Logic as Elaboration, not Pure Convention
Abstract
While logical expressivism and logical conventionalism share many commitments, the most prominent versions of these positions diverge in the kind of logical inferentialism they endorse. Jared Warren’s logical conventionalism adopts a form of unrestricted inferentialism, whereas logical expressivism naturally supports restricted inferentialism. This contrast is most evident in their respective treatments of the ‘tonk’ problem. This paper develops an expressivist defense of restricted inferentialism in light of Warren’s recent arguments for unrestricted inferentialism. I argue that the restricted inferentialist can accept Warren’s ‘Translation Mistake’ diagnosis of Unilateralist Tonklish, given that it interprets the addition of ‘tonk’ as yielding a semantically conservative extension of the original language. In the case of Bilateralist Tonklish, I argue that the restricted inferentialist can accept Warren’s verdict that it is a meaningless language because it is unfollowable, but that this unfollowability, in turn, is to be given a principled explanation in terms of constraints on inference rules. I contend that Warren’s discussion of ‘tonk’ reinforces the idea that logical connectives must play the expressive role that logical expressivists attribute to them, and that this role motivates restricted inferentialism.