 The existence of relatively consistent non-Euclidean geometries leads him to the view that geometric propositions cannot be determined by a priori intuitions and that it is necessary to study “the structural relations between Euclidean and non-Euclidean geometry” (Nye 1979: 111). Poincaré established a famous dictionary translating concepts and propositions of Lobachevskii’s geometry into Euclidean geometry in order to create a model to show the relative consistency of Lobachevskii’s geometry (Poincaré 1891: 771; cf. 1902: 68; 2017: 37). Concerning pure and applied geometry, Poincaré holds the modernist-sounding views that we have no pre-axiomatic understanding of geometric primitives, that rigor demands that we eliminate appeals to intuition in geometry, and that (metric) geometry is neither true nor false, not only because we cannot verify which one is true, but also because we cannot empirically determine the metric geometry of space ‘in principle.’ When we speak of space, all we can talk about is the relations of physical bodies: