Abstract

Following ideas elaborated by Hering in his celebrated analysis of color, the psychologist and gestalt theorist Otto Selz developed in the 1930s a theory of “natural space”, i.e., space as it is conceived by us. Selz’s thesis is that the geometric laws of natural space describe how the points of this space are related to each other by directions which are ordered in the same way as the points on a sphere. At the end of one of his articles, Selz tries to derive within his framework two of Hilbert’s axioms for Euclidean geometry. Such derivations would, according to Selz, disclose the psychological origin and meaning of the geometric axioms and would thus contribute to a clarification of their epistemological status. In the present article Selz’s theory is explained and analyzed, his basic principles are amended, and implicit assumptions are made explicit. It is shown that the resulting system is one of ordered affine geometry in which all of Hilbert’s axioms except the axioms of congruence and those of continuity are derivable. The primary aim of the present paper is to make explicit the basic principles behind Selz’s geometry of natural space. The question of the logical independence of these principle is not investigated.