Hypothesis and convention in Poincaré’s defense of Galilei spacetime

According to the conventionalist doctrine of space elaborated by the French philosopher-sci-entist Henri Poincar ¤ in the 1890s, the geometry of physical space is a matter of defini-tion, not of fact. Poincar¤’s Hertz-inspired view of the role of hypothesis in science guided his interpretation of the theory of relativity (1905), which he found to be in violation of the axiom of free mobility of invariable solids. In an effort to save the Euclidean geometry that relied on this axiom, Poincar ¤ extended the purview of his doctrine of space to cover both space and time. The centerpiece of this new doctrine is what he called the “principle of physical relativity, ” which holds the laws of mechanics to be covariant with respect to a certain group of transformations. For Poincar¤, the invariance group of classical mechanics defined physical space and time (Galilei spacetime), but he admitted that one could also define physical space and time in virtue of the invariance group of relativistic mechanics (Minkowski spacetime). Either way, physical space and time are the result of a conven-tion. Perhaps more than any other figure in contemporary science, Henri Poincaré focused the attention of both philosophers and scientists on the role played by hypothesis in the pursuit of scientific knowledge