Maudlin on the Triangle Inequality

Abstract

Tim Maudlin argues that we should take facts about distance to be analyzed in terms of facts about path lengths. His reason is that if we take distances to be fundamental, we must stipulate that constraints like the triangle inequality hold, but we get these constraints for free if we take path lengths to be prior. I argue that Maudlin is mistaken. Even if we take path lengths as primitive, the triangle inequality follows only if we stipulate that the fundamental properties and relations obey constraints that are just as puzzling as the triangle inequality.