the Kantian doctrine is said to be that Space, originating in the ego, when applied to the non-ego, results in phenomena (the non-ego meant being, in that case, necessarily the Ding-an-sich, or thing in itself); and that the phenomena so resulting become objective existences along with the Space given to them by the subject. The subject having imposed Space as a form on the primordial object, or thing in itself, and so created phenomena, this Space thereupon becomes an objective existence, independent of both the subject and the original thing in itself! To Dr. Hodgson this may seem a more tenable position than that which I ascribed to Kant; but to me it seems only a multiplication of inconceivabilities. I am content to leave it as it stands: not feeling my reasons for rejecting the Kantian hypothesis much weakened. The remaining reply which Dr. Hodgson makes runs thus:—
Had Dr. Hodgson quoted the whole of the passage from which he takes the above sentence; or had he considered it in conjunction with the Kantian doctrine to which it refers (namely, that Space survives in consciousness when all contents are expelled, which implies that then Space is the thing with which consciousness is occupied, or the object of consciousness), he would have seen that his reply has none of the cogency he supposes. If, taking his first illustration, he will ask himself whether it is possible to “syllogize about syllogism,” when syllogism has no content whatever, symbolic or other—has nonentity to serve for major, nonentity for minor, and nonentity for conclusion; he will, I think, see that syllogism, considered as surviving terms of every kind, cannot be syllogized about: the “pure form” of reason (supposing it to be syllogism, which it is not) if absolutely discharged of all it contains, cannot be represented in thought, and therefore cannot be reasoned about. Following Dr. Hodgson to his second illustration, I must express my surprise that a metaphysician of his acuteness should have used it. For an illustration to have any value, the relation between the terms of the analogous case {232} must have some parallelism to the relation between the terms of the case with which it is compared. Does Dr. Hodgson really think that the relation between a dog and the part of himself which he bites, is like the relation between matter and form? Suppose the dog bites his tail. Now the dog, as biting, stands, according to Dr. Hodgson, for the form as the containing mental faculty; and the tail, as bitten, stands for this mental faculty as contained. Now suppose the dog loses his tail. Can the faculty as containing and the faculty as contained be separated in the same way? Does the mental form when deprived of all content, even itself (granting that it can be its own content), continue to exist in the same way that a dog continues to exist when he has lost his tail? Even had this illustration been applicable, I should scarcely have expected Dr. Hodgson to remain satisfied with it. I should have thought he would prefer to meet my argument directly, rather than indirectly. Why has he not shown the invalidity of the reasoning used in the Principles of Psychology (§ 399, 2nd ed.)? Having there quoted the statement of Kant, that “Space and Time are not merely forms of sensuous intuition, but intuitions themselves;” I have written—
Now when Dr. Hodgson has shown me how that “which {233} effects that the content .... can be arranged under certain relations,” may also be that which effects its own arrangement under the same relations, I shall be ready to surrender my position; but until then, no analogy drawn from the ability of a dog to bite himself will weigh much with me. Having, as he considers, disposed of the reasons given by me for concluding that, considered in themselves, “Space and Time are wholly incomprehensible” (he continually uses on my behalf the word “inconceivable,” which, by its unfit connotations, gives a wrong aspect to my position), Dr. Hodgson goes on to say:-
This statement has caused me no little astonishment. That having before him the volume from which he quotes, so competent a reader should have so completely missed the meaning of the passages (§ 26) already referred to, in which I have contended against Hamilton and Mansel, makes me almost despair of being understood by any ordinary reader. In that section I have, in the first place, contended that the consciousness of an Ultimate Reality, though not capable of being made a thought, properly so called, because not capable of being brought within limits, nevertheless remains as a consciousness that is positive: is not rendered negative by the negations of limits. I have pointed out that—
This positive element of consciousness it is which, “at once necessarily indefinite and necessarily indestructible,” I regard as the consciousness of the Unknowable Reality. Yet Dr. Hodgson says “Mr. Spencer proceeds to use these inconceivable ideas as the basis of his philosophy:” implying that such basis consists of negations, instead of consisting of that which persists notwithstanding the negation of limits. And then, beyond this perversion, or almost inversion, of meaning, he conveys the notion that I take as the basis of philosophy, the “inconceivable ideas” “or self-contradictory notions” which result when we endeavour to comprehend Space and Time. He speaks of me as proposing to evolve substance out of form, or rather, out of the negations of forms—gives his readers no conception that the Power manifested to us is that which I regard as the Unknowable, while what we call Space and Time answer to the unknowable nexus of its manifestations. And yet the chapter from which I quote, and still more the chapter which follows it, makes this clear—as clear, at least, as I can make it by carefully-worded statements and re-statements. Philosophical systems, like theological ones, following the law of evolution in general, severally become in course of time more rigid, while becoming more complex and more definite; and they similarly become less alterable—resist all compromise, and have to be replaced by the more plastic systems that descend from them. It is thus with pure Empiricism and pure Transcendentalism. Down to the present time disciples of Locke have continued to hold that all mental phenomena are interpretable as results of accumulated individual experiences; and, by criticism, have been led simply to elaborate their interpretations—ignoring the proofs of inadequacy. On the other hand, disciples of Kant, {235} asserting this inadequacy, and led by perception of it to adopt an antagonist theory, have persisted in defending that theory under a form presenting fatal inconsistencies. And then, when there is offered a mode of reconciliation, the spirit of no-compromise is displayed: each side continuing to claim the whole truth. After it has been pointed out that all the obstacles in the way of the experiential doctrine disappear if the effects of ancestral experiences are joined with the effects of individual experiences, the old form of the doctrine is still adhered to. And meanwhile Kantists persist in asserting that the ego is born with intuitional forms which are wholly independent of anything in the non-ego, after it has been shown that the innateness of these intuitional forms may be so understood as to escape the insurmountable difficulties of the hypothesis as originally expressed. I am led to say this by reading the remarks concerning my own views, made with an urbanity I hope to imitate, by Professor Max MÜller, in a lecture delivered at the Royal Institution in March, 1873.
On this passage let me remark, first, that the word “pre-historic,” ordinarily employed only in respect to human history, is misleading when applied to the history of Life in general; and his use of it leaves me in some doubt whether Professor Max MÜller has rightly conceived the hypothesis he refers to. My second comment is, that the description of me as “quite at one with Kant,” “barring” the “theory of the prehistoric origin of these intuitions,” curiously implies that it is a matter of comparative indifference whether the forms of thought are held to be naturally generated by intercourse between the organism and its environing relations, during the evolution of the lowest into the highest types, or whether such forms are held to be supernaturally given to the human mind, and are independent both of environing relations and of ancestral minds. But now, addressing myself to the essential point, I must meet the statement that I have “misunderstood the exact meaning of what Kant calls the intuitions of Space and Time,” by saying that I think Professor Max MÜller has overlooked certain passages which justify my interpretation, and render his interpretation untenable. For Kant says “Space is nothing else than the form of all phenomena of the external sense;” further, he says that “Time is nothing but the form of our internal intuition;” and, to repeat words I have used elsewhere, “He distinctly shuts out the supposition that there are forms of the non-ego to which these forms of the ego correspond, by saying that ‘Space is not a conception which has been derived from outward experiences.’” Now so far from being in harmony with, these statements are in direct contradiction to, the view which I hold; and seem to me absolutely irreconcilable with it. How can it be said that, “barring” a difference represented as trivial, I am {237} “quite at one with Kant,” when I contend that these subjective forms of intuition are moulded into correspondence with, and therefore derived from, some objective form or nexus, and therefore dependent upon it; while the Kantian hypothesis is that these subjective forms are not derived from the object, but pre-exist in the subject—are imposed by the ego on the non-ego. It seems to me that not only do Kant’s words, as above given, exclude the view which I hold, but also that Kant could not consistently have held any such view. Rightly recognizing, as he did, these forms of intuition as innate, he was, from his stand-point, obliged to regard them as imposed on the matter of intuition in the act of intuition. In the absence of the hypothesis that intelligence has been evolved, it was not possible for him to regard these subjective forms as having been derived from objective forms. A disciple of Locke might, I think, say that the Evolution-view of our consciousness of Space and Time is essentially Lockian, with more truth than Professor Max MÜller can represent it as essentially Kantian. The Evolution-view is completely experiential. It differs from the original view of the experientialists by containing a great extension of that view. With the relatively-small effects of individual experiences, it joins the relatively-vast effects of the experiences of antecedent individuals. But the view of Kant is avowedly and absolutely unexperiential. Surely this makes the predominance of kinship manifest. In Professor Max MÜller’s replies to my criticisms on Kant, I cannot see greater validity than in this affiliation to which I have demurred. One of his arguments is that which Dr. Hodgson has used, and which I have already answered; and I think that the others, when compared with the passages of the Principles of Psychology which they concern, will not be found adequate. I refer to them here {238} chiefly for the purpose of pointing out that when he speaks of me as bringing “three arguments against Kant’s view,” he understates the number. Let me close what I have to say on this disputed question, by quoting the summary of reasons I have given for rejecting the Kantian hypothesis:—
Objections of another, though allied, class have been made in a review of the Principles of Psychology by Mr. H. Sidgwick—a critic whose remarks on questions of mental philosophy always deserve respectful consideration. Mr. Sidgwick’s chief aim is to show what he calls “the mazy inconsistency of his [my] metaphysical results.” More specifically, he expresses thus the proposition he seeks to justify—“His view of the subject appears to have a fundamental incoherence, which shows itself in various ways on the surface of his exposition, but of which the root lies {239} much deeper, in his inability to harmonise different lines of thought.” Before dealing with the reasons given for this judgment, let me say that, in addition to the value which candid criticisms have as showing where more explanation is needed, they are almost indispensable as revealing to a writer incongruities he had not perceived. Especially where, as in this case, the subject-matter has many aspects, and where the words supplied by our language are so inadequate in number that, to avoid cumbrous circumlocution, they have to be used in senses that vary according to the context, it is extremely difficult to avoid imperfections of statement. But while I acknowledge sundry such imperfections and the resulting incongruities, I cannot see that these are, as Mr. Sidgwick says, fundamental. Contrariwise, their superficiality seems to me proved by the fact that they may be rectified without otherwise altering the expositions in which they occur. Here is an instance. Mr. Sidgwick points out that, when treating of the “Data of Psychology,” I have said (in § 56) that, though we reach inferentially “the belief that mind and nervous action are the subjective and objective faces of the same thing, we remain utterly incapable of seeing, and even of imagining, how the two are related” (I quote the passage more fully than he does). He then goes on to show that in the “Special Synthesis,” where I have sketched the evolution of Intelligence under its objective aspect, as displayed in the processes by which beings of various grades adjust themselves to surrounding actions, I “speak as if” we could see how consciousness “naturally arises at a particular stage” of nervous action. The chapter he here refers to is one describing that “differentiation of the psychical from the physical life” which accompanies advancing organization, and more especially advancing development of the nervous system. In it I have shown {240} that, while the changes constituting physical life continue to be characterized by the simultaneity with which all kinds of them go on throughout the organism, the changes constituting psychical life, arising as the nervous system develops, become gradually more distinguished by their seriality. And I have said that as nervous integration advances, “there must result an unbroken series of these changes—there must arise a consciousness.” Now I admit that here is an apparent inconsistency. I ought to have said that “there must result an unbroken series of these changes,” which, taking place in the nervous system of a highly-organized creature, gives coherence to its conduct; and along with which we assume a consciousness, because consciousness goes along with coherent conduct in ourselves. If Mr. Sidgwick will substitute this statement for the statement as it stands, he will see that the arguments and conclusions remain intact. A survey of the chapter as a whole, proves that its aim is not in the least to explain how nervous changes, considered as waves of molecular motion, become the feelings constituting consciousness; but that, contemplating the facts objectively in living creatures at large, it points out the cardinal distinction between vital actions in general, and those particular vital actions which, in a creature displaying them, lead us to speak of it as intelligent. It is shown that the rise of such actions becomes marked in proportion as the changes taking place in the part called the nervous system, are made more and more distinctly serial, by union in a supreme centre of co-ordination. The introduction of the word consciousness, arises in the effort to show what fundamental character there is in these particular physiological changes which is parallel to a fundamental character in the psychological changes. Another instance of the way in which Mr. Sidgwick evolves an incongruity which he considers fundamental, out of what I should have thought he would see is a {241} defective expression, I will give in his own words. Speaking of a certain view of mine, he says:—
This apparent inconsistency, marked by the italics, would not have existed if, instead of “a cognition of it,” I had said, as I ought to have said, “what we call a cognition of it”—that is, a relative cognition as distinguished from an absolute cognition. In ordinary language we speak of as cognitions, those connexions in thought which so guide us in our dealings with things, that actual experience verifies ideal anticipation: marking off, by opposed words, those connexions in thought which mis-guide us. The difference between accepting a cognition as relatively true and accepting it as absolutely true, will be clearly shown by an illustration. There is no direct resemblance whatever between the sizes, forms, colours, and arrangements, of the figures in an account-book, and the moneys or goods, debts or credits, represented by them; and yet the forms and arrangements of the written symbols, are such as answer in a perfectly-exact way to stocks of various commodities and to various kinds of transactions. Hence we say, figuratively, that the account-book will “tell us” all about these stocks and transactions. Similarly, the diagram Mr. Sidgwick refers to, suggests a way in which symbols, registered in us by objects, may have forms and arrangements wholly unlike their objective causes and the nexus among those causes, while yet they are so related as to guide us correctly in our transactions {242} with those objective causes, and, in that sense, constitute cognitions of them; though they no more constitute cognitions in the absolute sense, than do the guiding symbols in the account-book constitute cognitions of the things to which they refer. So repeatedly is this view implied throughout the Principles of Psychology, that I am surprised to find a laxity of expression raising the suspicion that I entertain any other. To follow Mr. Sidgwick through sundry criticisms of like kind, which may be similarly met, would take more space than I can here afford. I must restrict myself now to the alleged “fundamental incoherence” of which he thinks these inconsistencies are signs. I refer to that reconciliation of Realism and Idealism considered by him as an impossible compromise. A difficulty is habitually felt in accepting a coalition after long conflict. Whoever has espoused one of two antagonist views, and, in defending it, has gained a certain comprehension of the opposite view, becomes accustomed to regard these as the only alternatives, and is puzzled by an hypothesis which is at once both and neither. Yet, since it turns out in nearly all cases that, of conflicting doctrines, each contains an element of truth, and that controversy ends by combination of their respective half-truths, there is a priori probability on the side of an hypothesis which qualifies Realism by Idealism. Mr. Sidgwick expresses his astonishment, or rather bespeaks that of his readers, because, while I accept Idealistic criticisms, I nevertheless defend the fundamental intuition of Common Sense; and, as he puts it, “fires his [my] argument full in the face of Kant, Mill, and ‘metaphysicians’ generally.”
