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.