How was Poincaré’s conventionalism connected to his relationism? How, in other words, is it the case that the basic principles of geometry and mechanics are, ultimately, freely chosen conventions and that, at the same time, science reveals to us the structure of the world? This lengthy study aims to address these questions by setting Poincaré’s philosophy within its historical context and by examining in detail Poincaré’s developing views about the status and role of conventions in science and the status and (...) role of relations in science. It is argued that Poincaré was a neither a rampant conventionalist nor a pure structuralist. But he was both a conventionalist and a relationist, aiming to delineate a position which allowed room for both freely, but not arbitrarily, chosen constitutive principles of science and the acquisition of objective, though, relational knowledge of the natural world. (shrink)