§ 1. Nature of the Problem.—We have to inquire how the spatial perception develops from indefinite and imperfect to more definite and perfect forms. We have then to consider whether the same conditions which determine its development may not also explain its first origin. To begin with, our inquiry must be limited to the perception of extension, strictly so called. This is a narrower inquiry than that concerning space in general. Sound and smell have spatial determinations. We speak of their direction and distance. But they are not extended. Extension is a continuous expanse composed of positions separated and connected by distances. Now sound and smell are never spread out in this way into an expanse composed of audible or odorous positions separated and connected by audible or odorous distances. Objects are extended only as presented to sight and touch. Our primary concern is therefore with these senses.

§ 2. Analysis of Extension. — If we consider extension as it is presented to the developed consciousness, we find in it two constituents, a material and a formal. The formal constituent consists in the relations of the parts of an extended whole in the way of position and distance. But position and distance must be position and distance of something: and this something is the material constituent. It is plain that the mere conception of position and distance is not sufficient to constitute the conception of an extended whole. For these determinations are found apart from extension. They are found in merely qualitative series, such as those in which colour sensations may be arranged. For instance, in the series of intermediate gradations connecting pure blue and pure green, any bluegreen or greenblue has a definite position, and a definite distance from other bluegreens or greenblues. If we select the interval between one bluegreen and another as a unit, we may measure the distance between any positions in the scale in terms of this unit. But this series of qualitative gradations is not a line in space: it does not depend on the juxtaposition of the colours, but only on their differences and likenesses as revealed to attentive comparison. It may be represented as a line in space, but only by analogy. In itself, it has no distinctively spatial character. What fixes the position of any special colour in the series is its own intrinsic quality. But in an extended whole, qua extended, this is not the case. If we ask why a point in an extended whole has a certain position, we cannot find the answer by considering the intrinsic sensible quality of the point itself, and by comparing it with the intrinsic sensible qualities of other points. Since position and distance do not constitute the whole of our conception of space, we must ask what is left when we think away these determinations. In the case of the colourseries the answer to this question would be easy. If we cease to arrange the colours in a series, each of them none the less retains unaffected its own intrinsic quality. In the case of an extended whole the answer must be partially similar. Its parts are distinguishable, and capable of being added and subtracted. There must therefore be some qualitative difference by which they are distinguished. This difference is commonly called a difference of local sign. Local signature is that differential quality of sensation which varies with the part of the sensitive surface stimulated and not with the nature of the stimulus. There must be some qualitative difference between a contact affecting the tip of the nose, and one affecting the big toe. Otherwise we could not with our eyes shut tell when the one and when the other was touched. It is sometimes said that this difference may be due to association. But this is impossible, because unless the qualities of contact n and contact t were different, association with n would be the same as association with t. t would tend to reproduce whatever n tended to reproduce, and there would be no distinction between them. We may therefore affirm that there is a difference in the quality of sensation according to the point of the tactile surface affected, and we must assume the same for the surface of the retina.* But two points must be carefully noted which distinguish this difference of local sign from other qualitative differences. In the first place, it does not depend on the nature of the stimulus applied, but only on the part of the sensitive surface affected. Difference of local signature cannot therefore be classed with the ordinary differences of colour and tactile sensations.

* It is difficult to determine the physiological conditions of local signature. They are probably rather central than peripheral.

The local sign of a visual sensation is not a colourquality such as red, green, white or black, and that of a tactile sensation is not a touch quality, such as roughness, smoothness, and the like. This brings us to the second point. Local sign differences exist unaffected, whether the sensitive surface is stimulated in a uniform manner or not. A uniform expanse of white or blue is still an expanse and contains local differences in spite of the sameness of the colouring. Local sign qualities differ from the qualities of the special senses inasmuch as they are not discrete and independent. They unite in one continuous total impression, forming a kind of quantity called extensive quantity or simply extensity. "Suppose," says Dr. Ward, "a postage stamp pasted on the back of the hand; we have in consequence a certain sensation. If another be added beside it, the new experience would not be adequately described by merely saying we have a greater quantity of sensation, for intensity involves quantity, and increased intensity is not what is meant. For a sensation of a certain intensity, say a sensation of red, cannot be changed into one having two qualities, red and blue, leaving the intensity unchanged; but with extensity this change is possible. For one of the postage stamps a piece of wet cloth of the same size might be substituted and the massiveness of the compound sensation remain very much the same."* Now the two postage stamps in this instance present to the touch an object which has not only extensity but extension. One stamp lies to the right or to the left of the other. A certain shape is presented, and within the whole we can distinguish distance, direction, and position. But we must abstract from all these determinations, and consider only the quantitative difference between the one postage stamp and the two. If we fix our attention purely on the quantitative aspect, we are considering extensity as distinguished from extension.

* Article "Psychology," Encyclopaedia Britannica, ninth edition, xx., p. 54.