[v.....n]

Further, the old rationalist claims that Euclidean geometry is a priori yet incorporates empirical knowledge about space becomes supported, too, in view of our insight into the praxeological constraints on knowledge. Since the discovery of non-Euclidean geometries and in particular since Einstein’s relativistic theory of gravitation, the prevailing position regarding geometry is once again empiricist and formalist. It conceives of geometry as either being part of empirical, a posteriori physics, or as being empirically meaningless formalisms. That geometry is either mere play or forever subject to empirical testing seems to be irreconcilable with the fact that Euclidean geometry is the foundation of engineering and construction, and that nobody in those fields ever thinks of such propositions as only hypothetically true. Recognizing knowledge as praxeologically constrained explains why the empiricist-formalist view is incorrect and why the empirical success of Euclidean geometry is no mere accident. Spatial knowledge is also included in the meaning of action. Action is the employment of a physical body in space. Without acting there could be no knowledge of spatial relations and no measurement. Measuring relates something to a standard. Without standards, there is no measurement, and there is no measurement which could ever falsify the standard. Evidently, the ultimate standard must be provided by the norms underlying the construction of bodily movements in space and the construction of measurement instruments by means of one’s body and in accordance with the principles of spatial constructions embodied in it. Euclidean geometry, as again Paul Lorenzen in particular has explained, is no more and no less than the reconstruction of the ideal norms underlying our construction of such homogeneous basic forms as points, lines, planes and distances which are in a more or less perfect but always perfectible way incorporated or realized in even our most primitive instruments of spatial measurements such as a measuring rod. Naturally, these norms and normative implications cannot be falsified by the result of any empirical measurement. On the contrary, their cognitive validity is substantiated by the fact that it is they that make physical measurements in space possible. Any actual measurement must already presuppose the validity of the norms leading to the construction of one’s measurement standards. It is in this sense that geometry is an a priori science and must simultaneously be regarded as an empirically meaningful discipline because it is not only the very precondition for any empirical spatial description, but it is also the precondition for any active orientation in space.

HHH str. 287-288.

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