On the epistemological foundations of the law of the lever

In this paper I challenge Paolo Palmieri's reading of the Mach-Vailati debate on Archimedes' proof of the law of the lever. I argue that the actual import of the debate concerns the possible epistemic (as opposed to merely pragmatic) role of mathematical arguments in empirical physics, and that construed in this light Vailati carries the upper hand. This claim is defended by showing that Archimedes' proof of the law of the lever is not a way of appealing to a non-empirical source of information, but a way of explicating the mathematical structure that can represent the empirical information at our disposal in the most general way.