The logical structure of linguistic commitment, part 3, Brandomian scorekeeping and incompatibility

Curiously, though he provides in Making It Explicit (MIE) elaborate account s of various representational idioms, of anaphora and deixis, and of quanti fication, Robert Brandom nowhere attempts to lay out how his understanding of content and his view of the role of logical idioms combine in even the s implest cases of what he calls paradigmatic logical vocabulary. That is, Br andom has a philosophical account of content as updating potential--as infe rential potential understood in the sense of commitment or entitlement pres ervation--and says that the point of logical vocabulary is to make availabl e the expressive resources to make explicit such semantic structures as ari se from discursive scorekeeping practice. Thus, one would expect an account of the updating or inferential potential of sentences involving logical vo cabulary, an account which is such as to assign to those sentences the infe rential significance necessary for this expressive job. In short, on would expect a semantics of logical vocabulary -& v, similar to --> - in terms of the difference an assertion of a sentence involving it makes to the atomic score of a linguistic agent, and a completeness proof for the logic genera ted by this semantics. Despite this, no such semantics is given in MIE. It is in the current paper.