Causalistic explanations and three-dimensionality

pp. 69-82

in: Peter Janich, Euclid's heritage, Berlin, Springer, 1992

Abstract

It is self-evident that the three-dimensionality of space must, in the end be grasped as a description of spatial states of affairs (Sachverhalte). ¹⁴ It is, in any case, open as to which "things' (Sachen) "behave" (verhalten) spatially in three-dimensions, and which reasons suggest (or even compel) their three-dimensional description. The purely spatial approaches seek reasons in geometry or in the description of bodies, their form, magnitude or position. The supplementation of motion (of bodies or of geometrical forms) assumes that the triad cannot be proven purely spatially. Finally, in the approach which deduces three-dimensionality from physical laws, the addition of the effects of force is taken as an argument for three-dimensionality for the first time. These are the three groups of approaches that have been discussed up to now.