Why neither diachronic universalism nor the Argument from Vagueness establishes perdurantism

One of the most influential arguments in favour of perdurantism is the Argument from Vagueness. The argument proceeds in three stages: The first aims to establish atemporal universalism. The second presents a parallel argument in favour of universalism in the context of temporalized parthood (‘diachronic universalism’). The third argues that diachronic universalism entails perdurantism. I offer a novel objection to the argument. I show that on the correct way of formulating diachronic universalism the principle does not entail perdurantism. On the other hand, if diachronic universalism is formulated as Sider (incorrectly) proposes, the argument fails to establish his principle, and thus perdurantism.