Note 76 — Introductory material

Before considering the subsequent method of definition, let us reflect on the theories involved in the above account of the conception of space as a magnitude. In the first place, it is assumed that conceptions cannot be formed unless we have a series of separate objects from which to abstract a common property—in other words, that the universal is always the general. In the second place, it is assumed that all definition is classification under a genus. In the third place, the conception of magnitude, if I am not mistaken, is fundamentally misunderstood when it is supposed applicable to space as a whole. But in the fourth place, even if such a conception existed, it could give none of the essential properties of space. Let us consider these four points successively.