Note 198 — Introductory material

Let us see whether, by this change, we can overcome the antinomy of the point. Spatial figures, we shall now say, are relations between the matter which differentiates empty space. Their divisibility, which seemed to contradict their relational character, may be explained in two ways: first, as holding of the figures considered as parts of empty space, which is itself not a relation; second, as denoting the possibility of continuous change in the relation expressed by the spatial figure. These two ways are, at bottom, the same; for empty space is a possibility of relations, and the figure, when viewed in connection with empty space, thus becomes a possible relation, with which other possible relations may be contrasted or compared. But the second way of regarding divisibility is the better way, since it introduces a reference to the matter which differentiates empty space, without which, spatial figures, and therefore Geometry, could not exist. It is empty space, then—so we must conclude—which gives rise to the antinomy in question; for empty space is a bare possibility of relations, undifferentiated and homogeneous, and thus wholly destitute of parts or of thinghood. To speak of parts of a possibility is nonsense; the parts and differentiations arise only through a reference to the matter which is differentiated in space.