ABSTRACT
What holds for pure absolute space holds also — mutatis mutandis — for the single mathematical spaces and parts of space, and for the idea of the so-called mathematical bodies, such as sphere, cylinder, cube, and prism. The psychological and logical foundations of these constructs are the corresponding empirical corporeal objects. The corporeal is reduced to a minimum, finally to zero; and therewith, from a strictly logical standpoint, the boundaries of these corporeal objects must fade away and, so to speak, merge into themselves. The boundaries of the empirical bodies are taken as such, and are abstracted and hypostasized; and with these imaginary constructs mathematics, and particularly geometry, operates. A point as a zero-dimensional construct is, in itself, entirely contradictory, though as necessary as it is absurd. A construct without any dimension is, in itself, a nothing. But the one-dimensional construct of the line and the two-dimensional construct of the surface are contradictory ideas.
