Geometry as a measurement-theoretical a priori

Lorenzen's defense of relativity against the ontology of its proponents

Oliver Schlaudt

pp. 21-43

in: Manuel Rebuschi, Gerhard Heinzmann, Michel Musiol, Alain Trognon (eds), Interdisciplinary works in logic, epistemology, psychology and linguistics, Berlin, Springer, 2014

Abstract

Lorenzen rejects ontological commitments of relativity. Realism of physical geometry already breaks down with Poincaré's arguments. Lorenzen agrees with Poincaré, but offers a constructive account: space is not an empirical entity described by means of conventions , but a purely constructive entity constituted by the norms of spatial measurement . This space however, as Lorenzen argues, is Euclidean. In this paper, we shall analyse Lorenzen arguments and explicate how they relate to arguments from empiricism and neo-kantianism. It will be shown that the originality of Lorenzen's position consists in systematically accounting for the role of measurement and measurement instruments.