Thus it appears indubitable that all space-relations except those of magnitude are nothing more or less than pure sensational objects. But magnitude appears to outstep this narrow sphere. We have relations of muchness and littleness between times, numbers, intensities, and qualities, as well as spaces. It is impossible, then, that such relations should form a particular kind of simply spatial feeling. This we must admit: the relation of quantity is generic and occurs in many categories of consciousness, whilst the other relations we have considered are specific and occur in space alone. When our attention passes from a shorter line to a longer, from a smaller spot to a larger, from a feebler light to a stronger, from a paler blue to a richer, from a march tune to a galop, the transition is accompanied in the synthetic field of consciousness by a peculiar feeling of difference which is what we call the sensation of more,—more length, more expanse, more light, more blue, more motion. This transitional sensation of more must be identical with itself under all these different accompaniments, or we should not give it the same name in every case. We get it when we pass from a short vertical line to a long horizontal one, from a small square to a large circle, as well as when we pass between those figures whose shapes are congruous. But when the shapes are congruous our consciousness of the relation is a good deal more distinct, and it is most distinct of all when, in the exercise of our analytic attention, we notice, first, a part, and then the whole, of a single line or shape. Then the more of the whole actually sticks out, as a separate piece of space, and is so envisaged. The same exact sensation of it is given when we are able to superpose one line or figure on another. This indispensable condition of exact measurement of the more has led some to think that the feeling itself arose in every case from original experiences of superposition. This is probably not an absolutely true opinion, but for our present purpose that is immaterial. So far as the subdivisions of a sense-space are to be measured exactly against each other, objective forms occupying one subdivision must directly or indirectly be superposed upon the other, and the mind must get the immediate feeling of an outstanding plus. And even where we only feel one subdivision to be vaguely larger or less, the mind must pass rapidly between it and the other subdivision, and receive the immediate sensible shock of the more.
We seem thus to have accounted for all space-relations, and made them clear to our understanding. They are nothing but sensations of particular lines, particular angles, particular forms of transition, or (in the case of a distinct more) of particular outstanding portions of space after two figures have been superposed. These relation-sensations may actually be produced as such, as when a geometer draws new lines across a figure with his pencil to demonstrate the relations of its parts, or they may be ideal representations of lines, not really drawn. But in either case their entrance into the mind is equivalent to a more detailed subdivision, cognizance, and measurement of the space considered. The bringing of subdivisions to consciousness constitutes, then, the entire process by which we pass from our first vague feeling of a total vastness to a cognition of the vastness in detail. The more numerous the subdivisions are, the more elaborate and perfect the cognition becomes. But inasmuch as all the subdivisions are themselves sensations, and even the feeling of 'more' or 'less' is, where not itself a figure, at least a sensation of transition between two sensations of figure, it follows, for aught we can as yet see to the contrary, that all spatial knowledge is sensational at bottom, and that, as the sensations lie together in the unity of consciousness, no new material element whatever comes to them from a supra-sensible source.[157]
The bringing of subdivisions to consciousness! This, then, is our next topic. They may be brought to consciousness under three aspects in respect of their locality, in respect of their size, in respect of their shape.
The Meaning of Localization.
Confining ourselves to the problem of locality for the present, let us begin with the simple case of a sensitive surface, only two points of which receive stimulation from without. How, first, are these two points felt as alongside of each other with an interval of space between them? We must be conscious of two things for this: of the duality of the excited points, and of the extensiveness of the unexcited interval. The duality alone, although a necessary, is not a sufficient condition of the spatial separation. We may, for instance, discern two sounds in the same place, sweet and sour in the same lemonade, warm and cold, round and pointed contact in the same place on the skin, etc.[158] In all discrimination the recognition of the duality of two feelings by the mind is the easier the more strongly the feelings are contrasted in quality. If our two excited points awaken identical qualities of sensation, they must, perforce, appear to the mind as one; and, not distinguished at all, they are, a fortiori, not localized apart. Spots four centimetres distant on the back have no qualitative contrast at all, and fuse into a single sensation. Points less than three thousandths of a millimetre apart awaken on the retina sensations so contrasted that we apprehend them immediately as two. Now these unlikenesses which arise so slowly when we pass from one point to another in the back, so much faster on the tongue and finger-tips, but with such inconceivable rapidity on the retina, what are they? Can we discover anything about their intrinsic nature?
The most natural and immediate answer to make is that they are unlikeness of place pure and simple. In the words of a German physiologist,[159] to whom psychophysics owes much:
"The sensations are from the outset (von vornherein) localized.... Every sensation as such is from the very beginning affected with the spatial quality, so that this quality is nothing like an external attribute coming to the sensation from a higher faculty, but must be regarded as something immanently residing in the sensation itself."
And yet the moment we reflect on this answer an insuperable logical difficulty seems to present itself. No single quale of sensation can, by itself, amount to a consciousness of position. Suppose no feeling but that of a single point ever to be awakened. Could that possibly be the feeling of any special whereness or thereness? Certainly not. Only when a second point is felt to arise can the first one acquire a determination of up, down, right or left, and these determinations are all relative to that second point. Each point, so far as it is placed, is then only by virtue of what it is not, namely, by virtue of another point. This is as much as to say that position has nothing intrinsic about it; and that, although a feeling of absolute bigness may, a feeling of place cannot, possibly form an immanent element in any single isolated sensation. The very writer we have quoted has given heed to this objection, for he continues (p. 335) by saying that the sensations thus originally localized "are only so in themselves, but not in the representation of consciousness, which is not yet present.... They are, in the first instance, devoid of all mutual relations with each other." But such a localization of the sensation 'in itself' would seem to mean nothing more than the susceptibility or potentiality of being distinctly localized when the time came and other conditions became fulfilled. Can we now discover anything about such susceptibility in itself before it has borne its ulterior fruits in the developed consciousness?