153. A pure spirit,—the existence of which we must always suppose; for, though all finite beings were annihilated, there would still remain the infinite being which is God,—a pure spirit would know the extended world just as it is in itself, and would not have the sensible representations either external or internal, which we have. This is certain, unless we mean to attribute imagination and sensibility to pure spirits, and even to God himself.
On this supposition I ask, what would a pure spirit know of the external world? or, to speak more properly, since the existence of such a spirit is certain and its intelligence infinite, what does this spirit know of the external world?
154. That which this spirit knows of the world is the world, because he cannot be deceived. But this spirit does not know the world under any sensible form. Therefore the world may be known without any of the forms of sensibility, and consequently may be the object of a pure intelligence.
There is no difficulty on this point in what regards sensations. It is only necessary that we should say that the pure spirit knows perfectly the principle of causality which resides in the object, and produces the impressions which we experience. There is no need of attributing to the intelligent spirit any sensation of the thing understood.
This question is more difficult when we come to explain what relates to extension. For, if we say that the spirit only knows the principle of causality of the subjective representation of the extended, it follows that there is no true extension in the objects, because the spirit sees all that there is, and if the spirit does not see it, it is because it is not. We fall into Berkeley's idealism; an external world without extension is not the world of common sense, but the world of the idealists. If, on the other hand, we say that this pure spirit does know extension, we seem to attribute to the spirit sensible representation; because the extension represented seems to involve sensible representation. What is an extension with lines, surfaces, and figures? And these objects, as we understand them, are sensible; if, however, they be taken in another sense, the extension of the world will be of another nature, it will be something of which we have no idea; and here again we fall into idealism.
155. To solve this difficulty, which is really a serious one, it is necessary to recollect the distinction on which I insisted so earnestly between extension as sensation and extension as idea. The former can become subjective only in a sensible being; the second may be, and is, subjective in a purely intellectual being. Extension as sensation is something subjective, it is an appearance; its object exists in reality, but without including in its essence any thing more than is necessary in order to produce the sensation. Extension as idea is also subjective; but it has a real object which corresponds to it, and satisfies all the conditions of the idea.
156. Does not this theory seem to establish two geometries? We must distinguish. The scientific and the pure ideal geometry will remain the same, save the difference of the intelligences which possess it. But notwithstanding this difference, what is true in one is true in the other. Empirical geometry as the representative part of geometry will be different: we have the idea only of our own.
157. In fact we observe two parts in geometry even in ourselves; the one purely scientific, the other of sensible representation. The former includes the connection of ideas; the latter the images and particular cases by means of which we make the ideas sensible: the first is the ground; the second is the form. But although the two are different, we cannot separate them entirely: we cannot have the geometrical idea without the sensible representation, we understand it only per conversionem ad phantasmata, as say the scholastics. Thus the two orders of geometry, the sensible and the intellectual, though different, are always joined in us; whether because the pure geometrical idea arises from the sensible, or is excited by it, or because this is perhaps a necessary primitive condition imposed on our mind by its union with the body.
158. This shows how the pure geometry may be separated from the sensible, and how it may exist in pure intellectual beings, without any of the forms which represent the geometrical idea in sensible beings.
159. But what becomes of extension in itself and stripped of all sensible form? When we speak of extension stripped of all sensible form, we do not mean to deprive it of its capacity to be perceived by the senses, we merely abstract the relations of this capacity to sensible beings. Extension is then reduced, not to an imaginary space, nor to an eternal and infinite being, but to an order of beings, to the sum of their constant relations subject to necessary laws. What then are these relations? I know not. But I know that they exist and that these necessary laws exist. That they exist in reality I know by experience, which gives testimony of their existence; that they are possible, I know on the authority of my ideas, the connection of which forces my assent to their intrinsical evidence.