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.