Jaroslav Peregrin has a nice book on structuralism and inferentialism called “Meaning and Structure”. In it he traces some of the roughly structuralist/holist approach to language through Quine, Davidson, Sellars, and Brandom. These philosophers are characterized by their holistic and inferential approaches to meaning. Of course, they differ on several points, e.g. empiricist or naturalist tendencies and acceptance of intensional constructions. The main thing I want to mention is Peregrin’s characterization of Brandom. First some background. Peregrin shows how to take the inferentialist approach to meaning and wed it to the more or less Montagovian approach to compositionality. In fact, he thinks that compositionality is a key feature of structuralism about meaning (the view that structure in the form of syntactic and semantic combination takes pride of place over parts combined). Next, why this is interesting. Brandom’s own presentation of his logic and semantics for his inferentialist semantics rejects compositionality. The semantics are recursive, but not compositional, thereby offering a counterexample to Fodor’s claim that learnable languages must be compositional. (This is in Brandom’s Locke lecture 5.)This is a neat move in and of itself. Peregrin presents Brandom as being compatible with the compositional camp though. Where do they differ?

Brandom has a view on the social dimension of pragmatics that he calls deontic scorekeeping. This is keeping track of who is committed and entitled to what and why. This is the game of giving and asking for reasons, roughly. The logic behind this deals in incompatibles. Each proposition p is assigned a set of incompatibilities, commitment to any member of which undermines entitlement to p and vice versa As an example, the proposition “that is a banana” is compatible with either “that is green” and “that is ripe” but not both together. As another example, one agent being committed to incompatibles can serve as reason for another agent not to endorse the relevant assertions by the first agent. There is a fairly complex picture that emerges. The logic and semantics that Brandom presents for this is not compositional, but it is an interagent affair. The determination of inferential role of subsentential parts is determined using substitution classes which looks like a version of categorial logic, at least superficially (from memory) of the kind that Lewis uses in “General Semantics”. This looks compositional. What’s non-compositional then? The propositional logic of the inter-agent incompatibility semantics is definitely not compositional. The official version of incompatibility logic doesn’t seem to have a first-order version yet. It looks like the categorial logical determination of subsentential inferential contribution is compositional, at least if Peregrin’s presentation is as correct as it seemed. However, the logical connectives are no longer compositional and what Brandom is most concerned with is the inferential role of propositions. This will not be compositional as the connectives are not.

What gives? Peregrin’s book came out in between Making It Explicit and the Locke lectures, and I think the incompatibility logic was developed in the period after Peregrin’s book before the Locke lectures, so he can’t be faulted for that. It looks like he gets the inferentialism of Making It Explicit as far as the subsentential parts are concerned. It looks like things shift at the propositional level in the Locke lectures from Making It Explicit, but I’d have to check them both again to be sure.

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