SENSATION OF EXTENSION.
43. Two of our senses perceive extension; sight and touch. Sound, taste, and smell accompany extension, but are something different from it. The sight perceives nothing not extended; extension is every way inseparable from this sensation. We may be so enchanted by the sweet harmony of many instruments as to forget the extension of the instruments, the air, and our organs; but we cannot, in contemplating a painting even in the midst of our most ardent enthusiasm, make its extension vanish. If we withdraw from theTransfigurationof Raphael its extension, the marvel disappears; for even considered as a simple phenomenon of our soul, continuity and distance enter of necessity into its very essence.
The same is true of touch, although less generally so. Hardness and softness, roughness and smoothness, squareness and roundness, all involve extension; but it cannot be denied that there are some impressions of touch, in which it is less clearly involved. The acute pain of a puncture, and others felt without any known external cause, are not so clearly referred to extension, but seem to have something of that simplicity which distinguishes the impressions of the other senses. However this may be, it is certain that the perception of extension belongs in a special manner to sight and touch.
44. In order to form a clear idea of extension in its relations to sensation, we will analyze it at some length.
And first of all, it is to be remarked, that extension involves multiplicity. An extended being is of necessity acollection of beings, more or less closely united by a bond which makes them all constitute one whole, but does not prevent them from continuing many. A splendid painting, wherein the unity of the artist's thought dominates, does not cease to be composed of many parts; themoralchain which unites, does not identify them; it only connects, co-ordinates them, and makes them conspire to one end. The firm adhesion of the molecules forming the diamond does not prevent these molecules from being distinct: the material chain unites, but does not identify them.
There is then no extension without multiplicity: where there is extension, there is, rigorously speaking, not one only being, but many beings.
45. Multiplicity does not constitute extension, for it may exist without extension. Neither the multiplicity of sounds, of tastes, nor of odors, constitutes extension. We conceive in the material, as in the moral and intellectual orders, multiplicity of beings of different orders, and yet this multiplicity involves no idea of extension. Even if we confine ourselves to the purely mathematical order, we find multiplicity without extension, in arithmetical and algebraic quantities. Therefore multiplicity, although necessary, does not alone suffice to constitute extension.
If we reflect upon the species of multiplicity required to constitute extension, we shall observe that it must be accompanied by continuity. Sensations of touch as well as of sight involve continuity; for it is impossible for us to see or to touch, without receiving the impression of objects continuous, immediately adjoining each other, co-existing in their duration, and at the same time presented as continuous one with another in space. Without this continuity, multiplicity does not constitute extension. If, for example, we take four or more points on the paper on which we now write, and by an abstraction consider them as indivisible,this multiplicity will not constitute extension: we must unite them by lines at least imaginary; and if continuity be wanting to the body in which we suppose them situated, we shall find it necessary to recur to the continuity of space; that is, to regard this space as a collection of points whose continuation connects the first points. No possible efforts can enable us to consider a collection of indivisible points, neither continuous nor united by lines, as extension; this collection will be to us as that of beings having no connection with extension. It is worthy of observation, that if we assign them a determinate position in space, this we do only by connecting them with other points, by means of imaginary lines: for we cannot otherwise conceive either distances or position in space. If we attempt to abstract all this, we either fall into intellectual nothingness, we annihilate all idea of the object, or we pass to another order of beings having no relation either to extension or space. We quit matter and sensations, and mount to the realm of spirits.
46. Multiplicity and continuity are therefore necessary to constitute extension; and we believe that these two conditions suffice; for where they exist, extension exists, and with them alone, we form the idea of extension. The object of geometry is extension; and only multiplicity and continuity constitute it. Lines, surfaces, solids, such as are the object of geometry, are only this continuity considered in its greatest abstraction. Empty space suffices, or rather is requisite for geometry; since, it does not, in making its applications to bodies, find all the exactness of continuity in the abstract.
47. If multiplicity and continuity constitute extension in space, it really exists in the objects which cause our sensations. Basing ourselves upon the relation of phenomena among themselves and to their causes, we have shown thatexternal objects correspond to sensations: thus it is that this relation also exists with respect to multiplicity and continuity; these two properties are therefore found in nature. The impressions that we receive by sight and touch, are, although we confine ourselves to a single object, multiple, and consequently correspond to many objects: they are continuous, and consequently correspond to continuous objects.
We will explain this reasoning. Looking at a painting, I receive an impression coming from many different points; and this impression, it must be observed, comes uninterruptedly from the whole surface presented. If, as we have shown, the sight of one external point sufficed to convince me of its existence, that of many will make me sure of the existence of many; and the continuity of the impression will also make me certain of the continuity of the impressing points.
If I touch the object seen, my touch will confirm that testimony of sight, in what corresponds to it, that is, the multiplicity and continuity, I experience the same continued succession of sensations; and this shows me the existence and continuity of the objects causing them.
48. In a few words, extension supposes the co-existence of many objects, in such a way, however, that they are one by continuation of others: of both, sensation makes us certain: therefore the testimony of the senses suffices to make us certain that there are external objects, and that they may produce various impressions. These ideas contain every thing included in the idea of body: therefore the testimony of the senses makes us certain of the existence of bodies.