An “inferentialist” semantic theory for some language L aims to account for the meanings of the sentences of L solely in terms of the inferential rules governing their use. A “hyper-inferentialist” theory admits into the semantics only “narrowly inferential” rules that normatively relate sentences of L to other sentences of L. A “strong inferentialist” theory also admits into the semantics “broadly inferential” rules that normatively relate perceptual states to sentences of L or sentences of L to intentional actions. It is (...) widely thought that only the latter of these two sorts of semantic theories is at all viable. I argue here that the opposite is so. Negatively, strong inferentialism is viciously circular: including rules into the semantic theory that relate perceptual states to sentences of the language requires us to appeal, in individuating those perceptual states, to the very meanings for which we are supposed to be inferentially accounting. Hyper-inferentialism does not face this problem because it does not appeal to any nonlinguistic states. Positively, though hyper-inferentialism is widely thought to be a theoretical non-starter, I argue here that it is a genuine theoretical possibility insofar as it essentially includes cross-perspectival inferences, inferences along the lines of the one from the sentences “The ball is in front of n,” “The ball is red,” and “The lighting is good” to the sentence “n sees that the ball is red.” I make the further exegetical claim that Robert Brandom, though unanimously taken to be a strong inferentialist, is in fact a hyper-inferentialist. (shrink)