On the face of it the anomaly seems great; but I should have thought that after reading the chapter on “Transfigured Realism,” a critic of Mr. Sidgwick’s acuteness would have seen the solution of it. He has overlooked an essential distinction. All which my argument implies is that the direct intuition of Realism must be held of superior authority to the arguments of Anti-Realism, where their deliverances cannot be reconciled. The one point on which their deliverances cannot be reconciled, is the existence of an objective reality. But while, against this intuition of Realism, I hold the arguments of Anti-Realism to be powerless, because they cannot be carried on without postulating that which they end by denying; yet, having admitted objective existence as a necessary postulate, it is possible to make valid criticisms upon all those judgments which Crude Realism joins with this primordial judgment: it is possible to show that a transfigured interpretation of properties and relations, is more tenable than the original interpretation. To elucidate the matter, let us take the most familiar case in which the indirect judgments of Reason correct the direct judgments of Common Sense. The direct judgment of Common Sense is that the Sun moves round the Earth. In course of time, Reason, finding some facts at variance with this, begins to doubt; and, eventually, hits upon an hypothesis which explains the anomalies, but which denies this apparently-certain dictum of Common Sense. What is the reconciliation? It consists in showing {244} to Common Sense that the new interpretation equally well corresponds with direct intuition, while it avoids all the difficulties. Common Sense is reminded that the apparent motion of an object may be due either to its actual motion or to the motion of the observer; and that there are terrestrial experiences in which the observer thinks an object he looks at is moving, when the motion is in himself. Extending the conception thus given, Reason shows that if the Earth revolves on its axis, there will result that apparent motion of the Sun which Common Sense interpreted into an actual motion of the Sun; and the common-sense observer thereupon becomes able to think of sunrise and sunset as due to his position as spectator on a vast revolving globe. Now if the astronomer, setting out by recognizing these celestial appearances, and proceeding to evolve the various anomalies following from the common-sense interpretation of them, had drawn the conclusion that there externally exist no Sun and no motion at all, he would have done what Idealists do; and his arguments would have been equally powerless against the intuition of Common Sense. But he does nothing of the kind. He accepts the intuition of Common Sense respecting the reality of the Sun and of the motion; but replaces the old interpretation of the motion by a new interpretation reconcilable with all the facts. Everyone must see that here, acceptance of the inexpugnable element in the common-sense judgment, by no means involves acceptance of the accompanying judgments; and I contend that the like discrimination must be made in the case we are considering. It does not follow that while, against the consciousness which Crude Realism has of an objective reality, the arguments of Anti-Realism are futile, they are therefore futile against the conceptions which Crude Realism forms of the objective reality. If Anti-Realism can show that, granting an objective reality, the interpretation of Crude Realism contains insuperable {245} difficulties, the process is quite legitimate. And, its primordial intuition remaining unshaken, Realism may, on reconsideration, be enabled to frame a new conception which harmonizes all the facts. To show that there is not here the “mazy inconsistency” alleged, let us take the case of sound as interpreted by Crude Realism, and as re-interpreted by Transfigured Realism. Crude Realism assumes the sound present in consciousness to exist as such beyond consciousness. Anti-Realism proves the inadmissibility of this assumption in sundry ways (all of which, however, set out by talking of sounding bodies beyond consciousness, just as Realism talks of them); and then Anti-Realism concludes that we know of no existence save the sound as a mode of consciousness: which conclusion, and all kindred conclusions, I contend are vicious—first, because all the words used connote an objective activity; second, because the arguments are impossible without postulating at the outset an objective activity; and third, because no one of the intuitions out of which the arguments are built, is of equal validity with the single intuition of Realism that an objective activity exists. But now the Transfigured Realism which Mr. Sidgwick thinks “has all the serious incongruity of an intense metaphysical dream,” neither affirms the untenable conception of Crude Realism, nor, like Anti-Realism, draws unthinkable conclusions by suicidal arguments; but, accepting that which is essential in Crude Realism, and admitting the difficulties which Anti-Realism insists upon, reconciles matters by a re-interpretation analogous to that which an astronomer makes of the solar motion. Continuing all along to recognize an objective activity which Crude Realism calls sound, it shows that the answering sensation is produced by a succession of separate impacts which, if made slowly, may be separately identified, and which will, if progressively increased in rapidity, produce tones higher and higher in pitch. It {246} shows by other experiments that sounding bodies are in states of vibration, and that the vibrations may be made visible. And it concludes that the objective activity is not what it subjectively seems, but is proximately interpretable as a succession of aËrial waves. Thus Crude Realism is shown that while there unquestionably exists an objective activity corresponding to the sensation known as sound, yet the facts are not explicable on the original supposition that this is like the sensation; while they are explicable by conceiving it as a rhythmical mechanical action. Eventually this re-interpretation, joined with kindred reinterpretations of other sensations, comes to be itself further transfigured by analysis of its terms, and re-expression of them in terms of molecular motion; but, however abstract the interpretation ultimately reached, the objective activity continues to be postulated: the primordial judgment of Crude Realism remains unchanged, though it has to change the rest of its judgments. In another part of his argument, however, Mr. Sidgwick implies that I have no right to use those conceptions of objective existence by which this compromise is effected. Quoting sundry passages to show that while I hold the criticisms of the Idealist to be impossible without “tacitly or avowedly postulating an unknown something beyond consciousness,” I yet admit that “our states of consciousness are the only things we can know;” he goes on to argue that I am radically inconsistent, because, in interpreting the phenomena of consciousness, I continually postulate, not an unknown something, but a something of which I speak in ordinary terms, as though its ascribed physical characters really exist as such, instead of being, as I admit they are, synthetic states of my consciousness. His objection, if I understand it, is that for the purposes of Objective Psychology I apparently profess to know Matter and Motion in the ordinary realistic way; while, as a result of subjective analysis, I reach the conclusion that {247} it is impossible to have that knowledge of objective existence which Realism supposes we have. Doubtless there seems here to be what he calls “a fundamental incoherence.” But I think it exists, not between my two expositions, but between the two consciousnesses of subjective and objective existence, which we cannot suppress and yet cannot put into definite forms. The alleged incoherence I take to be but another name for the inscrutability of the relation between subjective feeling and its objective correlate which is not feeling—an inscrutability which meets us at the bottom of all our analyses. An exposition of this inscrutability I have elsewhere summed up thus:—
Carrying a little further this simile, will, I think, show where lies the insuperable difficulty felt by Mr. Sidgwick. Taking x and y as the subjective and objective activities, unknown in their natures and known only as phenomenally manifested; and recognizing the fact that every state of consciousness implies, immediately or remotely, the action of object on subject or subject on object, or both; we may say that every state of consciousness will be symbolized by some modification of xy—the phenomenally-known product of the two unknown factors. In other words, xy', x'y, x'y', xy', x'y, &c., &c., will represent all perceptions and thoughts. Suppose, now, that these are thoughts about the object; composing some hypothesis respecting its characters as analyzed by physicists. Clearly, all such thoughts, be they about shapes, resistances, momenta, molecules, molecular motions, or what not, will contain forms of the subjective activity x. Now let the thoughts {248} be concerning mental processes. It must similarly happen that some mode of the unknown objective activity y, will be in every case a component. Now suppose that the problem is the genesis of mental phenomena; and that, in the course of the inquiry, bodily organization and the functions of the nervous system are brought into the explanation. It will happen, as before, that these, considered as objective, have to be described and thought about in modes of xy. And when by the actions of such a nervous system, conceived objectively in modes of xy, and acted upon by physical forces which are conceived in other modes of xy, we endeavour to explain the genesis of sensations, perceptions, and ideas, which we can think of only in other modes of xy, we find that all our factors, and therefore all our interpretations, contain the two unknown terms, and that no interpretation is imaginable that will not contain the two unknown terms. What is the defence for this apparently-circular process? Simply that it is a process of establishing congruity among our symbols. It is finding a mode of so symbolizing the unknown activities, subjective and objective, and so operating with our symbols, that all our acts may be rightly guided—guided, that is, in such ways that we can anticipate, when, where, and in what quantity some one of our symbols, or some combination of our symbols, will be found. Mr. Sidgwick’s difficulty arises, I think, from having insufficiently borne in mind the statements made at the outset, in “The Data of Philosophy,” that such conceptions as “are vital, or cannot be separated from the rest without mental dissolution, must be assumed as true provisionally;” that “there is no mode of establishing the validity of any belief except that of showing its entire congruity with all other beliefs;” and that “Philosophy, compelled to make those fundamental assumptions without which thought is impossible, has to justify them by showing their congruity with all other dicta of consciousness.” In {249} pursuance of this distinctly-avowed mode of procedure, I assume provisionally, an objective activity and a subjective activity, and certain general forms and modes (Space, Time, Matter, Motion, Force), which the subjective activity, operated on by the objective activity, ascribes to it, and which I suppose to correspond in some way to unknown forms and modes of the objective activity. These provisional assumptions, having been carried out to all their consequences, and these consequences proved to be congruous with one another and with the original assumptions, these original assumptions are justified. And if, finally, I assert, as I have repeatedly asserted, that the terms in which I express my assumptions and carry on my operations are but symbolic, and that all I have done is to show that by certain ways of symbolizing, perfect harmony results—invariable agreement between the symbols in which I frame my expectations, and the symbols which occur in experience—I cannot be blamed for incoherence. On the contrary, it seems to me that my method is the most coherent that can be devised. Lastly, should it be said that this regarding of everything constituting experience and thought as symbolic, has a very shadowy aspect; I reply that these which I speak of as symbols, are real relatively to our consciousness; and are symbolic only in their relation to the Ultimate Reality. That these explanations will make clear the coherence of views which before seemed “fundamentally incoherent,” I feel by no means certain; since, as I did not perceive the difficulties presented by the exposition as at first made, I may similarly fail to perceive the difficulties in this explanation. Originally, I had intended to complete the Principles of Psychology by a division showing how the results reached in the preceding divisions, physiological and psychological, analytic and synthetic, subjective and objective, harmonize with one another, and are but different aspects of the same aggregate of phenomena. But the work was already {250} bulky; and I concluded that this division might be dispensed with, because the congruities to be pointed out were sufficiently obvious. So little was I conscious of the alleged “inability to harmonize different lines of thought.” Mr. Sidgwick’s perplexities, however, show me that such an exposition of concords is needful. I have reserved to the last, one of the first objections made to the metaphysico-theological doctrine set forth in First Principles, and implied in the several volumes that have succeeded it. It was urged by an able metaphysician, the Rev. James Martineau, in an essay entitled “Science, Nescience, and Faith;” and, effective against my argument as it stands, shows the need for some development of my argument. That Mr. Martineau’s criticism may be understood, I must quote the passages it concerns. Continuing the reasoning employed against Hamilton and Mansel, to show that our consciousness of that which transcends knowledge is positive, and not, as they allege, negative, I have said:—
On this argument Mr. Martineau comments as follows; first re-stating it in other words:—
I admit this to be a telling rejoinder; and one which can be met only when the meanings of the words, as I have used them, are carefully discriminated, and the implications of the doctrine fully traced out. We will begin by clearing the ground of minor misconceptions. First, let it be observed that though I have used the word Absolute as the equivalent of Non-relative, because it is used in the passages quoted from the writers I am contending against; yet I have myself chosen for the purposes of my argument, the name Non-relative, and I do not necessarily commit myself to any propositions respecting the Absolute, considered as that which includes both Subject and Object. The Non-relative as spoken of by me, is to be understood rather as the totality of Being minus that which constitutes the individual consciousness, present to us under forms of Relation. Did I use the word in some Hegelian sense, as comprehensive of that which thinks and that which is thought about, and did I propose to treat of the order of things, not as phenomenally manifested but as noumenally proceeding, the objection would be fatal. But the aim being simply to formulate the order of things as present under relative forms, the antithetical Non-relative here named as {252} implied by the conception of the Relative, is that which, in any act of thought, is outside of and beyond it, rather than that which is inclusive of it. Further, it should be observed that this Non-relative, spoken of as a necessary complement to the Relative, is not spoken of as a conception but as a consciousness; and I have in sundry passages distinguished between those modes of consciousness which, having limits, and constituting thought proper, are subject to the laws of thought, and the mode of consciousness which persists when the removal of limits is carried to the uttermost, and when distinct thought consequently ceases. This opens the way to the reply here to be made to Mr. Martineau’s criticism—namely, that while by the necessities of thought the Relative implies a Non-relative; and while, to think of this antithesis completely, requires that the Non-relative shall be made a conception proper; yet, for the vague thought which is alone in this case possible, it suffices that the Non-relative shall be present as a consciousness which though undefined is positive. Let us observe what necessarily happens when thought is employed on this ultimate question. In a preceding part of the argument criticized, I have, in various ways, aimed to show that, alike when we analyze the product of thought and when we analyze the process of thought, we are brought to the conclusion that invariably “a thought involves relation, difference, likeness;” and that even from the very nature of Life itself, we may evolve the conclusion that “thinking being relationing, no thought can ever express more than relations.” What, now, must happen if thought, having this law, occupies itself with the final mystery? Always implying terms in relation, thought implies that both terms shall be more or less defined; and as fast as one of them becomes indefinite, the relation also becomes indefinite, and thought becomes indistinct. Take the {253} case of magnitudes. I think of an inch; I think of a foot; and having tolerably-definite ideas of the two, I have a tolerably-definite idea of the relation between them. I substitute for the foot a mile; and being able to represent a mile much less definitely, I cannot so definitely think of the relation between an inch and a mile—cannot distinguish it in thought from the relation between an inch and two miles, as clearly as I can distinguish in thought the relation between an inch and one foot from the relation between an inch and two feet. And now if I endeavour to think of the relation between an inch and the 240,000 miles from here to the Moon, or the relation between an inch and the 93,000,000 miles from here to the Sun, I find that while these distances, practically inconceivable, have become little more than numbers to which I frame no answering ideas, so, too, has the relation between an inch and either of them become practically inconceivable. Evidently then this partial failure in the process of forming thought-relations, which happens even with finite magnitudes when one of them is immense, passes into complete failure when one of them cannot be brought within any limits. The relation itself becomes unrepresentable at the same time that one of its terms becomes unrepresentable. Nevertheless, in this case it is to be observed that the almost-blank form of relation preserves a certain qualitative character. It is still distinguishable as belonging to the consciousness of extensions, not to the consciousnesses of forces or durations; and in so far remains a vaguely-identifiable