In Chapter 6 of Articulating Reasons, Brandom makes some distinctions among the proprieties of assertions in his sketch of how to make a semantics based on assertibility conditions work. The two main ones are commitments and entitlements. Commitments are what claims one is committed to by an assertion. These give inferential relations among contents. Asserting “This is red” commits one to “This is colored”, that is, the latter should be added to one’s assertion score if the former is. Entitlements are the subset of commitments to which one can supply justifying reasons. These two notions come together to define incompatibility, which is a relation between contents. A is incompatible with B iff commitment to A precludes entitlement to B. This gives us two basic notions and one derived from their interplay. Now there are a few things to note about these.

Commitment is generally asymmetric. “A commits one to B” would not seem to entail “B commits one to A” for many A and B. Incompatibility is a modal notion on, as far as I can tell, two counts. The first is that “precludes” seems to be modal. Commitment to A means that one cannot be entitled to B. There is, I suppose, a non-modal reading of “precludes”: commitment to A means that one is not entitled to B. Even in that case, incompatibility is a modal notion because entitlement is. To be entitled to A is to be able to give reasons in support of A. Entitlement is, it would seem, a modal notion. Incompatibility is a relation between contents, and a modal one at that. Incompatibility seems like it should be a symmetric relation, but, the definition doesn’t seem to guarantee this. Commitment to A may preclude entitlement to B, but commitment to B need not preclude entitlement to A. At least, a proof of symmetry would be needed and I don’t have one. At a minimum, incompatibility should be symmetric for A and ~A, since ‘~’ is supposed to express incompatibilities.

From here, Brandom defines three sorts of relations. (He describes them as three sorts of inferential relations, but one is not on inferences. This is primarily on p. 193-4 for the interested reader.) These relations are: commitive inferences, permissive inferences, and incompatibility entailment. Commitive inferences are those that preserve commitments. Similarly, permissive inferences preserve entitlement. One gripe here is that there is no explanation of what preservation is supposed to be. Most non-stuttering inferences (i.e. inferences not of the form A, therefore A) will lose commitments. Suppose we make the inference: that is vermillion, therefore that is red (to stick with the easy example). The conclusion has different commitments than the premiss, at the least, the conclusion does not commit me to the premiss. There’s an idea there that one can grab ahold of, but we’re not given a clear picture of it. Incompatibility entailment (I-entailment) is better defined, but it is surprisingly difficult to ferret out the definition. By “surprisingly” I mean that it requires any work at all; it should be clearer. (No philosophical gripe here, just a stylistic and pedagogical one.) Let’s say that Inc(A) is the set of contents that are incompatible with A, i.e. {C: A is incompatible with C, for B in the appropriate language(pardon the hand-waving)}. A I-entails B iff Inc(B)\subseteq Inc(A). The example from the book is “The swatch is vermillion” I-entails “The swatch is red” because everything incompatible with the latter is incompatible with the former. Do we have to restrict ourselves to single premises and conclusions? I think, with reservation, that all three relations can be generalized to be between sets of contents, with no restriction on the set of premises and with the restriction that the set of conclusions be a singleton. For I-entailment, this seems to be straightforward. For a set of contents H, Inc(H) equals the union of Inc(B), for all B\in H. I’m hesitant about extending this straightforwardly to commitive and permissive inferences since I’m unclear about what the preservation in their description is.

Why are these three notions important? I will get back to the relations at a later time. The two notions of commitment and entitlement are important because of how they figure in Brandom’s game of giving and asking for reasons. Brandom argues that there are two necessary conditions on any game to count as a reasons game for assertions. One necessary condition is that the moves be evaluable in terms of commitments. The short reason for this is that assertions must express conceptual content. Such content is inferentially expressed, so assertions must fit into inferential networks. Making a move must commit you to inferentially articulated consequences in order for it to count as an assertion. The other necessary condition is that there be a distinguished class of assertions to which one is entitled. The short argument for this is that undertaking commitments implicitly acknowledges that justification for the commitment can be requested, at least in some circumstances. In separating out the moves that are justified/justifiable from those that aren’t, one is creating a distinguished class of entitled assertions. Therefore, commitment and entitlement structures are necessary conditions for a game to count as a game of giving and asking for reasons for assertions. No sufficiency claim is being made. The notion of incompatibility, which links the other two normative notions, is important for what Brandom has to say about objectivity, which I will post on later.

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