109. There is no such discovery in Kant's doctrine of space, for on the one side he asserts a well known fact, that the intuition of space is a necessary subjective condition, without which it is impossible for us to perceive things, one outside of another; and on the other side he falls into idealism, inasmuch as he denies this extension all reality, and regards things and their position in space as pure phenomena, or mere appearances. The fact which he asserts is true at bottom; for it is, in fact, impossible to perceive things as distinct among themselves, and as outside of us, without the intuition of space; but, at the same time, it is not accurately expressed, for the intuition of space is this perception itself; and, consequently, he ought to have said that they are identical, not that one is an indispensable condition of the other.
110. Prior to the impressions, there is no such intuition, and if we regard it as a pure intuition and separated from intellectual conception, we can only conceive it as accompanied by some representation of one of the five senses. Let us imagine a pure space without any of these representations, without even that mysterious vagueness which we imagine in the most distant regions of the universe. The imagination finds no object; the intuition ceases; there remains only the purely intellectual conceptions which we form of extension, the ideas of an order of possible beings, and the assertion or denial of this order, according to our opinion of the reality or non-reality of space.
111. It is evident that a series of pure sensations cannot produce a general idea. Science requires some other foundation. The phenomena leave traces of the sensible object in the memory, and are so connected with each other, that the representation of one cannot be repeated without exciting the representation of the other, but they produce no general result which could serve as the basis of geometry. A dog sees a man stoop, and make a certain motion, and is immediately struck with a stone, which causes in him a sensation of pain; when the dog sees another man perform the motion, he runs away; because the sensations of the motions are connected in his memory with the sensation of pain, and his natural instinct of avoiding pain inspires him to fly.
112. When these sensations are produced in an intelligent being, they excite other internal phenomena, distinct from the mere sensitive intuition. Whether general ideas already exist in our mind, or are formed by the aid of sensation, it is certain that they are developed in the presence of sensation. Thus, in the present case we not only have the sensitive intuition of extension, but we also perceive something which is common to all extended objects. Extension ceases to be a particular object, and becomes a general form applicable to all extended things. There is then a perception of extension in itself, although there is no intuition of the extended; we then begin to reflect upon the idea and analyze it, and deduce from it those principles, which are the fruitful germs from the infinite development of which is produced the tree of science called geometry.
113. This transition from the sensation to the idea, from the contingent to the necessary, from the particular fact to the general science, presents important considerations on the origin and nature of ideas, and the high character of the human mind.
Kant seems to have confounded the imagination of space with the idea of space, and notwithstanding his attempts at analysis, he is not so profound as he thinks, when he considers space as the receptacle of phenomena. This a very common idea, and all that Kant has done is to destroy its objectiveness, making space a purely subjective condition. According to this philosopher, the world is the sum of the appearances which are presented to our mind; and just as we imagine in the external world an unlimited receptacle which contains every thing, but is distinct from what it contains, so he has placed space within us as a preliminary condition, as a form of the phenomena, as a capacity in which we may distribute and classify them.
114. In this he confounds, I say, the vague imagination with the idea. The limit between the two is strongly marked. When we see an object we have the sensation and intuition of extension. The space perceived or sensed is, in this case, the extension itself perceived. We imagine a multitude of extended objects, and a capacity which contains them all. We imagine this capacity as the immensity of the ethereal regions, a boundless abyss, a dark region beyond the limits of creation. So far there is no idea, there is only an imagination arising from the fact that when we begin to see bodies we do not see the air which surrounds them, and the transparency of the air permits us to see distant objects, and thus from our infancy we are accustomed to imagine an empty capacity in which all bodies are placed, but which is distinct from them.
But this is not the idea of space; it is only an imagination of it, a sort of rude, sensible idea, probably common to man and the beasts. The true idea, and the only one deserving the name, is that which our mind possesses when it conceives extension in itself, without any mixture of sensation, and which is, as it were, the seed of the whole science of geometry.
115. It should be observed that the word representation as applied to purely intellectual ideas must be taken in a purely metaphorical sense, unless we eliminate from its meaning all that relates to the sensible order. We know objects by ideas, but they are not represented to us. Representation, properly speaking, occurs only in the imagination which necessarily relates to sensible things. If I demonstrate the properties of a triangle, it is clear that I must know the triangle, that I must have an idea of it; but this idea is not the natural representation which is presented to me like a figure in a painting. All the world, even irrational animals have this representation, yet we cannot say that brutes have the idea of a triangle. This representation has no degrees of perfection, but is equally perfect in all. Any one who imagines three lines with an area enclosed, possesses the representation of a triangle with as much perfection as Archimedes; but the same cannot be said of the idea of a triangle, which is evidently susceptible of various degrees of perfection.
116. The representation of a triangle is always limited to a certain size and figure. When we imagine a triangle, it is always with such or such extension and with greater or smaller angles. The imagination representing an obtuse angled triangle sees something very different from an acute or right angled triangle. But the idea of the triangle in itself is not subject to any particular size or figure; it extends to all triangular figures of every size. The general idea of triangle abstracts necessarily all species of triangles, whilst the representation of a triangle is necessarily the representation of a triangle of a determinate species. Therefore the representation and the idea are very different, even in relation to sensible objects.