The manner in which distances are compared in such a space is this.
[…]
After pure mathematics, pass we to dynamics, field in our day of perhaps the grandest discovery science has ever made, I mean the Conservation of Energy. Besides what is to be learned from this, another lesson dynamics has for philosophy, long ago signalized by Whewell, but obscured by Stuart Mill’s skillful-shallow objections. This last mentioned lesson lies in the historical fact that dynamics, most perfect of physical sciences, has been in large part pumped up from the well of truth within us. No doubt observation afforded indispensible correctives and kept us from going quite wrong; but there were no observations at all adequate to determining the precise laws of motion. Only read Galileo, I pray you, and see how much he relies on il lume naturale, and how amazingly slender is his experimentation.
So, in dynamics, at least, simple theories have a tolerable chance of being true. Observe, that the character of a theory as to being simple or complicated depends entirely on the constitution of the intellect that apprehends it. Bodies left to themselves move in straight lines, and to us straight lines appear as the simplest of all curves. This is because when we turn an object about and scrutinize it, the line of sight is a straight line; and our minds have been formed under that influence. But abstractly considered, a system of like parabolas similarly placed, or any one of an infinity of systems of curves, is as simple as the system of straight lines. Again, motions and forces are combined according to the principle of the parallelogram, and a parallelogram appears to us a very simple figure. Yet the whole system of parallelograms is no more simple than any relief-perspective of them, or than any one of an infinity of other systems. As Sir Isaac Newton well said, geometry is but a branch of mechanics. No definition of the straight line is possible except that it is the path of a particle undisturbed by any force; and no definitions of parallels, etc. are possible which do not depend upon the definition of equal distances as measured by a rigid body, or other mechanical means.
Thus, in dynamics, the natural ideas of the human mind tend to approximate to the truth of nature, because the mind has been formed under the influence of dynamical laws. Now, logical considerations show that if there is no tendency for natural ideas to be true, there can be no hope of ever reaching true inductions and hypotheses. So that philosophy is committed to the postulate,—without which it has no chance of success,—[…]
Psychology has only lately become a positive science, and in my humble opinion the new views are now carried too far. I cannot see, for example, why psychologists should make such a bugbear of “faculties.” If in dynamics it has proved safe to rely upon our natural ideas, checked, controlled, and corrected by experience, why should not our natural ideas about mind, formed as they certainly have been under the influence of the true laws of mental action, be likely to approximate to the truth as much as natural ideas of space, force, and the like have been found to do? Upon this point, I must confess to entertaining somewhat heterodox opinions. The Herbartian philosophy, with the mode of reasoning which leads to it, seems to me thoroughly unsound and illusory,—though I fully admit the value and profundity of some of the suggestions of that philosophy. But to trust to such reasoning in the slightest degree seems to me ever so much less safe than trusting to one’s native or natural notions about mind, though these no doubt need to be modified by observation and experiment.
For my part it seems to me that the elementary phenomena of mind fall into three categories. First, we have feelings, comprising all that is immediately present, such as pleasure and pain, blue, cheerfulness, and the feeling which arises upon the contemplation of a complete theory. It is hard to define what I mean by feeling. If I say it is what is present, I shall be asked what I mean by present, and must confess I mean nothing but feeling again. The only way is to state how any state of consciousness is to be modified so as to render it a feeling, although feeling does not essentially involve consciousness proper. But imagine a state of consciousness reduced to perfect simplicity, so that its object is entirely unanalyzed, then that consciousness reduced to that rudimentary condition, unattainable by us, would be a pure feeling, and not properly consciousness at all. Let the quality of blue, for example, override all other ideas, of form, of contrast, of commencement or cessation, and there would be pure feeling. When I say that such impossible states exist as elements of all consciousness, I mean that there are ideas which might conceivably thus exist alone and monopolize the whole mind.
Besides feelings, we have in our minds sensations of reaction, as when a person blindfold suddenly runs against a post, when we make a muscular effort, or when any feeling gives way to another feeling. Suppose I had nothing in my mind but a feeling of blue, which were suddenly to give place to a feeling of red; then, at the instant of transition there would be a sense of reaction, my blue life being transmuted to red life. If I were now also endowed with a memory, that sense would continue for some time. This state of mind would be more than pure feeling, since in addition to the feeling of red a feeling analogous to blue would be present, and not only that but a sense of reaction between the two. This sense of reaction would itself carry along with it a peculiar feeling which might conceivably monopolize the mind to the exclusion of the feelings of blue and red. But were this to happen, though the feeling associated with a sense of reaction would be there, the sense of reaction as such would be quite gone; for a sense of reaction cannot conceivably exist independent of at least two feelings between which the reaction takes place. A feeling, then, is a state of mind having its own living quality, independent of any other. A sense of reaction, or say for short a sensation, is a state of mind containing two states of mind between which we are aware of a connection, even if that connection is no more than a contrast. No analysis can reduce such sensations to feelings. Looking at the matter from a physiological point of view, a feeling only calls for an excited nerve-cell,—or indeed a mere mass of excited nerve-matter without any cell, or shut up in any number of cells. But sensation supposes the discharge or excitation of a nerve-cell, or a transfer of excitement from one part of a mass of nerve-matter to another, or the spontaneous production or cessation of an excited condition.
Besides feelings and sensations, we have general conceptions; that is, we are conscious that a connection between feelings is determined by a general rule; or, looking at the matter from another point of view, a general conception is the being aware of being governed by a habit. Intellectual power is simply facility in taking habits and in following them in cases essentially analogous to, but in non-essentials widely remote from, the normal cases of sensation, or connection of feelings, under which those habits were formed.
The one primordial law of mental action is a tendency to generalization; that is, every connection between feelings tends to spread to neighboring feelings. If you ask what are neighboring feelings, it is like the question that was answered by the parable of the Good Samaritan. A neighboring feeling is simply a connected feeling. These connections are of two kinds, internal or manifest, and external or occult. A feeling is manifestly connected with feelings which it resembles or contrasts with; the connection is merely an identity of feeling. A feeling is occultly connected with feelings bound to it by some external power, as the roll of thunder with the flash of lightning.
The mental law belongs to a widely different category of law from physical laws. A physical law determines that a certain component motion must take place, otherwise