relation. But now suppose we ask what happens when one term of the relation has not simply magnitude having no known limits, and duration of which neither beginning nor end is cognizable, but is also an existence not to be defined? In other words, what must happen if one term of the relation is not only quantitatively but also qualitatively unrepresentable? Clearly in this case the {254} relation does not simply cease to be thinkable except as a relation of a certain class, but it lapses completely. When one of the terms becomes wholly unknowable, the law of thought can no longer be conformed to; both because one term cannot be present, and because relation itself cannot be framed. That is to say, the law of thought that contradictories can be known only in relation to each other, no longer holds when thought attempts to transcend the Relative; and yet, when it attempts to transcend the Relative, it must make the attempt in conformity with its law—must in some dim mode of consciousness posit a Non-relative, and, in some similarly dim mode of consciousness, a relation between it and the Relative. In brief then, to Mr. Martineau’s objection I reply, that the insoluble difficulties he indicates arise here, as elsewhere, when thought is applied to that which transcends the sphere of thought; and that just as when we try to pass beyond phenomenal manifestations to the Ultimate Reality manifested, we have to symbolize it out of such materials as the phenomenal manifestations give us; so we have simultaneously to symbolize the connexion between this Ultimate Reality and its manifestations, as somehow allied to the connexions among the phenomenal manifestations themselves. The truth Mr. Martineau’s criticism adumbrates, is that the law of thought fails where the elements of thought fail; and this is a conclusion quite conformable to the general view I defend. Still holding the validity of my argument against Hamilton and Mansel, that in pursuance of their own principle the Relative is not at all thinkable as such, unless in contradistinction to some existence posited, however vaguely, as the other term of a relation, conceived however indefinitely; it is consistent on my part to hold that in this effort which thought inevitably makes to pass beyond its sphere, not only does the product of thought become a dim symbol of a product, but the process of thought becomes a dim {255} symbol of a process; and hence any predicament inferable from the law of thought cannot be asserted. I may fitly close this reply by a counter-criticism. To the direct defence of a proposition, may be added the indirect defence which results from showing the untenability of an alternative proposition. This criticism on the doctrine of an Unknowable Existence manifested to us in phenomena, Mr. Martineau makes in the interests of the doctrine held by him, that this existence is, to a considerable degree, knowable. We are quite at one in holding that there is an indestructible consciousness of Power behind Appearance; but whereas I contend that this Power cannot be brought within the forms of thought, Mr. Martineau contends that there can be consistently ascribed certain attributes of personality—not, indeed, human characteristics so concrete as were ascribed in past times; but still, human characteristics of the more abstract and higher class. His general doctrine is this:—Regarding Matter as independently existing; regarding as also independently existing, those primary qualities of Body “which are inseparable from the very idea of Body, and may be evolved a priori from the consideration of it as solid extension or extended solidity;” and saying that to this class “belong Triple Dimension, Divisibility, Incompressibility;” he goes on to assert that as these—
Before the major criticism which I propose to make on this hypothesis, let me make a minor one. Not only of space-relations, but also of primary physical properties, Mr. Martineau asserts the necessity: not a necessity to our minds simply, but an ontological necessity. What is true for human thought, is, in respect of these, true absolutely: “the laws of curvature, measure, and proportion,” as we know them, are unchangeable even by Divine power; as are also the Divisibility and Incompressibility of Matter. But if, in these cases, Mr. Martineau holds that a necessity in thought implies an answering necessity in things, why does he refrain from saying the like in other cases? Why, if he tacitly asserts it in respect of space-relations and the statical attributes of Body, does he not also assert it in respect of the dynamical attributes of Body? The laws conformed to by that mode of force now distinguished as “energy,” are as much necessary to our thought as are the laws of space-relations. The axioms of Mechanics lie on the same plane with the axioms of pure Mathematics. Now if Mr. Martineau admits this—if he admits, as he must, the corollary that there can be no such manifestation of energy as that displayed in the motion of a planet, save at the expense of equivalent energy which pre-existed—if he draws the further necessary corollary that the direction of a motion cannot be changed by any action, without an equal reaction in an opposite direction on something acting—if he bears in mind that this holds not only of all visible motions, celestial and terrestrial, but that those activities of Body which affect us as secondary properties, are also known only through other forms of {257} energy, which are equivalents of mechanical energy and conform to these same laws—and if, lastly, he infers that none of these derivative energies can have given to them their characters and directions, save by pre-existing forces, statical and dynamical, conditioned in special ways; what becomes of that “realm of Divine originality” which Mr. Martineau describes as remaining within the realm of necessity? Consistently carried out, his argument implies a universally-inevitable order, in which volition can have no such place as that he alleges. Not pushing Mr. Martineau’s reasoning to this conclusion, so entirely at variance with the one he draws, but accepting his statement just as it stands, let us consider the solution it offers us. We are left by it without any explanation of Space and Time; we are not helped in conceiving the origin of Matter; and there is afforded us no idea how Matter came to have its primary attributes. All these are tacitly assumed to exist uncreated. Creative activity is represented as under the restrictions imposed by mathematical necessities, and as having for datum (mark the word) a substance which, in respect of certain characters, defies modification. But surely this is not an interpretation of the mystery of things. The mystery is simply relegated to a remoter region, respecting which no inquiry is to be made. But the inquiry must be made. After every such solution there arises afresh the question—what is the origin and nature of that which imposes these limits on creative power? what is the primary God which dominates over this secondary God? For, clearly, if the “Omnipotent Architect himself” (to use Mr. Martineau’s somewhat inconsistent name) is powerless to change the “material datum objective” to him, and powerless to change the conditions under which it exists, and under which he works, there is obviously implied a power to which he is subject. So that in Mr. Martineau’s doctrine also, there is an Ultimate {258} Unknowable; and it differs from the doctrine he opposes, only by intercalating a partially Knowable between this and the wholly Knowable. Finding, as explained above, that this interpretation is not consistent with itself; and finding, as just shown, that it leaves the essential mystery unsolved; I do not see that it has an advantage over the doctrine of the Unknowable in its unqualified shape. There cannot, I think, be more than temporary rest in a proximate solution which takes for its basis the ultimately insoluble. Just as thought cannot be prevented from passing beyond Appearance, and trying to conceive the Cause behind; so, following out the interpretation Mr. Martineau offers, thought cannot be prevented from asking what Cause it is which restricts the Cause he assigns. And if we must admit that the question under this eventual form cannot be answered, may we not as well confess that the question under its immediate form cannot be answered? Is it not better candidly to acknowledge the incompetence of our intelligence, rather than to persist in calling that an explanation which does but disguise the inexplicable? Whatever answer each may give to this question, he cannot rightly blame those who, finding in themselves an indestructible consciousness of an ultimate Cause, whence proceed alike what we call the Material Universe and what we call Mind, refrain from affirming anything respecting it; because they find it as inscrutable in nature as it is inconceivable in extent and duration. POSTSCRIPT.—With the concluding paragraph of the foregoing article, I had hoped to end, for a long time, all controversial writing; and, if the article had been published entire in the November number of the Fortnightly, as originally intended, the need for any addition would not have been pressing. But while it was in the printer’s {259} hands, two criticisms, more elaborate than those dealt with above, made their appearance; and now that the postponed publication of this latter half of the article affords the opportunity, I cannot, without risking misinterpretations, leave these criticisms unnoticed.Especially do I feel called upon by courtesy to make some response to one who, in the Quarterly Review for October, 1873, has dealt with me in a spirit which, though largely antagonistic, is not wholly unsympathetic; and who manifestly aims to estimate justly the views he opposes. In the space at my disposal, I cannot of course follow him through all the objections he has urged. I must content myself with brief comments on the two propositions he undertakes to establish. His enunciation of these runs thus:—
On this passage, ending in these two startling assertions, let me first remark that I am wholly without this consciousness the reviewer ascribes to me. Remembering that I have expended some little labour in developing what I conceive to be a system of truths, I am surprised by the supposition that “the denial of all truth” is an implication which I am “doubtless” aware may be alleged against this system. Remembering, too, that by its programme this system is shown to close with two volumes on The Principles of Morality, the statement that it is “necessarily opposed to all sound principles of morals,” naturally astonishes me; and still more the statement that I am doubtless conscious it may be so regarded. Saying thus much by way of repudiating that latent scepticism {260} attributed to me by the reviewer, I proceed to consider what he says in proof of these propositions. On those seeming incongruities of Transfigured Realism commented on by him, I need say no more than I have already said in reply to Mr. Sidgwick; by whom also they have been alleged. I will limit myself to the corollary he draws from the doctrine of the Relativity of Knowledge, as held by me. Rightly pointing out that I hold this in common with “Messrs. Mill, Lewes, Bain, and Huxley;” but not adding, as he should have done, that I hold it in common with Hamilton, Mansel, and the long list of predecessors through whom Hamilton traced it; the reviewer proceeds to infer from this doctrine of relativity that no absolute truth of any kind can be asserted—not even the absolute truth of the doctrine of relativity itself. And then he leaves it to be supposed by his readers, that this inference tells especially against the system he is criticizing. If, however, the reviewer’s inference is valid, this “denial of all truth” must be charged against the doctrines of thinkers called orthodox, as well as against the doctrines of those many philosophers, from Aristotle down to Kant, who have said the same thing. But now I go further, and reply that against that form of the doctrine of relativity held by me, this allegation cannot be made with the same effect as it can against preceding forms of the doctrine. For I diverge from other relativists in asserting that the existence of a non-relative is not only a positive deliverance of consciousness, but a deliverance transcending in certainty all others whatever; and is one without which the doctrine of relativity cannot be framed in thought. I have urged that “unless a real Non-relative or Absolute be postulated, the Relative itself becomes absolute; and so brings the argument to a contradiction;” The justification of his second proposition the reviewer commences by saying that—“In the first place the process of Evolution, as understood by Mr. Spencer, compels him to be at one with Mr. Darwin in his denial of the existence of any fundamental and essential distinction between Duty and Pleasure.” Following this by a statement respecting the genesis of moral sentiments as understood by me (which is extremely unlike the one I have given in the Principles of Psychology, § 215, §§ 503–512, and §§ 524–532), the reviewer goes on to say that “We yield with much reluctance to the necessity of affirming that Mr. Spencer gives no evidence of ever having acquired a knowledge of the meaning of the term ‘morality,’ according to the true sense of the word.” Just noting that, as shown by the context, the assertion {262} thus made is made against all those who hold the Doctrine of Evolution in its unqualified form, I reply that in so far as it concerns me, it is one the reviewer would scarcely have made had he more carefully examined the evidence: not limiting himself to those works of mine named at the head of his article. And I cannot but think that had the spirit of fairness which he evidently strives to maintain, been fully awake when these passages were written, he would have seen that, before making so serious an allegation, wider inquiry was needful. If he had simply said that, given the doctrine of mental evolution as held by me, he failed to see how moral principles are to be established, I should not have objected; provided he had also said that I believe they can be established, and had pointed out what I hold to be their bases. As it is, however, he has so presented his own inference from my premises, as to make it seem an inference which I also must draw from my premises. Quite a different and much more secure foundation for moral principles is alleged by me, than that afforded by moral sentiments and conceptions; which he refers to as though they formed the sole basis of the ethical conclusions I hold. While the reviewer contends that “Mr. Spencer’s moral system is even yet more profoundly defective, as it denies any objective distinction between right and wrong in any being, whether men are or are not responsible for their actions;” I contend, contrariwise, that it is distinguished from other moral systems by asserting the objectivity of the distinction, and by endeavouring to show that the subjective distinction is derived from the objective distinction. In my first work, Social Statics, published twenty-three years ago, the essential thesis is that, apart from their warrant as alleged Divine injunctions, and apart from their authority as moral intuitions, the principles of justice are primarily deducible from the laws of life as carried on under social conditions. I argued throughout that these principles so derived have {263} a supreme authority, to which considerations of immediate expediency must yield; and I was for this reason classed by Mr. Mill as an anti-utilitarian. More recently, in a letter drawn from me by this misapprehension of Mr. Mill, and afterwards published by Professor Bain in his Mental and Moral Science, I have re-stated this position. Already, in an explanatory article entitled Morals and Moral Sentiments, published in the Fortnightly Review for April, 1871, I have quoted passages from that letter; and here, considering the gravity of the assertions made by the Quarterly reviewer, I hope to be excused for re-quoting them:—
And the comment I then made on these passages I may make now, that “I do not see how there could well be a more emphatic assertion that there exists a primary basis of morals independent of, and in a sense antecedent to, that which is furnished by experiences of utility; and consequently independent of, and in a sense antecedent to, those moral sentiments which I conceive to be generated by such experiences.” I will only add that, had my beliefs been directly opposite to those I have enunciated, {264} the reviewer might, I think, have found good reasons for his assertion. If, instead of demurring to the doctrine “that greatest happiness should be the immediate aim of man,” I quite agree with the reviewer that the prevalence of a philosophy “is no mere question of speculative interest, but is one of the highest practical importance.” I join him, too, in the belief that “calamitous social and political changes” may be the outcome of a mistaken philosophy. Moreover, writing as he does under the conviction that there can be no standard of right and wrong save one derived from a Revelation interpreted by an Infallible Authority, I can conceive the alarm with which he regards so radically opposed a system. Though I could have wished that the sense of justice he generally displays had prevented him from ignoring the evidence I have above given, I can understand how, from his point of view, the Doctrine of Evolution, as I understand it, “seems absolutely fatal {265} to every germ of morality,” and “entirely negatives every form of religion.” But I am unable to understand that modified Doctrine of Evolution which the reviewer hints at as an alternative. For, little as the reader would anticipate it after these expressions of profound dissent, the reviewer displays such an amount of agreement as to suggest that the system he is criticizing might be converted, “rapidly and without violence, into an ‘allotropic state,’ in which its conspicuous characters would be startlingly diverse from those that it exhibits at present.” May I, using a different figure, suggest a different transformation, having a subjective instead of an objective character? As in a stereoscope, the two views representing diverse aspects, often yield at first a jumble of conflicting impressions, but, after a time, suddenly combine into a single whole which stands out quite clearly; so, may it not be that the seemingly-inconsistent Idealism and Realism dwelt on by the reviewer, as well as the other seemingly-fundamental incongruities he is struck by, will, under more persistent contemplation, unite as complementary sides of the same thing? My excuse for devoting some space to a criticism of so entirely different a kind as that contained in the British Quarterly Review for October, 1873, must be that, under the circumstances, I cannot let it pass unnoticed without seeming to admit its validity. Saying that my books should be dealt with by specialists, and tacitly announcing himself as an expert in Physics, the reviewer takes me to task both for errors in the statement of physical principles and for erroneous reasoning in physics. That he discovers no mistakes I do not say. It would be marvellous if in such a multitude of propositions, averaging a dozen per page, I had made all criticism-proof. Some are inadvertencies which I should have been obliged to the reviewer for pointing out as such, but which he prefers to {266} instance as proving my ignorance. In other cases, taking advantage of an imperfection of statement, he proceeds to instruct me about matters which either the context, or passages in the same volume, show to be quite familiar to me. Here is a sample of his criticisms belonging to this class:—
