Chapter 3 of Making It Explicit introduces Brandom’s important notion of “deontic scorekeeping”, which I would prefer to call accounting, to avoid connotations of some sort of competition.
Brandom uses his notion of such scorekeeping as the basis for a pragmatist linguistic account of intentionality in general. It also provides a very detailed low-level model of single acts of recognition within the much larger process of temporally extended, recursively expanded, networked mutual recognition by which normativity is constituted in A Spirit of Trust.
Intentionality will be addressed not in terms of mental acts or representations, but in terms of linguistic practices and discursive commitments. (It seems to me that Aristotle would like this idea very much. My old structuralist sensibilities also take it favorably.) Michael Dummet’s view that assertion is not the expression of an interior act of judgment, but rather that judgment is the interiorization of external assertion, is cited with approval, as is his attention to the inferential role of both conditions and consequences. Belief will be understood in terms of the inferentially articulated commitment involved in making an assertion. Brandom will eventually want to say that even the attribution of rudimentary forms of nonlinguistic intentionality to animals depends on the linguistic capability of an interpreter making the attribution.
Linguistic pragmatics will explain the significance of speech acts in terms of proprieties of tracking discursive commitments and entitlements — “what moves are appropriate given a certain score, and what difference those moves make to that score” (p.142). Discursive practice is all about Wilfrid Sellars’ “game of giving and asking for reasons” (p.159). It will be important to think in terms of material incompatibility rather than formal negation.
The philosophical relevance of natural-language semantics is in showing how conceptual contentfulness reciprocally interacts with proprieties of practice such as judging and inferring. Brandom notes that associating content by stipulation, as is usual in formal model-theoretic semantics, is useless for this. The inferential practices that give significance to assertions are said to be subject to a three-dimensional distinction of commitment versus entitlement; intrapersonal versus interpersonal inheritance of deontic statuses like commitment and entitlement; and authority versus responsibility.
He says the very act of asserting something is intelligible only “as part of a practice in which reasons can be asked for or required” (p.171). This is huge. In some sense, Kant already implied it (and Plato and Aristotle before him), but the world still has not caught up. I believe this would also apply a fortiori to any sort of demand or command, which necessarily presupposes an assertion that the thing demanded or commanded should be done. Similarly, Brandom says actions are not intelligible except in a context that includes the assertional giving of reasons. Similarly again, commitments without entitlement lack authority.
In making assertions, we authorize further assertions, and undertake responsibility to show that we are entitled to the corresponding commitments. To avoid worries about a regress of entitlements, he suggests a default-and-challenge model of entitlement, where a speaker is considered entitled to a commitment by default, but this entitlement is defeasible by a challenge that meets a standard of reasonableness. There is a good deal more technical detail.