Glossary
5-5MATHEMATISM (Gemini)
[13] Just as little is it legitimate to regard the sum of perceptual characteristics as the thing. It might be quite possible for a spirit to receive the concept at the same time as, and united with, the percept. It would never occur to such a spirit that the concept did not belong to the thing. It would have to ascribe to the concept an existence indivisibly bound up with the thing.
[14] I will make myself clearer by an example. If I throw a stone horizontally through the air, I perceive it in different places one after the other. I connect these places so as to form a line. Mathematics teaches me to know various kinds of lines, one of which is the parabola. I know the parabola to be a line which is produced when a point moves according to a particular law. If I examine the conditions under which the stone thrown by me moves, I find the path traversed is identical with the line I know as a parabola. That the stone moves just in a parabola is a result of the given conditions and follows necessarily from them. The form of the parabola belongs to the whole phenomenon as much as any other feature of it does. The spirit described above who has no need of the detour of thinking would find itself presented not only a sequence of visual percepts at different points but, as part and parcel of these phenomena, also with the parabolic form of the path which we add to the phenomenon only by thinking.
[15] It is not due to the objects that they are given us at first without the corresponding concepts, but to our mental organization. Our whole being functions in such a way that from every real thing the relevant elements come to us from two sides, from perceiving and from thinking.
[16] The way I am organized for apprehending the things has nothing to do with the nature of the things themselves. The gap between perceiving and thinking exists only from the moment that I as spectator confront the things. Which elements do, and which do not, belong to the things cannot depend at all on the manner in which I obtain my knowledge of these elements.
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