REPLIES TO CRITICISMS. (continued 2)

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,”33 I had endorsed that doctrine—if, instead of explaining and justifying “a belief in the special sacredness of these highest principles, and a sense of the supreme authority of the altruistic sentiments answering to them,”34 I had denied the sacredness and the supreme authority—if, instead of saying of the wise man that “the highest truth he sees he will fearlessly utter; knowing that, let what may come of it, he is thus playing his right part in the world,”35 I had said that the wise man will not do this; the reviewer might with truth have described me as not understanding “the term ‘morality’ according to the true sense of the word.” And he might then have inferred that the Doctrine of Evolution as I hold it, implies denial of the “distinction between Duty and Pleasure.” But as it is, I think the evidence will not generally be held to warrant his assertion.

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:―

“Nor should we counsel a man to venture upon physical speculations who converts the proposition ‘heat is insensible motion’ into ‘insensible motion is heat,’ and hence concludes that when a force is applied to a mass so large that no motion is seen to result from it, or when, as in the case of sound, motion gets so dispersed that it becomes insensible, it turns to heat.”

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?36

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―

“Natural philosophy is an experimental, and not an intuitive science. No à priori reasoning can conduct us demonstratively to a single physical truth.”

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.37

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 the notice of Mr. Spencer’s works that appeared in the last number of this Review, we had occasion to point out that he held mistaken notions of the most fundamental gen­er­al­i­za­tions of dynamics; that he had shown an ignorance of the nature of proof in his treatment of the Newtonian Law; that he had used phrases such as the Persistence of Force in various and inconsistent significations; and more especially that he had put forth proofs logically faulty in his endeavour to demonstrate certain physical propositions by à priori methods, and to show that such proofs must exist. To this article Mr. Spencer has replied in the December number of the Fortnightly Review. His reply leaves every one of the above positions unassailed.”

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:―

“Had Mr. Spencer, however, read the sentence that follows it, we doubt whether we should have heard aught of this quotation. It is ‘Without further remark we shall give Newton’s Three Laws; it being remembered that as the properties of matter might have been such as to render a totally different set of laws axiomatic, these laws must be considered as resting on convictions drawn from observation and experiment and not on intuitive perception.’ This not only shows that the term ‘axiomatic’ is used in the previous sentence in a sense that does not exclude an inductive origin, but it leaves us indebted to Mr. Spencer for the discovery of the clearest and most authoritative expression of disapproval of his views respecting the nature of the Laws of Motion.”

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:―

“On the utterly erroneous character of these statements we do not care to dwell, we wish simply to call our reader’s attention to the conclusion arrived at. Is that a disproof of the possibility of an inductive proof? We thought 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.”

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:―

“Mr. Spencer asserts that Newton gave no proof of the Laws of Motion. The whole of the Principia was the proof, and the fact that, taken as a system, these laws account for the lunar and planetary motions, is the warrant on which they chiefly rest to this day.”

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―

“Those of them which are vital, or cannot be severed from the rest without mental dissolution, must be assumed as true provisionally . . . . leaving the assumption of their un­ques­tion­able­ness to be justified by the results.

“§ 40. How is it to be justified by the results? As any other assumption is justified—by ascertaining that all the conclusions deducible from it, correspond with the facts as directly observed—by showing the agreement between the experiences it leads us to anticipate, and the actual experiences. There is no mode of establishing the validity of any belief, except that of showing its entire congruity with all other beliefs.”

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.38 If the reviewer means to ask, whence I get the implied assumption that central forces act only in straight lines, I reply that this assumption has a warrant akin to that of Newton’s first axiom, that a moving body will continue moving in a straight line unless interfered with. For that the force exerted by one centre on another should act in a curved line, implies the conception of some second force, complicating the direct effect of the first. And, even could a central force be truly conceived as acting in lines not straight, the average {291} distribution of its effects upon the inner surface of the surrounding sphere, would still follow the same law. Thus, whether or not the law be accepted on a priori grounds, the assumed absurdity of representing it to have a priori grounds, is not very obvious. Respecting this statement of mine the reviewer goes on to say―

“This is a wisdom far higher than that possessed by the discoverer of the great law of attraction, who was led to consider it from no cogitations on the relations of space, but from observations of the movements of the planets; and who was so far from rising to that clearness of view of the truth of his great discovery, which is expressed by the phrase, ‘its negation is inconceivable,’ that he actually abandoned it for a time, because (through an error in his estimate of the earth’s diameter) it did not seem fully to account for the motion of the moon.”

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,39 I cited this fact {292} (using these same words) at a time when he was at school, or before he went there.40 I have next to assert that this fact is irrelevant; and that Newton, while probably seeing it to be a necessary implication of geometrical laws that central forces vary inversely as the squares of the distances, did not see it to be a necessary implication of any laws, geometrical or dynamical, that there exists a force by which the celestial bodies affect one another; and therefore doubtless saw that there was no a priori warrant for the doctrine of gravitation. The reviewer, however, aiming to substitute for my “confused notions” his own clear ones, wishes me to identify the proposition—Central forces vary inversely as the squares of the distances—with the proposition—There exists a cosmical attractive force which varies inversely as the squares of the distances. But I decline to identify them; and I suspect that a considerable distinction between them was recognized by Newton. Lastly, apart from all this, I have to point out that even had Newton thought the existence of an attractive force throughout space was an a priori truth, as well as the law of variation of such a force if it existed; he would still, naturally enough, pause before asserting gravitation and its law, when he found his deductions did not correspond with the facts. To suppose otherwise, is to ascribe to him a rashness which no disciplined man of science could be guilty of.

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}

THESES.

1. If A produces B, then 2 A will produce 2 B.

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, 2 A will produce 2 B, 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}

APPENDIX A.

(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:―

“The alteration of motion is ever proportional to the motive force impressed; and is made in the direction of the right line in which that force is impressed.

“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 this motion (being always directed the same way with the generating force), if the body moved before, is added to or subducted from the former motion, according as they directly conspire with or are directly contrary to each other; or obliquely joined, when they are oblique, so as to produce a new motion compounded from the determination of both.”

As this, like each of the other Laws of Motion, is called an axiom;41 as the paragraph appended to it is simply an amplification, or re-statement in a more concrete form; as there are no facts named as bases of induction, nor any justifying experiment; and as Newton proceeds forthwith to draw deductions; it was a legitimate inference that he regarded this truth as a priori. My statement to this effect was based on the contents of the Principia itself; and I think I was warranted in assuming that the nature of the Laws of Motion, as conceived by Newton, was to be thence inferred.

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:―

“Hitherto I have laid down such principles as have been received by mathematicians, and are confirmed by abundance of experiments. By the two first Laws and the two first Corollaries, Galileo discovered that the descent of bodies observed the duplicate ratio of the time, and that the motion of projectiles was in the curve of a parabola; experience agreeing with both,” &c.

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.42

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.

“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:―

“‘When we would lay down general rules for guiding and facilitating our search, among a great mass of assembled facts, for their common cause, we must have regard to the characters of that relation which we intend by cause and effect.’

“Of these ‘characters’ he sets down the third and fourth in the following terms:―

“‘Increase or diminution of the effect, with the increased or diminished intensity of the cause, in cases which admit of increase and diminution.’

“‘Proportionality of the effect to its cause in all cases of direct unimpeded action.’

“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, June 21st, 1874. 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.43 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., HERBERT SPENCER.