Abstract

This essay presents a critique of the ontological conventionalism which A. Grunbaum advances with respect to the metric of space and space-time. ;I explicate Grunbaum's thesis, in particular his RMH claim and also a version of it advanced recently by Wesley Salmon. Analysis of Grunbaum's key concepts, eg. intrinsicality of properties of a manifold, is provided. ;The central criticism advanced is that Grunbaum's arguments for the metrical amorphousness of space or space-time are inadequate to their conclusion. Nothing in the manifold structure of these objects, and nothing in the facts proven about manifolds by Cantor, compel the amorphousness conclusion. ;I consider also the issue of the determinateness of the geometry of space from the point of view of theories of space. Here I develop an argument of C. Glymour's which shows that the empirically equivalent theory pairs given by Grunbaum are not equally well-tested by the data. ;Finally I have considered the historical issue of the extent to which Riemann held a metric conventionalism. I argue that Riemann and the geometers who developed his approach to geometry, eg. Helmholtz, favoured realist views of the metric of space.