 One objection to case-based logical pluralism is to allow that ‘case’ is underspecified and admits of various interpretations, but reject the further step that those interpretations correspond to different relations of logical consequence. We can do this is by insisting on the largest possible domain for the quantifier ‘every’ in the context of the GTT. There is a tradition in logic that holds that in order for an argument to be logically valid, the conclusion must be true in (unrestrictedly) all cases in which the premises are true. So when ‘every’ is used in defining logical consequence, we might argue, it must be understood in the broadest possible way: if there are any cases at all—anywhere, of any kind—in which the premises are true and the conclusion is false, the argument will be invalid, and if not, then the argument will be valid. The One True Logic, then, will be the one that describes the relation of truth-preservation over all cases—where ‘all’ is construed as broadly as possible (Beall &amp; Restall 2006, 92; Priest 2006, 202). 