Respecting the first of the two statements contained in this sentence, I will observe that the reader, if not misled by the quotation-marks into the supposition that I have made, in so many words, the assertion that “insensible motion is heat,” will at any rate infer that this assertion is distinctly involved in the passage named. And he will infer that the reviewer would never have charged me with such an absurd belief, if there was before him evidence proving that I have no such belief. What will the reader say, then, when he learns, not simply that there is no such statement, and not simply that on the page referred to, which I have ascertained to be the one intended, there is no such implication visible, even to an expert (and I have put the question to one); but when he further learns that in other passages, the fact that heat is one only of the modes of insensible motion is distinctly stated (see First Prin. §§ 66, 68, 171); and when he learns that elsewhere I have specified the several forms of insensible motion? If the reviewer, who looks so diligently for flaws as to search an essay in a volume he is not reviewing to find one term of an incongruity, had sought with equal diligence to learn what I thought about insensible motion, he would have found in the Classification of the Sciences, Table II., that insensible motion is described by me as having the forms of Heat, Light, Electricity, Magnetism. Even had there been in {267} the place he names, an unquestionable implication of the belief which he ascribes to me, fairness might have led him to regard it as an oversight when he found it at variance with statements I have elsewhere made. What then is to be thought of him when, in the place named, no such belief is manifest; either to an ordinary reader or to a specially-instructed reader? No less significant is the state of mind betrayed in the second clause of the reviewer’s sentence. By representing me as saying that when the motion constituting sound “gets so dispersed that it becomes insensible, it turns to heat,” does he intend to represent me as thinking that when sound-undulations become too weak to be audible, they become heat-undulations? If so, I reply that the passage he refers to has no such meaning. Does he then allege that some part of the force diffused in sound-waves is expended in generating electricity, by the friction of heterogeneous substances (which, however, eventually lapses from this special form of molecular motion in that general form constituting heat); and that I ought to have thus qualified my statement? If so, he would have had me commit a piece of scientific pedantry hindering the argument. If he does not mean either of these things, what does he mean? Does he contest the truth of the hypothesis which enabled Laplace to correct Newton’s estimate of the velocity of sound—the hypothesis that heat is evolved by the compression each sound-wave produces in the air? Does he deny that the heat so generated is at the expense of so much wave-motion lost? Does he question the inference that some of the motion embodied in each wave is from instant to instant dissipated, partly in this way and partly in the heat evolved by fluid friction? Can he show any reason for doubting that when the sound-waves have become too feeble to affect our senses, their motion still continues to undergo this transformation and diminution until it is all lost? If not, why does he implicitly deny that {268} the molar motion constituting sound, eventually disappears in producing the molecular motion constituting heat? I will dwell no longer on the exclusively-personal questions raised by the reviewer’s statements; but, leaving the reader to judge of the rest of my “stupendous mistakes” by the one I have dealt with, I will turn to a question worthy to occupy some space, as having an impersonal interest—the question, namely, respecting the nature of the warrant we have for asserting ultimate physical truths. The contempt which, as a physicist, the reviewer expresses for the metaphysical exploration of physical ideas, I will pass over with the remark that every physical question, probed to the bottom, opens into a metaphysical one; and that I should have thought the controversy now going on among chemists, respecting the legitimacy of the atomic hypothesis, might have shown him as much. On his erroneous statement that I use the phrase “Persistence of Force” as an equivalent for the now-generally-accepted phrase “Conservation of Energy,” I will observe only that, had he not been in so great a hurry to find inconsistencies, he would have seen why, for the purposes of my argument, {269} I intentionally use the word Force: Force being the generic word, including both that species known as Energy, and that species by which Matter occupies space and maintains its integrity—a species which, whatever may be its relation to Energy, and however clearly recognized as a necessary datum by the theory of Energy, is not otherwise considered in that theory. I will confine myself to the proposition, disputed at great length by the reviewer, that our cognition of the Persistence of Force is a priori. He relies much on the authority of Professor Tait, whom he twice quotes to the effect that—
Were I to take a hypercritical attitude, I might dwell on the fact that Professor Tait leaves the extent of his proposition somewhat doubtful, by speaking of “Natural philosophy” as one science. Were I to follow further the reviewer’s example, I might point out that “Natural philosophy,” in that Newtonian acceptation adopted by Professor Tait, includes Astronomy; and, going on to ask what astronomical “experiments” those are which conduct us to astronomical truths, I might then “counsel” the reviewer not to depend on the authority of one who (to use the reviewer’s polite language) “blunders” by confounding experiment and observation. I will not, however, thus infer from Professor Tait’s imperfection of statement that he is unaware of the difference between the two; and shall rate his authority as of no less value than I should, had he been more accurate in his expression. Respecting that authority I shall simply remark that, if the question had to be settled by the authority of any physicist, the authority of Mayer, who is diametrically opposed to Prof. Tait on this point, and who has been specially honoured, both by the Royal Society and by the French Institute, might well counter-weigh his, if not out-weigh it. I am not aware, {270} however, that the question is one in Physics. It seems to me a question respecting the nature of proof. And, without doubting Professor Tait’s competence in Logic and Psychology, I should decline to abide by his judgment on such a question, even were there no opposite judgment given by a physicist, certainly of not less eminence. Authority aside, however, let us discuss the matter on its merits. In the Treatise on Natural Philosophy, by Profs. Thomson and Tait, § 243 (1st ed.), I read that “as we shall show in our chapter on ‘Experience,’ physical axioms are axiomatic to those only who have sufficient knowledge of the action of physical causes to enable them to see at once their necessary truth.” In this I agree entirely. It is in Physics, as it is in Mathematics, that before necessary truths can be grasped, there must be gained by individual experience, such familiarity with the elements of the thoughts to be framed, that propositions about those elements may be mentally represented with distinctness. Tell a child that things which are equal to the same thing are equal to one another, and the child, lacking a sufficiently-abstract notion of equality, and lacking, too, the needful practice in comparing relations, will fail to grasp the axiom. Similarly, a rustic, never having thought much about forces and their results, cannot form a definite conception answering to the axiom that action and reaction are equal and opposite. In the last case as in the first, ideas of the terms and their relations require to be made, by practice in thinking, so vivid that the involved truths may be mentally seen. But when the individual experiences have been multiplied enough to produce distinctness in the representations of the elements dealt with; then, in the one case as in the other, those mental forms generated by ancestral experiences, cannot be occupied by the elements of one of these ultimate truths without perception of its necessity. If Professor Tait does not admit this, what {271} does he mean by speaking of “physical axioms,” and by saying that the cultured are enabled “to see at once their necessary truth?” Again, if there are no physical truths which must be classed as a priori, I ask why Professor Tait joins Sir W. Thomson in accepting as bases for Physics, Newton’s Laws of Motion? Though Newton gives illustrations of prolonged motion in bodies that are little resisted, he gives no proof that a body in motion will continue moving, if uninterfered with, in the same direction at the same velocity; nor, on turning to the enunciation of this law quoted in the above-named work, do I find that Professor Tait does more than exemplify it by facts which can themselves be asserted only by taking the law for granted. Does Professor Tait deny that the first law of motion is a physical truth? If so, what does he call it? Does he admit it to be a physical truth, and, denying that it is a priori, assert that it is established a posteriori—that is, by conscious induction from observation and experiment? If so, what is the inductive reasoning which can establish it? Let us glance at the several conceivable arguments which we must suppose him to rely on. A body set in motion soon ceases to move if it encounters much friction, or much resistance from the bodies struck. If less of its energy is expended in moving, or otherwise affecting, other bodies, or in overcoming friction, its motion continues longer. And it continues longest when, as over smooth ice, it meets with the smallest amount of obstruction. May we then, proceeding by the method of concomitant variations, infer that were it wholly unobstructed its motion would continue undiminished? If so, we assume that the diminution of its motion observed in experience, is proportionate to the amount of energy abstracted from it in producing other motion, either molar or molecular. We assume that no variation has taken place in its rate, save that caused by deductions in moving other matter; for if {272} its motion be supposed to have otherwise varied, the conclusion that the differences in the distances travelled result from differences in the obstructions met with, is vitiated. Thus the truth to be established is already taken for granted in the premises. Nor is the question begged in this way only. In every case where it is remarked that a body stops the sooner, the more it is obstructed by other bodies or media, the law of inertia is assumed to hold in the obstructing bodies or media. The very conception of greater or less retardation so caused, implies the belief that there can be no retardations without proportionate retarding causes; which is itself the assumption otherwise expressed in the first law of motion. Again, let us suppose that instead of inexact observations made on the movements occurring in daily experience, we make exact experiments on movements specially arranged to yield measured results; what is the postulate underlying every experiment? Uniform velocity is defined as motion through equal spaces in equal times. How do we measure equal times? By an instrument which can be inferred to mark equal times only if the oscillations of the pendulum are isochronous; which they can be proved to be only if the first and second laws of motion are granted. That is to say, the proposed experimental proof of the first law, assumes not only the truth of the first law, but of that which Professor Tait agrees with Newton in regarding as a second law. Is it said that the ultimate time-measure referred to is the motion of the Earth round its axis, through equal angles in equal times? Then the obvious rejoinder is that the assertion of this, similarly involves an assertion of the truth to be proved; since the undiminished rotatory movement of the Earth is itself a corollary from the first law of motion. Is it alleged that this axial movement of the Earth through equal angles in equal times, is ascertainable by reference to the stars? I answer that a developed system of Astronomy, leading through complex {273} reasonings to the conclusion that the Earth rotates, is, in that case, supposed to be needful before there can be established a law of motion which this system of Astronomy itself postulates. For even should it be said that the Newtonian theory of the Solar System is not necessarily pre-supposed, but only the Copernican; still, the proof of this assumes that a body at rest (a star being taken as such) will continue at rest; which is a part of the first law of motion, regarded by Newton as not more self-evident than the remaining part. Not a little remarkable, indeed, is the oversight made by Professor Tait, in asserting that “no a priori reasoning can conduct us demonstratively to a single physical truth,” when he has before him the fact that the system of physical truths constituting Newton’s Principia, which he has joined Sir William Thomson in editing, is established by a priori reasoning. That there can be no change without a cause, or, in the words of Mayer, that “a force cannot become nothing, and just as little can a force be produced from nothing,” is that ultimate dictum of consciousness on which all physical science rests. It is involved alike in the assertion that a body at rest will continue at rest, in the assertion that a body in motion must continue to move at the same velocity in the same line if no force acts on it, and in the assertion that any divergent motion given to it must be proportionate to the deflecting force; and it is also involved in the axiom that action and reaction are equal and opposite. The reviewer’s doctrine, in support of which he cites against me the authority of Professor Tait, illustrates in Physics that same error of the inductive philosophy which, in Metaphysics, I have pointed out elsewhere (Principles of Psychology, Part VII.). It is a doctrine implying that we can go on for ever asking the proof of the proof, without finally coming to any deepest cognition which is unproved and unprovable. That this is an untenable doctrine, I need {274} not say more to show. Nor, indeed, would saying more to show it be likely to have any effect, in so far at least as the reviewer is concerned; seeing that he thinks I am “ignorant of the very nature of the principles” of which I am speaking, and seeing that my notions of scientific reasoning “remind” him “of the Ptolemists,” who argued that the heavenly bodies must move in circles because the circle is the most perfect figure. Not to try the reader’s patience further, I will end by pointing out that, even were the reviewer’s criticisms all valid, they would leave unshaken the theory he contends against. Though one of his sentences (p. 480) raises the expectation that he is about to assault, and greatly to damage, the bases of the system contained in the second part of First Principles, yet all those propositions which constitute the bases, he leaves, not only uninjured, but even untouched,—contenting himself with trying to show (with what success we have seen) that the fundamental one is an a posteriori truth and not an a priori truth. Against the general Doctrine of Evolution, considered as an induction from all classes of concrete phenomena, he utters not a word; nor does he utter a word to disprove any one of those laws of the redistribution of matter and motion, by {275} which the process of Evolution is deductively interpreted. Respecting the law of the Instability of the Homogeneous, he says no more than to quarrel with one of the illustrations. He makes no criticism on the law of the Multiplication of Effects. The law of Segregation he does not even mention. Nor does he mention the law of Equilibration. Further, he urges nothing against the statement that these general laws are severally deducible from the ultimate law of the Persistence of Force. Lastly, he does not deny the Persistence of Force; but only differs respecting the nature of our warrant for asserting it. Beyond pointing out, here a cracked brick and there a quoin set askew, he merely makes a futile attempt to show that the foundation is not natural rock, but concrete. From his objections I may, indeed, derive much satisfaction. That a competent critic, obviously anxious to do all the mischief he can, and not over-scrupulous about the means he uses, has done so little, may be taken as evidence that the fabric of conclusions attacked will not be readily overthrown. In the British Quarterly Review for January, 1874, the writer of the article I have dealt with above, makes a rejoinder. It is of the kind which might have been anticipated. There are men to whom the discovery that they have done injustice is painful. After proof of having wrongly ascribed to another such a nonsensical belief as that insensible motion is heat because heat is insensible motion, some would express regret. Not so my reviewer. Having by forced interpretations debited me with an absurdity, he makes no apology; but, with an air implying that he had all along done this, he attacks the allegation I had really made—an allegation which is at least so far from an absurdity, that he describes it only as not justified by “the present state of science.” And here, having incidentally referred to this point, I may as well, before {276} proceeding, deal with his substituted charge at the same time that I further exemplify his method. Probably most of those who see the British Quarterly, will be favourably impressed by the confidence of his assertion; but those who compare my statement with his travesty of it, and who compare both with some authoritative exposition, will be otherwise impressed. To his statement that I conclude “that friction must ultimately transform all [the italics are his] the energy of a sound into heat,” I reply that it is glaringly untrue: I have named friction as a second cause only. And when he pooh-poohs the effect of compression because it is “merely momentary,” is he aware of the meaning of his words? Will he deny that, from first to last, during the interval of condensation, heat is being generated? Will he deny to the air the power of radiating such heat? He will not venture to do so. Take then the interval of condensation as one-thousandth of a second. I ask him to inform those whom he professes to instruct, what is the probable number of heat-waves which have escaped in this interval. Must they not be numbered by thousands of millions? In fact, by his “merely momentary,” he actually assumes that what is momentary in relation to our time-measures, is momentary in relation to the escape of ethereal undulations! Let me now proceed more systematically, and examine his rejoinder point by point. It sets out thus:—
