[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.
PROF. GREEN’S EXPLANATIONS.
[From the Contemporary Review for Feb. 1881. It would not have occurred to me to reproduce this essay, had it not been that there has lately been a reproduction of the essay to which it replies. But as Mr. Nettleship, in his editorial capacity, has given a permanent shape to Professor Green’s unscrupulous criticism, I am obliged to give a permanent shape to the pages which show its unscrupulousness.]
Dreary at best, metaphysical controversy becomes especially dreary when it runs into rejoinders and re-rejoinders; and hence I feel some hesitation in inflicting, even upon those readers of the Contemporary who are interested in metaphysical questions, anything further concerning Prof. Green’s criticism, Mr. Hodgson’s reply to it, and Prof. Green’s explanations. Still, it appears to me that I can now hardly let the matter pass without saying something in justification of the views attacked by Prof. Green; or, rather, in disproof of the allegations he makes against them.
I did not, when Prof. Green’s two articles appeared, think it needful to notice them: my wish to avoid hindrance to my work, being supported partly by the thought that very few would read a discussion so difficult to follow, and partly by the thought that, of the few who did read it, most would be those whose knowledge of The Principles of Psychology enabled them to see how unlike the argument {322} I have used is the representation of it given by Prof. Green, and how inapplicable his animadversions therefore are. This last belief was, I find, quite erroneous; and I ought to have known better than to form it. Experience might have shown me that readers habitually assume a critic’s version of an author’s statement to be the true version, and that they rarely take the trouble to see whether the meaning ascribed to a detached passage is the meaning which it bears when taken with the context. Moreover, I should have remembered that in the absence of disproofs it is habitually assumed that criticisms are valid; and that inability rather than pre-occupation prevents the author from replying. I ought not, therefore, to have been surprised to learn, as I did from the first paragraph of Mr. Hodgson’s article, that Prof. Green’s criticisms had met with considerable acceptance.
I am much indebted to Mr. Hodgson for undertaking the defence of my views; and after reading Prof. Green’s rejoinder, it seems to me that Mr. Hodgson’s chief allegations remain outstanding. I cannot here, of course, follow the controversy point by point. I propose to deal simply with the main issues.
At the close of his answer, Prof. Green refers to “two other misapprehensions of a more general nature, which he [Mr. Hodgson] alleges against me at the outset of his article.” Not admitting these, Prof. Green postpones replies for the present; though by what replies he can show his apprehensions to be true ones, I do not see. Further misapprehensions of a general nature, which stand as preliminaries to his criticisms, may here be instanced, as serving, I think, to show that those criticisms are misdirected.