This conclusion, however, seems to present a double difficulty. It is admitted that we perceive things as they look, and not as they are. How, then, is it possible for the belief that things _are_ spatial to arise? For how can we advance from knowledge of what they look to knowledge of what they are but do not look? Again, given that the belief has arisen, may it not after all be illusion? No vindication seems possible. For how can it be possible to base the knowledge of what things are, independently of perception, upon the knowledge of what they look? Nevertheless, the answer is simple. In the case of the perception of what is spatial there is no transition _in principle_ from knowledge of what things look to knowledge of what things are, though there is continually such a transition _in respect of details_. It is, of course, often necessary, and often difficult, to determine the precise position, shape, &c., of a thing, and if we are to come to a decision, we must appeal to what the thing looks or appears under various conditions. But, from the very beginning, our consciousness of what a thing appears in respect of spatial characteristics implies the consciousness of it as spatial and therefore also as, in particular, three-dimensional. If we suppose the latter consciousness absent, any assertion as to what a thing appears in respect of spatial characteristics loses significance. Thus, although there is a process by which we come to learn that railway lines are really parallel, there is no process by which we come to learn that they are really spatial. Similarly, although there is a process by which we become aware that a body is a cube, there is no process by which we become aware that it has a solid shape of some kind; the process is only concerned with the determination of the precise shape of the body. The second difficulty is, therefore, also removed. For if assertions concerning the apparent shape, &c. of things presuppose the consciousness that the things _are_ spatial, to say that this consciousness may be illusory is to say that all statements concerning what things _appear_, in respect of spatial relations, are equally illusory. But, since it is wholly impossible to deny that we can and do state what things appear in this respect, the difficulty must fall to the ground.