In my “Replies to Criticisms,” which, as it was, trespassed unduly on the pages of the Fortnightly Review, I singled {277} out from those of his allegations which touched me personally, one that might be briefly dealt with as an example; and I stated that, passing over other personal questions, as not interesting to the general reader, I should devote the small space available to an impersonal one. Notwithstanding this, the reviewer, in the foregoing paragraph, enumerates his chief positions; asserts that I have not assailed any of them (which is untrue); and then leads his readers to the belief that I have not assailed them because they are unassailable. Leaving this misbelief to be dealt with presently, I continue my comments on his rejoinder. After referring to the passage I have quoted from Prof. Tait’s statement about physical axioms, and after indicating the nature of my criticism, the reviewer says:—
Let us analyze this “authoritative expression.” It contains several startling implications, the disclosure of which the reader will find not uninteresting. Consider, first, what is implied by framing the thought that “the properties of matter might have been such as to render a totally different set of laws axiomatic.” I will not stop to make the inquiry whether matter having properties fundamentally unlike its present ones, can be conceived; though such an inquiry, leading to the conclusion that no conception of the kind is possible, would show that the proposition is merely a verbal one. It will suffice if I examine the nature of this proposition that “the properties of matter might have been” {278} other than they are. Does it express an experimentally-ascertained truth? If so, I invite Prof. Tait to describe the experiments. Is it an intuition? If so, then along with doubt of an intuitive belief concerning things as they are, there goes confidence in an intuitive belief concerning things as they are not. Is it an hypothesis? If so, the implication is that a cognition of which the negation is inconceivable (for an axiom is such) may be discredited by inference from that which is not a cognition at all, but simply a supposition. Does the reviewer admit that no conclusion can have a validity greater than is possessed by its premises? or will he say that the trustworthiness of cognitions increases in proportion as they are the more inferential? Be his answer what it may, I shall take it as unquestionable that nothing concluded can have a warrant higher than that from which it is concluded, though it may have a lower. Now the elements of the proposition before us are these:—As “the properties of matter might have been such as to render a totally different set of laws axiomatic” [therefore] “these laws [now in force] must be considered as resting ... not on intuitive perception:” that is, the intuitions in which these laws are recognized, must not be held authoritative. Here the cognition posited as premiss, is that the properties of matter might have been other than they are; and the conclusion is that our intuitions relative to existing properties are uncertain. Hence, if this conclusion is valid, it is valid because the cognition or intuition respecting what might have been, is more trustworthy than the cognition or intuition respecting what is! Scepticism respecting the deliverances of consciousness about things as they are, is based upon faith in a deliverance of consciousness about things as they are not! I go on to remark that this “authoritative expression of disapproval” by which I am supposed to be silenced, even were its allegation as valid as it is fallacious, would leave {279} wholly untouched the real issue. I pointed out how Prof. Tait’s denial that any physical truths could be reached a priori, was contradicted by his own statement respecting physical axioms. The question thus raised the reviewer evades, and substitutes another with which I have just dealt. Now I bring forward again the evaded question. In the passage I quoted, Prof. Tait, besides speaking of physical “axioms,” says of them that due familiarity with physical phenomena gives the power of seeing “at once” “their necessary truth.” These last words, which express his conception of an axiom, express also the usual conception. An axiom is defined as a “self-evident truth,” or a truth that is seen at once; and the definition otherwise worded is—a “truth so evident at first sight, that no process of reasoning or demonstration can make it plainer.” Now I contend that Prof. Tait, by thus committing himself to a definition of physical axioms identical with that which is given of mathematical axioms, tacitly admits that they have the same a priori character; and I further contend that no such nature as that which he describes physical axioms to have, can be acquired by experiment or observation during the life of an individual. Axioms, if defined as truths of which the necessity is at once seen, are thereby defined as truths of which the negation is inconceivable; and the familiar contrast between them and the truths established by individual experiences, is that these last never become such that their negations are inconceivable, however multitudinous the experiences may be. Thousands of times has the sportsman heard the report that follows the flash from his gun, but still he can imagine the flash as occurring silently; and countless daily experiments on the burning of coal, leave him able to conceive coal as remaining in the fire without ignition. So that the “convictions drawn from observation and experiment” during a single life, can never acquire that character which Prof. Tait admits physical axioms to have: in other words, physical axioms cannot be {280} derived from personal observation and experiment. Thus, otherwise applying the reviewer’s words, I “doubt whether we should have heard aught of this quotation” to which he calls my attention, had he studied the matter more closely; and he “leaves us indebted to” him “for the discovery of” a passage which serves to make clearer the untenability of the doctrine he so dogmatically affirms. I turn now to what the reviewer says concerning the special arguments I used to show that the first law of motion cannot be proved experimentally. After a bare enunciation of my positions, he says:—
Probably the reviewer expects his readers to conclude that he could easily dispose of the statements referred to if he tried. Among scientific men, however, this cavalier passing over of my arguments will perhaps be ascribed to another cause. I will give him my reason for saying this. Those arguments, read in proof by one of the most eminent physicists, and by a specially-honoured mathematician, had their entire concurrence; and I have since had from another mathematician, standing among the very first, such qualified agreement as is implied in saying that the first law of motion cannot be proved by terrestrial observations (which is in large measure what I undertook to show in the paragraphs which the reviewer passes over so contemptuously). But his last sentence, telling us what he thought “every tolerably educated man was aware” of, is the one which chiefly demands attention. In it he uses the word law—a word which, conveniently wide in meaning, suits his purpose remarkably well. But we are here speaking of physical axioms. The question is whether the justification of a physical {281} axiom consists in showing that by assuming its truth, we can explain the observed phenomena. If it does, then all distinction between hypothesis and axiom disappears. Mathematical axioms, for which there is no other definition than that which Prof. Tait gives of physical axioms, must stand on the same footing. Henceforth we must hold that our warrant for asserting that “things which are equal to the same thing are equal to one another,” consists in the observed truth of the geometrical and other propositions deducible from it and the associated axioms—the observed truth, mind; for the fabric of deductions yields none of the required warrant until these deductions have been tested by measurement. When we have described squares on the three sides of a right-angled triangle, cut them out in paper, and, by weighing them, have found that the one on the hypothenuse balances the other two; then we have got a fact which, joined with other facts similarly ascertained, justifies us in asserting that things which are equal to the same thing are equal to one another! Even as it stands, this implication will not, I think, be readily accepted; but we shall find that its unacceptability becomes still more conspicuous when the analysis is pursued to the end. Continuing his argument to show that the laws of motion have no a priori warrant, the reviewer says:—
I have first to point out that here, as before, the reviewer escapes by raising a new issue. I did not ask what he thinks about the Principia, and the proof of the laws of motion by it; nor did I ask whether others at this day, hold the assertion of these laws to be justified mainly by the evidence the Solar System affords. I asked what Newton thought. The reviewer had represented the belief that the second law of motion is knowable a priori, as too {282} absurd even for me openly to enunciate. I pointed out that since Newton enunciates it openly under the title of an axiom, and offers no proof whatever of it, he did explicitly what I am blamed for doing implicitly. And thereupon I invited the reviewer to say what he thought of Newton. Instead of answering, he gives me his opinion to the effect that the laws of motion are proved true by the truth of the Principia deduced from them. Of this hereafter. My present purpose is to show that Newton did not say this, and gave every indication of thinking the contrary. He does not call the laws of motion “hypotheses;” he calls them “axioms.” He does not say that he assumes them to be true provisionally; and that the warrant for accepting them as actually true, will be found in the astronomically-proved truth of the deductions. He lays them down just as mathematical axioms are laid down—posits them as truths to be accepted a priori, from which follow consequences that must therefore be accepted. And though the reviewer thinks this an untenable position, I am quite content to range myself with Newton in thinking it a tenable one—if, indeed, I may say so without undervaluing the reviewer’s judgment. But now, having shown that the reviewer evaded the issue I raised, which it was inconvenient for him to meet, I pass to the issue he substitutes for it. I will first deal with it after the methods of ordinary logic, before dealing with it after the methods of what may be called transcendental logic. To establish the truth of a proposition postulated, by showing that the deductions from it are true, requires that the truth of the deductions shall be shown in some way that does not directly or indirectly assume the truth of the proposition postulated. If, setting out with the axioms of Euclid, we deduce the truths that “the angle in a semi-circle is a right angle,” and that “the opposite angles of any quadrilateral figure described in a circle, are together equal to two right angles,” and so forth; and if, because {283} these propositions are true, we say that the axioms are true, we are guilty of a petitio principii. I do not mean simply that if these various propositions are taken as true on the strength of the demonstrations given, the reasoning is circular, because the demonstrations assume the axioms; but I mean more—I mean that any supposed experimental proof of these propositions by measurement, itself assumes the axioms to be justified. For even when the supposed experimental proof consists in showing that some two lines demonstrated by reason to be equal, are equal when tested in perception, the axiom that things which are equal to the same thing are equal to one another, is taken for granted. The equality of the two lines can be ascertained only by carrying from the one to the other, some measure (either a moveable marked line or the space between the points of compasses), and by assuming that the two lines are equal to one another, because they are severally equal to this measure. The ultimate truths of mathematics, then, cannot be established by any experimental proof that the deductions from them are true; since the supposed experimental proof takes them for granted. The same thing holds of ultimate physical truths. For the alleged a posteriori proof of these truths, has a vice exactly analogous to the vice I have just indicated. Every evidence yielded by astronomy that the axioms called “the laws of motion” are true, resolves itself into a fulfilled prevision that some celestial body or bodies, will be seen in a specified place, or in specified places, in the heavens, at some assigned time. Now the day, hour, and minute of this verifying observation, can be fixed only on the assumption that the Earth’s motion in its orbit and its motion round its axis, continue undiminished. Mark, then, the parallelism. One who chose to deny that things which are equal to the same thing are equal to one another, could never have it proved to him by showing the truth of deduced propositions; since the testing process would in {284} every case assume that which he denied. Similarly, one who refused to admit that motion, uninterfered with, continues in the same straight line at the same velocity, could not have it proved to him by the fulfilment of an astronomical prediction; because he would say that both the spectator’s position in space, and the position of the event in time, were those alleged, only if the Earth’s motions of translation and rotation were undiminished, which was the very thing he called in question. Evidently such a sceptic might object that the seeming fulfilment of the prediction, say a transit of Venus, may be effected by various combinations of the changing positions of Venus, of the Earth, and of the spectator on the Earth. The appearances may occur as anticipated, though Venus is at some other place than the calculated one; provided the Earth also is at some other place, and the spectator’s position on the Earth is different. And if the first law of motion is not assumed, it must be admitted that the Earth and the spectator may occupy these other places at the predicted time: supposing that in the absence of the first law, this predicted time can be ascertained, which it cannot. Thus the testing process inevitably begs the question. That the perfect congruity of all astronomical observations with all deductions from “the laws of motion,” gives coherence to this group of intuitions and perceptions, and so furnishes a warrant for the entire aggregate of them which it would not have were any of them at variance, is unquestionable. But it does not therefore follow that astronomical observations can furnish a test for each individual assumption, out of the many which are simultaneously made. I will not dwell on the fact that the process of verification assumes the validity of the assumptions on which acts of reasoning proceed; for the reply may be that these are shown to be valid apart from astronomy. Nor will I insist that the assumptions underlying mathematical inferences, geometrical and {285} numerical, are involved; since it may be said that these are justifiable separately by our terrestrial experiences. But, passing over all else that is taken for granted, it suffices to point out that, in making every astronomical prediction, the three laws of motion and the law of gravitation are all assumed; that if the first law of motion is to be held proved by the fulfilment of the prediction, it can be so only by taking for granted that the two other laws of motion and the law of gravitation are true; and that non-fulfilment of the prediction would not disprove the first law of motion, since the error might be in one or other of the three remaining assumptions. Similarly with the second law: the astronomical proof of it depends on the truth of the accompanying assumptions. So that the warrants for the assumptions A, B, C, and D, are respectively such that A, B, and C being taken as trustworthy, prove the validity of D; D being thus proved valid, joins C, and B, in giving a character to A; and so throughout. The result is that everything comes out right if they happen to be all true; but if one of them is false, it may destroy the characters of the other three, though these are in reality exact. Clearly, then, astronomical prediction and observation can never test any one of the premises by itself. They can only justify the entire aggregate of premises, mathematical and physical, joined with the entire aggregate of reasoning processes leading from premises to conclusions. I now recall the reviewer’s “thought,” uttered in his habitual manner, “that every tolerably educated man was aware that the proof of a scientific law consisted in showing that by assuming its truth, we could explain the observed phenomena.” Having from the point of view of ordinary logic dealt with this theory of proof as applied by the reviewer, I proceed to deal with it from the point of view of transcendental logic, as I have myself applied it. And here I have to charge the reviewer with either being ignorant of, or else deliberately ignoring, a cardinal {286} doctrine of the System of Philosophy he professes to review—a doctrine set forth not in those four volumes of it which he seems never to have looked into; but in the one volume of it he has partially dealt with. For this principle which, in respect to scientific belief, he enunciates for my instruction, is one which, in First Principles, I have enunciated in respect to all beliefs whatever. In the chapter on the “Data of Philosophy,” where I have inquired into the legitimacy of our modes of procedure, and where I have pointed out that there are certain ultimate conceptions without which the intellect can no more stir “than the body can stir without help of its limbs,” I have inquired how their validity or invalidity is to be shown; and I have gone on to reply that—
