Sobre las implicaciones epistemológicas del convencionalismo geométrico

In 1902 Henri Poincaré published an article about the nature of the geometry in his book “Science and Hypothesis”. He pretended to show the equivalence of the di"erent geometrical theories developed during the 19th century by empirical facts using a historical mental experiment. Certainly, we have proofs of the relative consistency of the non-Euclidean geometries to the Euclidean one but Poincaré also established that choosing which geometry describes the world is not only impossible but useless. He wrote that Phenomena can be equally described by any chosen geometry and any election is only a matter of convention. Since then, all re!ection upon geometrical nature of the Space-time has driven us to confront, one way or ano ther, the Conventionalism Problem. This kind of positions seems to bring us back to an epistemologically sceptical point of view. If our geometry of the world comes from convention, attending comfort and practical behaviour (conceptual or heuristical), reaching the true nature of the Universe seems unlikely. However, we keep our efforts to understand it and we could test the possibility or review the concept of intelligibility in order to reach the world using concepts as regularity and prediction in a free interpretation of the Kantian explanation of the ontological base of phenomena.