A reconstruction of the hierarchical relations between incompatibility- entailment, committive, and permisive consequences

In this paper we propose to investigate the mutual relations among Brandom's three dimensions of semantic inferential articulation, namely, incompatibility entailment, committive, and permissive consequences. Brandom (Unpub.) argues (1) that incompatibility entailment implies committive consequence, and (2) that committive consequence in turn implies permissive consequence. However, under a closer scrutiny of this hierarchy, we see that a number of points are in need of further clarification. First, we question Brandom's claim that the hierarchy is strict. We show that, under reasonable assumptions, all three inferential relations are equivalent. Secondly, we discuss the soundness of Brandom's proofs of (1) and (2). We discuss both results against the background of the main pillars of Brandom's philosophy of language.