Proceeding avowedly and rigorously on this principle, I have next inquired what is the fundamental process of thought by which this congruity is to be determined, and what is the fundamental product of thought yielded by this process. This fundamental product I have shown to be the coexistence of subject and object; and then, describing this as a postulate to be justified by “its subsequently-proved congruity with every result of experience, direct and indirect,” I have gone on to say that “the two divisions of self and not-self, are re-divisible into certain most general forms, the reality of which Science, as well as Common Sense, from moment to moment assumes.” Nor is this all. Having thus assumed, only provisionally, this deepest of all intuitions, far transcending an axiom in self-evidence, I {287} have, after drawing deductions occupying four volumes, deliberately gone back to the assumption (Prin. of Psy., § 386). After quoting the passage in which the principle was laid down, and after reminding the reader that the deductions drawn had been found congruous with one another; I have pointed out that it still remained to ascertain whether this primordial assumption was congruous with all the deductions; and have thereupon proceeded, throughout eighteen chapters, to show the congruity. And yet having before him the volumes in which this principle is set forth with a distinctness, and acted upon with a deliberation, which I believe are nowhere paralleled, the reviewer enunciates for my benefit this principle of which he “thought that every tolerably educated man was aware”! He enunciates it as applying to limited groups of beliefs, to which it does not apply; and shuts his eyes to the fact that I have avowedly and systematically acted upon it in respect to the entire aggregate of our beliefs (axioms included) for which it furnishes the ultimate justification! Here I must add another elucidatory statement, which would have been needless had the reviewer read that which he criticizes. His argument proceeds throughout on the assumption that I understand a priori truths after the ancient manner, as truths independent of experience; and he shows this more tacitly, where he “trusts” that he is “attacking one of the last attempts to deduce the laws of nature from our inner consciousness.” Manifestly, a leading thesis of one of the works he professes to review, is entirely unknown to him—the thesis that forms of thought, and consequently the intuitions which those forms of thought involve, result entirely from the effects of experiences, organized and inherited. With the Principles of Psychology before him, not only does he seem unaware that it contains this doctrine, but though this doctrine, set forth in its first edition published nearly twenty years ago, has gained {288} considerable currency, he seems never to have heard of it. The implication of this doctrine is, not that the “laws of nature” are deducible from “our inner consciousness,” but that our consciousness has a pre-established correspondence with such of those laws (simple, perpetually presented, and never negatived) as have, in the course of practically-infinite ancestral experiences, registered themselves in our nervous structure. Had he taken the trouble to acquaint himself with this doctrine, he would have learned that the intuitions of axiomatic truths are regarded by me as latent in the inherited brain, just as bodily reflex actions are latent in the inherited nervous centres of a lower order; that such latent intuitions are made potentially more distinct by the greater definiteness of structure due to individual action and culture; and that thus, axiomatic truths, having a warrant entirely a posteriori for the race, have for the individual a warrant which, substantially a priori, is made complete a posteriori. And he would then have learned that as, during evolution, Thought has been moulded into increasing correspondence with Things; and as such correspondence, tolerably complete in respect of the simple, ever-present, and invariable relations, as those of space, has made considerable advance in respect of the primary dynamical relations; the assertion that the resulting intuitions are authoritative, is the assertion that the simplest uniformities of nature, as experienced throughout an immeasurable past, are better known than they are as experienced during an individual life. All which conceptions, however, being, as it seems, unheard of by the reviewer, he regards my trust in these primordial intuitions as like that of the Ptolemists in their fancies about perfection! Thus far my chief antagonists, passive if not active, have been Prof. Tait and, by implication, Sir William Thomson, {289} his coadjutor in the work quoted against me—men of standing, and the last of them of world-wide reputation as a mathematician and physicist. Partly because the opinions of such men demand attention, I have dealt with the questions raised at some length; and partly, also, because the origin and consequent warrant of physical axioms are questions of general and permanent interest. The reviewer, who by citing against me these authorities has gained for some of his criticisms consideration they would otherwise not deserve, I must, in respect of his other criticisms, deal with very briefly. Because, for reasons sufficiently indicated, I did not assail sundry of his statements, he has reiterated them as unassailable. I will here add no more than is needful to show how groundless is his assumption. What the reviewer says on the metaphysical aspects of the propositions we distinguish as physical, need not detain us long. His account of my exposition of “Ultimate Scientific Ideas,” he closes by saying of me that “he is not content with less than showing that all our fundamental conceptions are inconceivable.” Whether the reviewer knows what he means by an inconceivable conception, I cannot tell. It will suffice to say that I have attempted no such remarkable feat as that described. My attempt has been to show that objective activities, together with their objective forms, are inconceivable by us—that such symbolic conceptions of them as we frame, and are obliged to use, are proved, by the alternative contradictions which a final analysis of them discloses, to have no likeness to the realities. But the proposition that objective existence cannot be rendered in terms of subjective existence, the reviewer thinks adequately expressed by saying that “our fundamental conceptions” (subjective products) “are inconceivable” (cannot be framed by subjective processes)! Giving this as a sample from which may be judged his fitness for discussing these ultimate questions, I pass over his physico-metaphysical criticisms, and proceed at once to {290} those which his special discipline may be assumed to render more worthy of attention. Quoting a passage relative to the law that “all central forces vary inversely as the squares of the distances,” he derides the assertion that “this law is not simply an empirical one, but one deducible mathematically from the relations of space—one of which the negation is inconceivable.” Now whether this statement can or cannot be fully justified, it has at any rate none of that absurdity alleged by the reviewer. When he puts the question—“Whence does he [do I] get this?” he invites the suspicion that his mind is not characterized by much excursiveness. It seems never to have occurred to him that, if rays like those of light radiate in straight lines from a centre, the number of them falling on any given area of a sphere described from that centre, will diminish as the square of the distance increases, because the surfaces of spheres vary as the squares of their radii. For, if this has occurred to him, why does he ask whence I get the inference? The inference is so simple a one as naturally to be recognized by those whose thoughts go a little beyond their lessons in geometry.
To the first clause in this sentence, I have simply to give a direct denial; and to assert that neither Newton’s “observations of the movements of the planets” nor other such observations continued by all astronomers for all time, would yield “the great law of attraction.” Contrariwise, I contend that when the reviewer says, by implication, that Newton had no antecedent hypothesis respecting the cause of the planetary motions, he (the reviewer) is not only going beyond his possible knowledge, but he is asserting that which even a rudimentary acquaintance with the process of discovery, might have shown him was impossible. Without framing, beforehand, the supposition that there was at work an attractive force varying inversely as the square of the distance, no such comparison of observations as that which led to the establishment of the theory of gravitation could have been made. On the second clause of the sentence, in which the reviewer volunteers for my benefit the information that Newton “actually abandoned” his hypothesis for a while because it did not bring out right results, I have first to tell him that, in an early number of the very periodical containing his article, See, then, the critical capacity variously exhibited in the space of a single sentence. The reviewer, quite erroneously, thinks that observations unguided by hypotheses suffice for physical discoveries. He seems unaware that, on a priori grounds, the law of the inverse square had been suspected as the law of some cosmical force, before Newton. He asserts, without warrant, that no such a priori conception preceded, in Newton’s mind, his observations and {293} calculations. He confounds the law of variation of a force, with the existence of a force varying according to that law. And he concludes that Newton could have had no a priori conception of the law of variation, because he did not assert the existence of a force varying according to this law in defiance of the evidence as then presented to him! Now that I have analyzed, with these results, the first of his criticisms, the reader will neither expect me to waste time in similarly dealing with the rest seriatim, nor will he wish to have his own time occupied in following the analysis. To the evidence thus furnished of the reviewer’s fitness for the task he undertakes, it will suffice if I add an illustration or two of the animus which leads him to make grave imputations on trivial grounds, and to ignore the evidence which contradicts his interpretations. Because I have spoken of a balanced system, like that formed by the sun and planets, as having the “peculiarity, that though the constituents of the system have relative movements, the system, as a whole, has no movement,” he unhesitatingly assumes me to be unaware that in a system of bodies whose movements are not balanced, it is equally true that the centre of gravity remains constant. Ignorance of a general principle in dynamics is alleged against me solely because of this colloquial use of the word “peculiarity,” where I should have used a word (and there is no word perfectly fit) free from the implication of exclusiveness. If the reviewer were to assert that arrogance is a “peculiarity” of critics; and if I were thereupon to charge him with entire ignorance of mankind, many of whom besides critics are arrogant, he would rightly say that my conclusion was a very large one to draw from so small a premise. To this example of strained inference I will join an example of what seems like deliberate misconstruction. From one of my essays (not among the works he professes to deal with) the reviewer, to strengthen his attack, brings {294} a strange mistake; which, even without inquiry, any fair-minded reader would see must be an oversight. A statement true of a single body acted on by a tractive force, I have inadvertently pluralized: being so possessed by another aspect of the question, as to overlook the obvious fact that with a plurality of bodies the statement became untrue. Not only, however, does the reviewer ignore various evidences furnished by the works before him, that I could not really think what I had there said, but he ignores a direct contradiction contained in the paragraph succeeding that from which he quotes. So that the case stands thus:—On two adjacent pages I have made two opposite statements, both of which I cannot be supposed to believe. One of them is right; and this the reviewer assumes I do not believe. One of them is glaringly wrong; and this the reviewer assumes I do believe. Why he made this choice no one who reads his criticism will fail to see. Even had his judgments more authority than is given to them by his mathematical honours, this brief characterization would, I think, suffice. Perhaps already, in rebutting the assumption that I did not answer his allegations because they were unanswerable, I have ascribed to them an unmerited importance. For the rest, suggesting that their value may be measured by the value of that above dealt with as a sample, I leave them to be answered by the works they are directed against. Here I end. The foregoing pages, while serving, I think, the more important purpose of making clearer the relations of physical axioms to physical knowledge, incidentally justify the assertion that the reviewer’s charges of fallacious reasoning and ignorance of the nature of proof, recoil on himself. When, in his confident way, he undertakes to teach me the nature of our warrant for scientific beliefs, ignoring absolutely the inquiry contained in Principles of Psychology, concerning the relative values of direct intuitions and reasoned conclusions, he lays himself open to {295} a sarcasm which is sufficiently obvious. And when a certain ultimate principle of justification for our beliefs, set forth and acted upon in the System of Synthetic Philosophy more distinctly than in any other work, is enunciated by him for my instruction, as one which he “thought that every tolerably educated man was aware” of, his course is one for which I find no fit epithet in the vocabulary I permit myself to use. That in some cases he has shown eagerness to found charges on misinterpretations little less than deliberate, has been sufficiently shown; as also that, in other cases, his own failure to discriminate is made the ground for ascribing to me beliefs that are manifestly untenable. Save in the single case of a statement respecting collisions of bodies, made by me without the needful qualification, I am not aware of any errors he detects, except errors of oversight or those arising from imperfect expression and inadequate exposition. When he unhesitatingly puts the worst constructions on these, it cannot be because his own exactness is such that no other constructions occur to him; for he displays an unusual capacity for inadvertencies, and must have had many experiences showing him how much he might be wronged by illiberal interpretations of them. One who in twenty-three professed extracts makes fifteen mistakes—words omitted, or added, or substituted—should not need reminding how largely mere oversight may raise suspicion of something worse. One who shows his notions of accurate statement by asserting that as I substitute “persistence” for “conservation,” I therefore identify Persistence of Force with Conservation of Energy, and debits me with the resulting incongruities—one who, in pursuance of this error, confounds a special principle with the general principle it is said to imply, and thereupon describes a wider principle as being included in a narrower (p. 481)—one who speaks of our “inner consciousness” (p. 488), so asserting, by implication, that we have an outer consciousness—one who {296} talks of an inconceivable conception; ought surely to be aware how readily lax expressions may be turned into proofs of absurd opinions. And one who, in the space of a few pages, falls into so many solecisms, ought to be vividly conscious that a whole volume thus written would furnish multitudinous statements from which a critic, moved by a spirit like his own, might evolve abundant absurdities; supplying ample occasion for blazoning the tops of pages with insulting words. [A letter, drawn from Prof. Tait by the foregoing criticisms, and published by him in Nature, initiated a controversy carried on in that periodical between March 26th and June 18th, 1874. Partly in justification of my position, and partly as tending to make clearer the nature and origin of physical axioms, I append certain portions of the correspondence, with some additional explanations and comments. For the purpose of elucidation I prefix the theses I have maintained.] {297} 1. If A produces B, then 2A will produce 2B. This is the blank form of causal relation quantitatively considered, when the causes and effects are simple—that is, are unimpeded by other causes and uncomplicated by other effects; and whenever two or more causes co-operate, there is no possibility of determining the relation between the compound cause and the compound effect except by assuming that between each co-operating cause and its separate effect there exists this same quantitative relation. 2. This truth holds whatever the natures of the simple causes and simple effects; and is an a priori assumption made in conducting every experiment and in reasoning from it. Every process of weighing, every chemical analysis, every physical investigation, proceeds on this truth without assigning warrant for it; and in allowing for the effect of any minor cause that interferes with the major cause, this same truth is assumed. 3. When A is an impressed force and B the produced motion, then the general truth that if A produces B, 2A will produce 2B, becomes the more special truth called the Second Law of Motion. Newton’s amplified statement of this Law is:—“If any force generates a motion, a double force will generate double the motion, a triple force triple the motion, whether that force be impressed altogether and at once, or gradually and successively.” And his further clause, asserting that this law holds whether the directions of the forces are or are not the same, asserts a proportionality between each force and its produced motion, such as we have seen to be invariably assumed between each cause and its separate effect, when there are co-operating causes. 4. This Law may be affirmed, without specification of the modes in which the impressed force and the resulting motion are to be estimated. Newton’s statement is abstract. Taking for granted right modes of measurement, it asserts that the alteration of motion (rightly measured) is proportional to the impressed force (rightly measured). 5. No a posteriori proof of the general ultimate physical truth (or of this more special truth it includes) is possible; because every supposed process of verification assumes it. These, cleared from entanglements, are the theses held by me, and defended in the following pages. {298} (From Nature, April 16, 1874.) Absence from town has delayed what further remarks I have to make respecting the disputed origin of physical axioms. The particular physical axiom in connection with which the general question was raised, was the Second Law of Motion. It stands in the Principia as follows:—
