Wittgenstein famously introduced the notion of ‘hinge propositions’: propositions that are assumptions or presuppositions of our languages, conceptual schemes, and language games, presuppositions that cannot themselves be rationally established, defended, or challenged. This idea has given rise to an epistemological approach, ‘hinge epistemology’, which itself has important (negative) ... [Show full abstract] implications for argumentation. In particular, it develops and provides support for Robert Fogelin’s case for deep disagreements: disagreements that cannot be rationally resolved by processes of rational argumentation. In this paper, I first examine hinge epistemology in its own right, and then explore its implications for arguments and the theory of argumentation. I argue that (1) the Wittgensteinian approach to hinge propositions is problematic, and that, suitably understood, they can be rationally challenged, defended, and evaluated; (2) there are no well-formed, coherent propositions, ‘hinge’ or otherwise, that are beyond epistemic evaluation, critical scrutiny, and argumentative support/critique; and (3) good arguments concerning hinge propositions are not only possible but common. My arguments will rely on a thoroughgoing fallibilism, a rejection of ‘privileged’ frameworks, and an insistence on the challengeability of all frameworks, both from within and from without.