24 Principles of Psychology, Second Edition, § 425, note.

25 Le Sentiment Religieux, par A. Grotz. Paris, J. Cherbuliez, 1870.

26 Instead of describing me as mis­un­der­stand­ing Kant on this point, Dr. Hodgson should have described Kant as having, in successive sentences, so changed the meanings of the words he uses, as to make either interpretation possible. At the outset of his Critique of Pure Reason, he says:—“The effect of an object upon the faculty of rep­re­sen­ta­tion, so far as we are affected by the said object, is sensation. That sort of intuition which relates to an object by means of sensation, is called an empirical intuition. The undetermined object of an empirical intuition, is called phænomenon. That which in the phænomenon corresponds to the sensation, I term its matter;” [here, remembering the definition just given of phenomenon, objective existence is manifestly referred to] “but that which effects that the content of the phænomenon can be arranged under certain relations, I call its form” [so that form, as here applied, refers to objective existence]. “But that in which our sensations are merely arranged, and by which they are susceptible of assuming a certain form, cannot be itself sensation.” [In which sentence the word form obviously refers to subjective existence.] At the outset, the ‘phenomenon’ and the ‘sensation’ are distinguished as objective and subjective respectively; and then, in the closing sentences, the form is spoken of in connexion first with the one and then with the other, as though they were the same.

27 See Fraser’s Magazine for May, 1873.

28 First Principles, § 26.

29 Ibid. § 76 (1st ed.)

30 Compare Principles of Psychology, §§ 88, 95, 391, 401, 406.

31 First Principles, §§ 39–45.

32 Principles of Psychology, part vii.

33 Social Statics, chap. iii.

34 Principles of Psychology, § 531.

35 First Principles, § 34.

36 Only after the foregoing paragraphs were written, did the remark of a distinguished friend show me how certain words were misconstrued by the reviewer in a way that had never occurred to me as possible. In the passage referred to, I have said that sound-waves “finally die away in generating thermal undulations that radiate into space;” meaning, of course, that the force embodied in the sound-waves is finally exhausted in generating thermal undulations. In common speech, the dying-away of a prolonged sound, as that of a church-bell, includes its gradual diminution as well as its final cessation. But rather than suppose I gave to the words this ordinary meaning, the reviewer supposes me to believe, not simply that the longitudinal waves of air can pass, without discontinuity, into the transverse waves of ether, but he also debits me with the belief that the one order of waves, having lengths measurable in feet, and rates expressed in hundreds per second, can, by mere enfeeblement, pass into the other order of waves, having lengths of some fifty thousand to the inch, and rates expressed in many billions per second! Why he preferred so to interpret my words, and that, too, in the face of contrary implications elsewhere (instance § 100), will, however, be manifest to every one who reads his criticisms.

37 Other examples of these amenities of controversy, in which I decline to imitate my reviewer, have already been given. What occasions he supplies me for imitation, were I minded to take advantage of them, an instance will show. Pointing out an implication of certain reasonings of mine, he suggests that it is too absurd even for me to avow explicitly; saying:—“We scarcely think that even Mr. Spencer will venture to claim as a datum of con­scious­ness the Second Law of Motion, with its attendant complexities of component velocities, &c.” Now any one who turns to Newton’s Principia, will find that to the enunciation of the Second Law of Motion, nothing whatever is appended but an amplified re-statement—there is not even an illustration, much less a proof. And from this law, this axiom, this immediate intuition or “datum of con­scious­ness,” Newton proceeds forthwith to draw those corollaries respecting the composition of forces which underlie all dynamics. What, then, must be thought of Newton, who explicitly assumes that which the reviewer thinks it absurd to assume implicitly?

38 That I am certainly not singular in this view, is shown to me, even while I write, by the just-issued work of Prof. Jevons on the Principles of Science: a Treatise on Logic and Scientific Method. In vol. ii., p. 141, Prof. Jevons remarks respecting the law of variation of the attractive force, that it “is doubtless connected at this point with the primary properties of space itself, and is so far conformable to our necessary ideas.”

