 This twist on the Kantian doctrine of the unknowability of the Ding an sich (the thing in itself) and our confinement to the world of appearances, was congenial to Poincaré as a working physicist. Even though he agreed with Riemann to a large extent, Riemann had hoped that empirical matters would guide the choice of geometry, while Poincaré could not agree. The viewpoint just explained is Poincaré’s philosophy of geometrical conventionalism. But there is an important distinction to make. Notice that this is not like the conventionality of words, but rather like social or legal conventions (where some basic facts have to be taken into account, see De Paz 2018). The situation is far from total arbitrariness, since physical experience plays a decisive role and restricts the choice; but there is no absolute determination either, in the end a choice has to be made, and simplicity has the final word.