As this, like each of the other Laws of Motion, is called an axiom; The passages quoted by the British Quarterly Reviewer from Newton’s correspondence, which were unknown to me, show that this was not Newton’s conception of them. Thus far, then, my opponent has the best of the {299} argument. Several qualifying considerations have to be set down, however. (1) Clearly, the statements contained in the Principia do not convey Newton’s conception; otherwise there would have been no need for his explanations. The passages quoted prove that he wished to exclude these cardinal truths from the class of hypotheses, which he said he did not make; and to do this he had to define them. (2) By calling them “axioms,” and by yet describing them as principles “deduced from phenomena,” he makes it manifest that he gives the word “axiom” a sense widely unlike the sense in which it is usually accepted. (3) Further, the quotations fail to warrant the statement that the Laws of Motion are proved true by the truth of the Principia. For if the fulfilment of astronomical predictions made in pursuance of the Principia, is held to be the evidence “on which they chiefly rest to this day,” then, until thus justified, they are unquestionably hypotheses. Yet Newton says they are not hypotheses. Newton’s view may be found without seeking for it in his letters: it is contained in the Principia itself. The scholium to Corollary VI. begins thus:—
Now as this passage precedes the deductions constituting the Principia, it shows conclusively, in the first place, that Newton did not think “the whole of the Principia was the proof” of the Laws of Motion, though the Reviewer asserts that it is. Further, by the words I have italicised, Newton implicitly describes Galileo as having asserted these Laws of Motion, if not as gratuitous hypotheses (which he says they are not), then as a priori intuitions. For a proposition which is confirmed by {300} experiment, and which is said to agree with experience, must have been entertained before the alleged verifications could be reached. And as before he made his experiments on falling bodies and projectiles, Galileo had no facts serving as an inductive basis for the Second Law of Motion, the law could not have been arrived at by induction. Let me end what I have to say on this vexed question by adding a further reason to those I have already given, for saying that physical axioms cannot be established experimentally. The belief in their experimental establishment rests on the tacit assumption that experiments can be made, and conclusions drawn from them, without any truths being postulated. It is forgotten that there is a foundation of pre-conceptions without which the perceptions and inferences of the physicist cannot stand—pre-conceptions which are the products of simpler experiences than those yielded by consciously-made experiments. Passing over the many which do not immediately concern us, I will name only that which does,—the exact quantitative relation [of proportionality] between cause and effect. It is taken by the chemist as a truth needing no proof, that if two volumes of hydrogen unite with one volume of oxygen to form a certain quantity of water, four volumes of hydrogen uniting with two volumes of oxygen will form double the quantity of water. If a cubic foot of ice at 32° is liquefied by a specified quantity of heat, it is taken to be unquestionable that three times the quantity of heat will liquefy three cubic feet. And similarly with mechanical forces, the unhesitating assumption is that if one unit of force acting in a given direction produces a certain result, two units will produce twice the result. Every process of measurement in a physical experiment takes this for granted; as we see in one of the simplest of them—the process of weighing. If a measured quantity of metal, gravitating towards the Earth, counterbalances a quantity of some other substance, the truth postulated in every act {301} of weighing is, that any multiple of such weight will counterbalance an equi-multiple of such substance. That is to say, each unit of force is assumed to work its equivalent of effect in the direction in which it acts. Now this is nothing else than the assumption which the Second Law of Motion expresses in respect to effects of another kind. “If any force generates a motion, a double force will generate a double motion,” &c., &c.; and when carried on to the composition of motions, the law is, similarly, the assertion that any other force, acting in any other direction, will similarly produce in that direction a proportionate motion. So that the law simply asserts the exact equivalence [or proportionality] of causes and effects of this particular class, while all physical experiments assume this exact equivalence [or proportionality] among causes and effects of all classes. Hence, the proposal to prove the Laws of Motion experimentally, is the proposal to make a wider assumption for the purpose of justifying one of the narrower assumptions included in it. Reduced to its briefest form, the argument is this:—If definite quantitative relations [of proportionality] between causes and effects be assumed a priori, then, the Second Law of Motion is an immediate corollary. If there are not definite quantitative relations [of proportionality] between causes and effects, all the conclusions drawn from physical experiments are invalid. And further, in the absence of this a priori assumption of equivalence, the quantified conclusion from any experiment may be denied, and any other quantification of the conclusion asserted. HERBERT SPENCER. Entire misconstruction of the view expressed above, {302} having been shown by a new assailant, who announced himself as also “A Senior Wrangler,” Mr. James Collier [my secretary at that time] wrote on my behalf an explanatory letter, published in Nature for May 21, 1874, from which the following passages are extracts:— “The cue may be taken from an experience described in Mr. Spencer’s Principles of Psychology (§ 468, note), where it is shown that when with one hand we pull the other, we have in the feeling of tension produced in the limb pulled, a measure of the reaction that is equivalent to the action of the other limb. Both terms of the relation of cause and effect are in this case present to consciousness as muscular tensions, which are our symbols of forces in general. While no motion is produced they are felt to be equal, so far as the sensations can serve to measure equality; and when excess of tension is felt in the one arm, motion is experienced in the other. Here, as in the examples about to be given, the relation between cause and effect, though numerically indefinite, is definite in the respect that every additional increment of cause produces an additional increment of effect; and it is out of this and similar experiences that the idea of the relation of proportionality grows and becomes organic. “A child, when biting his food, discovers that the harder he bites the deeper is the indentation; in other words, that the more force applied, the greater the effect. If he tears an object with his teeth, he finds that the more he pulls the more the thing yields. Let him press against something soft, as his own person, or his clothes, or a lump of clay, and he sees that the part or object pressed yields little or much, according to the amount of the muscular strain. He can bend a stick the more completely the more force he applies. Any elastic object, as a piece of india-rubber or a catapult, can be stretched the farther the harder he pulls. If he tries to push a small body, there is little resistance and it is easy to move; but he finds that a {303} big body presents greater resistance and is harder to move. The experience is precisely similar if he attempts to lift a big body and a little one; or if he raises a limb, with or without any object attached to it. He throws a stone: if it is light, little exertion propels it a considerable distance; if very heavy, great exertion only a short distance. So, also, if he jumps, a slight effort raises him to a short height, a greater effort to a greater height. By blowing with his mouth he sees that he can move small objects, or the surface of his morning’s milk, gently or violently according as the blast is weak or strong. And it is the same with sounds: with a slight strain on the vocal organs he produces a murmur; with great strain he can raise a shout. “The experiences these propositions record all implicate the same consciousness—the notion of proportionality between force applied and result produced; and it is out of this latent consciousness that the axiom of the perfect quantitative equivalence of the relations between cause and effect is evolved. To show how rigorous, how irreversible, this consciousness becomes, take a boy and suggest to him the following statements:—Can he not break a string he has, by pulling? tell him to double it, and then he will break it. He cannot bend or break a particular stick: let him make less effort and he will succeed. He is unable to raise a heavy weight: tell him he errs by using too much force. He can’t push over a small chest: he will find it easier to upset a larger one. By blowing hard he cannot move a given object: if he blows lightly, he will move it. By great exertion he cannot make himself audible at a distance: but he will make himself heard with less exertion at a greater distance. Tell him to do all or any of these, and of course he fails. The propositions are unthinkable, and their unthinkableness shows that the consciousness which yields them is irreversible. These, then, are preconceptions, properly so called, which have {304} grown unconsciously out of the earliest experiences, beginning with those of the sucking infant, which are perpetually confirmed by fresh experiences, and which have at last become organized in the mental structure. thought-break “Mr. Spencer’s argument appears to be briefly this:—1. There are numberless experiences unconsciously acquired and unconsciously accumulated during the early life of the individual (in harmony with the acquisitions of all ancestral individuals) which yield the preconception, long anteceding anything like conscious physical experiments, that physical causes and effects vary together quantitatively. This is gained from all orders of physical experiences, and forms a universal preconception respecting them, which the physicist or other man of Science brings with him to his experiments. “2. Mr. Spencer showed in three cases—chemical, physical, and mechanical—that this preconception, so brought, was tacitly involved in the conception which the experimenter drew from the results of his experiments. “3. Having indicated this universal preconception, and illustrated its presence in these special conceptions, Mr. Spencer goes on to say that it is involved also in the special conception of the relation between force and motion, as formulated in the ‘Second Law of Motion.’ He asserts that this is simply one case out of the numberless cases in which all these consciously-reasoned conclusions rest upon the unconsciously-formed conclusions that precede reasoning. Mr. Spencer alleges that as it has become impossible for a boy to think that by a smaller effort he can jump higher, and for a shopman to think that smaller weights will outbalance greater quantities, and for the physicist to think that he will get increased effects from diminished causes, so it is impossible to think that ‘alteration of motion’ is not ‘proportional to the motive force impressed.’ And he maintains that this is, in fact, a {305} latent implication of unconsciously-organized experiences, just as much as those which the experimenter necessarily postulates.” To meet further misinterpretations, a second letter was written by Mr. Collier and published in Nature for June 4, 1874. The following are passages from it:— “Having but limited space, and assuming that the requisite qualifications would be made by unbiased readers, I passed over all those details of the child’s experiences which would have been required in a full exposition. Of course I was aware that in the bending of a stick the visible effect does not increase in the same ratio as the force applied; and hardly needed the ‘Senior Wrangler’ to tell me that the resistance to a body moving through a fluid increases in a higher ratio than the velocity. It was taken for granted that he, and those who think with him, would see that out of all these experiences, in some of which the causes and effects are simple, and in others of which they are complex, there grows the consciousness that the proportionality is the more distinct the simpler the antecedents and consequents. This is part of the preconception which the physicist brings with him and acts upon. Perhaps it is within the ‘Senior Wrangler’s’ knowledge of physical exploration, that when the physicist finds a result not bearing that ratio to its assigned cause which the two were ascertained in other cases to have, he immediately assumes the presence of some perturbing cause or causes, which modify the ratio. There is, in fact, no physical determination made by any experimenter which does not assume, as an a priori necessity, that there cannot be a deviation from proportion without the presence of such additional cause. “Returning to the general issue, perhaps the ‘Senior Wrangler’ will pay some respect to the judgment of one {306} who was a Senior Wrangler too, and a great deal more—who was distinguished not only as a mathematician but as an astronomer, a physicist, and also as an inquirer into the methods of science: I mean Sir John Herschel. In his Discourse on the Study of Natural Philosophy, he says:—
“Of these ‘characters’ he sets down the third and fourth in the following terms:—
“Observe that, in Sir J. Herschel’s view, these are ‘characters’ of the relation of cause and effect to be accepted as ‘general rules for guiding and facilitating our search’ among physical phenomena—truths that must be taken for granted before the search, not truths derived from the search. Clearly, the ‘proportionality of the effect to its cause in all cases of direct and unimpeded action’ is here taken as a priori. Sir J. Herschel would, therefore, have asserted, with Mr. Spencer, that the Second Law of Motion is a priori; since this is one of the cases of the ‘proportionality of the effect to its cause.’ “And now let the ‘Senior Wrangler’ do what Sir J. Herschel has not done or thought of doing—prove the proportionality of cause and effect. Neither he, nor any other of Mr. Spencer’s opponents, has made the smallest attempt to deal with this main issue. Mr. Spencer alleges that this cognition of proportionality is a priori: not in the old sense, but in the sense that it grows out of experiences that precede reasoning. His opponents, following Prof. Tait in the assertion that Physics is a purely experimental science, containing, therefore, no a priori truths, affirm that this {307} cognition is a posteriori—a product of conscious induction. Let us hear what are the experiments. It is required to establish the truth that there is proportionality between causes and effects, by a process which nowhere assumes that if one unit of force produces a certain unit of effect, two units of such force will produce two units of such effect. Until the ‘Senior Wrangler’ has done this he has left Mr. Spencer’s position untouched.” APPENDIX B.[After publication of the letters from which the foregoing are reproduced, there appeared in Nature certain rejoinders containing misrepresentations even more extreme than those preceding them. There resulted a direct correspondence with two of the writers—Mr. Robert B. Hayward, of Harrow, and Mr. J. F. Moulton, my original assailant, the author of the article in the British Quarterly Review. This correspondence, in which I demanded from these gentlemen the justifications for their statements, formed part of this Appendix in its pamphlet form, as distributed among those who are competent to judge of the questions at issue. It is needless to give permanence to the replies and rejoinders. The character of Mr. Moulton’s allegations, quite congruous with those I have exposed in the “Replies to Criticisms,” may be inferred from one of the sentences closing my reply—“Wonderful to relate, my inductive proof that proportionality [of cause and effect] is taken for granted, he cites as my inductive proof of proportionality itself!” The result of the interchange of letters with Mr. Hayward, was to make it clear that “the thing I assert is not really disputed; and the thing disputed, I have nowhere asserted.” While, however, the controversial part of the correspondence may fitly disappear, {308} I retain an expository part embodied in the following letter to Mr. Hayward.] 