39 See Essay on “The Genesis of Science,” in the British Quarterly Review for July, 1854, p. 127.

40 I do not say this at random. The reviewer, who has sought rather to make known than to conceal his identity, took his degree in 1868.

41 It is true that in Newton’s time, “axiom” had not the same rigorously defined meaning as now; but it suffices for my argument that, standing unproved as a basis for physical deductions, it bears just the same relation to them that a mathematical axiom does to mathematical deductions.

42 The above letter, written after absence at Easter had involved a week’s delay, and written somewhat hurriedly to prevent the delay of a second week, was less carefully revised than it should have been. The words in square brackets, obviously implied by the reasoning, and specifically implied by the illustrations, were not in the letter as originally published.

43 Here, in explaining the genesis of special space-intuitions, I have singled out a group of experiences which, in Nature, May 28, Mr. Hayward had chosen as illustrating the absurdity of supposing that the scientific conception of pro­por­tion­al­i­ty could be reached as alleged. He said:—

“It is hardly a parody of Mr. Collier’s remarks to say:—‘A child discovers that the greater the angle between his legs the greater the distance between his feet, an experience which implicates the notion of pro­por­tion­al­i­ty between the angle of a triangle and its opposite side;’ a preconception, as it appears to me, with just as good a basis as that whose formation Mr. Collier illustrates, but one which, as I need hardly add, is soon corrected by a conscious study of geometry or by actual measurement.”

I am indebted to Mr. Hayward for giving this instance. It conveniently serves two purposes. It serves to exemplify the connexion between the crude preconceptions un­con­scious­ly formed by earlier experiences, and the conceptions consciously evolved out of them by the help of later experiences, when the requisite powers of analysis and abstraction have been reached. And at the same time it serves to show the failure of my opponents to understand how, in the genesis of intelligence, the scientific conception of exact pro­por­tion­al­i­ty develops from the crude, vague, and inaccurate preconception. For while the notion of pro­por­tion­al­i­ty acquired by the child in Mr. Hayward’s example, is not true, it is an approximation towards one which is true, and one which is reached when its more developed intelligence is brought critically to bear on the facts. Eventually it is discovered that the angle is not proportional to the subtending side, but to the subtending arc; and this is discovered in the process of disentangling a simple relation from other relations which complicate and disguise it. Between the angle and the arc there is exact pro­por­tion­al­i­ty, for the reason that only one set of direct­ly-con­nect­ed space-re­la­tions are concerned: the distance of the subtending arc from the subtended angle, remains constant—there is no change in the relation between the increasing angle and the increasing arc; and therefore the two vary together in direct proportion. But it is otherwise with the subtending side. The parts of this stand in different relations of distance from the subtended angle; and as the line is lengthened, each added part differs from the preceding parts in its distance from the angle. That is to say, one set of simple direct­ly-con­nect­ed geometrical relations, is here involved with another set; and the relation between the side and the angle is such that the law of relative increase involves the co-operation of two sets of factors. Now the distinguishing the true pro­por­tion­al­i­ty (between the angle and the arc) from the relation which simulates pro­por­tion­al­i­ty (between the angle and the side) is just that process of final development of exact conceptions, which I assert to be the finishing step of all the preceding development; and to be impossible in its absence. And the truth to which my assailants shut their eyes, is that, just as among these conceptions of space-re­la­tions, the conception of exact pro­por­tion­al­i­ty can be reached only by evolution from the crude notion of pro­por­tion­al­i­ty, formed before reasoning begins; so, among the force-relations, the conception of pro­por­tion­al­i­ty finally reached, when simple causes and their effects are disentangled by analytical intelligence, can be reached only by evolution of the crude notion of pro­por­tion­al­i­ty, established as a preconception by early experiences which reinforce ancestral experiences.