CONSEQUENCES OF CONVENTIONALISM IN THE GEOMETRIC THEORIES OF SPACE-TIME

The development, of the non-euclidean geometries throughout the century XIX, contributed to discard any pretension to determine the geometry of the space-time, establishing, thus, the bases of Poincare's conventionalism. Nevertheless, the conventionalism seems to hesitate between a strong version that proposes the complete equivalence between different theories, and a weak version that limits itself defending the empirical equivalence. In this paper I will try to explain the epistemological consequences on both versions of the conventionalism from three different perspectives: realistic, logical positivism and pragmatism. Likewise, I will criticize the idea, as which, each and every of the theorems and propositions of a geometrical theory are translatable in terms of the theorems and propositions of another theory it is sufficient to infer the complete equivalence. Finally, I will defend the weak version of the conventionalism arguing on the base of the geometrical theories of the space-time that come from the Newtonian theory and from the theories of relativity.