38, Queen’s Gardens, Bayswater, SIR,—Herewith I send you a copy of your letter with my interposed comments. I think those comments will make it clear to you that I have not committed myself to three different definitions of our consciousness of the Second Law of Motion. As others may still feel a difficulty such as you seem to have felt, in understanding that which familiarity has made me regard as simple, I will endeavour, by a synthetic exposition, to make clear the way in which these later and more complex products of organized experiences stand related to earlier and simpler products. To make this exposition easier to follow, I will take first our Space-consciousness and the derived conceptions. On the hypothesis of Evolution, the Space-consciousness results from organized motor, tactual, and visual experiences. In the Principles of Psychology, §§ 326–346, I have described in detail what I conceive to have been its genesis. Such Space-consciousness so generated, is one possessed in greater or less degree by all creatures of any intelligence; becoming wider, and more definite, according to the degree of mental evolution which converse with the environment has produced. How deeply registered the external relations have become in the internal structure, is shown by the facts that the decapitated frog pushes away with one or both legs the scalpel applied to the hind part of its body, and that the chick, as soon as it has recovered from the exhaustion of escaping from the egg, performs correctly-guided actions (accompanied by consciousness of distance and direction) in picking up grains. Ascending at once to such organized and inherited Space-consciousness as exists in the child, and which from moment to moment {309} it is making more complete by its own experiences (aiding the development of its nervous system into the finished type of the adult, by the same exercises which similarly aid the development of its muscular system), we have to observe that, along with increasingly-definite ideas of distance and direction, it gains unawares certain more special ideas of geometrical relations. Take one group of these. Every time it spreads open its fingers it sees increase of the angles between them, going along with increase of the distances between the finger-tips. In opening wide apart its own legs, and in seeing others walk, it has continually before it the relation between increase or decrease of base in a triangle having equal sides, and increase or decrease of the angle included by those sides. [The relation impressed on it being simply that of concomitant variation: I do not speak of any more definite relation, which, indeed, is unthinkable by the young.] It does not observe these facts in such way as to be conscious that it has observed them; but they are so impressed upon it as to establish a rigid association between certain mental states. Various of its activities disclose space-relations of this class more definitely. The drawing of a bow exhibits them in another way and with somewhat greater precision; and when, instead of the ends of a bow, capable of approaching one another, the points of attachment are fixed and the string elastic, the connexion between increasing length in the sides of an isosceles triangle and increasing acuteness of the included angle, is still more forced upon the attention; though it still does not rise into a conscious cognition. This is what I mean by an “unconsciously-formed preconception.” When, in course of time, the child, growing into the boy, draws diagrams on paper, and, among other things, draws isosceles triangles, the truth that, the base being the same, the angle at the apex becomes more acute as the sides lengthen, is still more definitely displayed to him; and when his attention is drawn to this relation he finds that he {310} cannot think of it as being otherwise. If he imagines the lengths of the sides to change, he cannot exclude the consciousness of the correlative change in the angle; and presently, when his mental power is sufficiently developed, he perceives that if he continues to lengthen the sides in imagination, the lines approach parallelism as the angle approaches zero: yielding a conception of the relations of parallel lines. Here the consciousness has risen into the stage of definite conception. But, manifestly, the definite conception so reached is but a finishing of the preconceptions previously reached, and would have been impossible in their absence; and these unconsciously-formed preconceptions would similarly have been impossible in the absence of the still earlier consciousnesses of distance, direction, relative position, embodied in the consciousness of Space. The whole evolution is one; the arrival at the distinct conception is the growing up to an ultimate definiteness and complexity; and it can no more be reached without passing through the earlier stages of indefinite consciousness, than the adult bodily structure can be reached without passing through the structures of the embryo, the infant, and the child. Through a parallel evolution arises, first the vague {311} consciousness of forces as exerted by self and surrounding things; presently, some discrimination in respect of their amounts as related to their effects; later, an association formed unawares between greatness of quantity in the two, and between smallness of quantity in the two; later still, a tacit assumption of proportionality, though without a distinct consciousness that the assumption has been made; and, finally, a rising of this assumption into definite recognition, as a truth necessarily holding where the forces are simple. Throughout its life every creature has, within the actions of its moving parts, forces and motions conforming to the Laws of Motion. {312} If it has a nervous system, the differences among the muscular tensions and the movements initiated, register themselves in a vague way in that nervous system. As the nervous system develops, along with more developed limbs, there are at once more numerous different experiences ... of momentum generated, of connected actions and reactions (as when an animal tears the food which it holds with its paws); and, at the same time, there are, in its more developed nervous system, increased powers of appreciating and registering these differences. All the resulting connexions in consciousness, though unknowingly formed and unknowingly entertained, are ever present as guides to action: witness the proportion between the effort an animal makes and the distance it means to spring; or witness the delicate adjustments of muscular strains to changes of motion, made by a swallow catching flies or a hawk swooping on its quarry. Manifestly, then, these experiences, organized during the earlier stages of mental evolution, form a body of consciousnesses, not formulated into cognitions, nor present even as preconceptions, but nevertheless present as a mass of associations in which the truths of relation between force and motion are potentially present. On ascending to human beings of the uncultured sort, we reach a stage at which some nascent generalization of these experiences occur. The savage has not expressed to himself the truth that if he wants to propel his spear further he must use more force; nor does the rustic put into a distinct thought the truth that to raise double the weight he must put forth twice the effort; but in each there is a tacit assumption to this effect, as becomes manifest on calling it in question. So that, in respect of these and other simple mechanical actions, there exist unconsciously-formed preconceptions. And just as the geometrical truths presented in a rude way by the relations among surrounding objects, are not overtly recognized until there is some familiarity with straight lines, and diagrams made of them; {313} so, until linear measures, long used, have led to the equal-armed lever, or scales, and thus to the notion of equal units of force, this mechanical preconception cannot rise into definiteness. Nor after it has risen into definiteness does it for a long time reach the form of a consciously-held cognition; for neither the village huxter nor the more cultivated druggist in the town, recognizes the general abstract truth that, when uninterfered with, equi-multiples of causes and their effects are necessarily connected. But now observe that this truth, acted upon with more or less distinct consciousness of it by the man of science, and perfected by him through analysis and abstraction, is thus perfected only as the last step in its evolution. This definite cognition is but the finished form of a consciousness long in preparation—a consciousness the body of which is present in the brute, takes some shape in the primitive man, reaches greater definiteness in the semi-civilized, becomes afterwards an assumption distinct though not formulated, and takes its final development only as it rises into a consciously-accepted axiom. Just as there is a continuous evolution of the nervous system, so is there a continuous evolution of the consciousness accompanying its action. Just as the one grows in volume, complexity, and definiteness, so does the other. And just as necessary as the earlier stages are to the later in the one case, are they in the other. To suppose that the finished conceptions of science can exist without the unfinished common knowledge which precedes them, or this without still earlier mental acquisitions, is the same thing as to suppose that we can have the correct judgments of the adult without passing through the crude judgments of the youth, the narrow, incoherent ones of the child, and the vague, feeble ones of the infant. So far is it from being true that the view of physical axioms held by me, is one which bases cognitions on some other source than experience, it asserts experience to be the only possible source of these, as of other cognitions; but it asserts, further, that {314} not simply is the consciously-acquired experience of present actions needful, but that for the very possibility of gaining this we are indebted to the accumulated experiences of all past actions. Not I, but my antagonists, are really chargeable with accepting the ancient a priori view; since, without any explanation of them or justification of them, they posit as unquestionable the assumptions underlying every experiment and the conclusion drawn from it. The belief in physical causation, assumed from moment to moment as necessary in every experiment and in all reasoning from it, is a belief which, if not justified by the hypothesis above set forth, is tacitly asserted as an a priori belief. Contrariwise, my own position is one which affiliates all such beliefs upon experiences acquired during the whole past; which alleges those experiences as the only warrant for them; which asserts that during the converse between the mind and its environment, necessary connexions in Thought, such as those concerning Space, have resulted from infinite experiences of corresponding necessary connexions in Things; and that, similarly, out of perpetual converse with the Forces manifested to us in Space, there has been a progressive establishment of internal relations answering to external relations, in such wise that there finally emerge as physical axioms, certain necessities of Thought which answer to necessities in Things. I need scarcely say that I have taken the trouble of making my comments on your letter, and of writing this further exposition, with a view to their ulterior use. I am, &c., APPENDIX C. SUMMARY OF RESULTS.Those who deny a general doctrine enunciated by Mayer as the basis of his reasonings, habitually assumed by Faraday {315} as a guiding principle in drawing his conclusions, distinctly held by Helmholtz, and tacitly implied by Sir John Herschel—those, I say, who deny this general doctrine and even deride it, should be prepared with clear and strong reasons for doing this. Having been attacked, not in the most temperate manner, for enunciating this doctrine and its necessary implications in a specific form, I have demanded such reasons. Observe the responses to the demand. 1. The British Quarterly Reviewer quoted for my instruction the dictum of Professor Tait, that “Natural Philosophy is an experimental, and not an intuitive science. No À priori reasoning can conduct us demonstratively to a single physical truth.” Thereupon I inquired what Professor Tait meant “by speaking of ‘physical axioms,’ and by saying that the cultured are enabled ‘to see at once their necessary truth?’”... No reply. 2. Instead of an answer to the question, how this intuition of necessity can be alleged by Professor Tait consistently with his other doctrine, the Reviewer quotes, as though it disposed of my question, Professor Tait’s statement that “as the properties of matter might have been such as to render a totally different set of laws axiomatic, these laws [of motion] must be considered as resting on convictions drawn from observation and experiment, and not on intuitive perception.” Whereupon I inquired how Professor Tait knows that “the properties of matter might have been” other {316} than they are. I asked how it happened that his intuition concerning things as they are not, is so certain that, by inference from it, he discredits our intuitions concerning things as they are... No reply: Professor Tait told, À propos of my question, a story of which no one could discover the application; but, otherwise, declined to answer. Nor was any answer given by his disciple. 3. Further, I asked how it happened that Professor Tait accepted as bases for Physics, Newton’s Laws of Motion; which were illustrated but not proved by Newton, and of which no proofs are supplied by Professor Tait, in the Treatise on Natural Philosophy. I went on to examine what conceivable a posteriori warrant there can be if there is no warrant a priori; and I pointed out that neither from terrestrial nor from celestial phenomena can the First Law of Motion be deduced without a petitio principii... No reply: the Reviewer characterized my reasoning as “utterly erroneous” (therein differing entirely from two {317} eminent authorities who read it in proof); but beyond so characterizing it he said nothing. 4. To my assertion that Newton gave no proof of the Laws of Motion, the Reviewer rejoined that “the whole of the Principia was the proof.” On which my comment was that Newton called them “axioms,” and that axioms are not commonly supposed to be proved by deductions from them... The Reviewer quotes from one of Newton’s letters a passage showing that though he called the Laws of Motion “axioms,” he regarded them as principles “made general by induction;” and that therefore he could not have regarded them as a priori. 5. In rejoinder, I pointed out that whatever conception Newton may have had of these “axioms,” he explicitly and distinctly excluded them from the class of “hypotheses.” Hence I inferred that he did not regard the whole of the {318} Principia as the proof, which the Reviewer says it is; since an assumption made at the outset, to be afterwards justified by the results of assuming it, is an “hypothesis”... No reply. 6. Authority aside, I examined on its merits the assertion that the Laws of Motion are, or can be, proved true by the ascertained truth of astronomical predictions; and showed that the process of verification itself assumed those Laws. No reply. 7. To make still clearer the fact that ultimate physical truths are, and must be, accepted as a priori, I pointed out that in every experiment the physicist tacitly assumes a relation between cause and effect, such that, if one unit of cause produces its unit of effect, two units of the cause will produce two units of the effect; and I argued that this general assumption included the special assumption asserted in the Second Law of Motion.... No reply: that is to say, no endeavour to show the untruth of this statement, but a quibble based on my omission of the word “proportionality” in places where it was implied, though not stated. 8. Attention was drawn to a passage {319} from Sir John Herschel’s Discourse on the Study of Natural Philosophy, in which the “proportionality of the effect to its cause in all cases of direct unimpeded action” is included by him among “the characters of that relation which we intend by cause and effect;” and in which this assumption of proportionality is set down as one preceding physical exploration, and not as one to be established by it... No reply. 9. Lastly, a challenge to prove this proportionality. “It is required to establish the truth that there is proportionality between causes and effects, by a process which nowhere assumes that if one unit of force produces a certain unit of effect, two units of such force will produce two units of such effect.”... No reply. Thus on all these essential points my three mathematical opponents allow judgment to go against them by default. The attention of readers has been drawn off from the main issues by the discussion of side issues. Fundamental questions have been evaded, and new questions of subordinate kinds raised. What is the implication? One who is able to reach and to carry the central position of his antagonist, does not spend his strength on small outposts. If he declines to assault the stronghold, it must be because he sees it to be impregnable. The trouble I have thus taken to meet criticisms and dissipate misapprehensions, I have taken because the attack {320} made on the special doctrine defended, is part of an attack on the ultimate doctrine underlying the deductive part of First Principles—the doctrine that the quantity of existence is unchangeable. I agree with Sir W. Hamilton that our consciousness of the necessity of causation, results from the impossibility of conceiving the totality of Being to increase or decrease. The proportionality of cause and effect is an implication: denial of it involves the assertion that some quantity of cause has disappeared without effect, or some quantity of effect has arisen without cause. I have asserted the a priori character of the Second Law of Motion, under the abstract form in which it is expressed, simply because this, too, is an implication, somewhat more remote, of the same ultimate truth. And my sole reason for insisting on the validity of these intuitions, is that, on the hypothesis of Evolution, absolute uniformities in things have produced absolute uniformities in thoughts; and that necessary thoughts represent infinitely-larger accumulations of experiences than are formed by the observations, experiments, and reasonings of any single life.
I am indebted to Mr. Hayward for giving this instance. It conveniently serves two purposes. It serves to exemplify the connexion between the crude preconceptions unconsciously formed by earlier experiences, and the conceptions consciously evolved out of them by the help of later experiences, when the requisite powers of analysis and abstraction have been reached. And at the same time it serves to show the failure of my opponents to understand how, in the genesis of intelligence, the scientific conception of exact proportionality develops from the crude, vague, and inaccurate preconception. For while the notion of proportionality acquired by the child in Mr. Hayward’s example, is not true, it is an approximation towards one which is true, and one which is reached when its more developed intelligence is brought critically to bear on the facts. Eventually it is discovered that the angle is not proportional to the subtending side, but to the subtending arc; and this is discovered in the process of disentangling a simple relation from other relations which complicate and disguise it. Between the angle and the arc there is exact proportionality, for the reason that only one set of directly-connected space-relations are concerned: the distance of the subtending arc from the subtended angle, remains constant—there is no change in the relation between the increasing angle and the increasing arc; and therefore the two vary together in direct proportion. But it is otherwise with the subtending side. The parts of this stand in different relations of distance from the subtended angle; and as the line is lengthened, each added part differs from the preceding parts in its distance from the angle. That is to say, one set of simple directly-connected geometrical relations, is here involved with another set; and the relation between the side and the angle is such that the law of relative increase involves the co-operation of two sets of factors. Now the distinguishing the true proportionality (between the angle and the arc) from the relation which simulates proportionality (between the angle and the side) is just that process of final development of exact conceptions, which I assert to be the finishing step of all the preceding development; and to be impossible in its absence. And the truth to which my assailants shut their eyes, is that, just as among these conceptions of space-relations, the conception of exact proportionality can be reached only by evolution from the crude notion of proportionality, formed before reasoning begins; so, among the force-relations, the conception of proportionality finally reached, when simple causes and their effects are disentangled by analytical intelligence, can be reached only by evolution of the crude notion of proportionality, established as a preconception by early experiences which reinforce ancestral experiences. |
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