I've been slogging through Brandom's Articulating Reasons: An Introduction to Inferentialism, and I think I'm just missing something with the big argument in Chapter 4.
Brandom tries to semantically differentiate singular terms from predicates solely by their substitutional behavior. His big conclusion is that valid material inferences involving substitution of singular terms are symmetric, whereas those involving substitution of predicates are asymmetric (not anti-symmetric!).
Take "X entails Y" just to mean that the in some primitive sense the inference from X to Y is licit. So "Charlie is happy" both entails and is entailed by "The small dog on Hearthstone Drive is happy." But "Frank is joyous" entails "Frank is in an emotional state," but not vice versa.
Weirdly Brandom uses definite descriptions ("the so and so") in his examples and counts them as singular terms. But indefinite descriptions ("a so and so") are not symmetric. "Charlie is happy" entails "A small dog on Hearthstone Drive is happy," but not necessarily the other way around. Their might be two small dogs on Hearthstone Drive such that the one other than Charlie is happy.
Footnote 15 on page 215 sort of addresses this, but it is really pretty opaque. In full it reads:
Maybe I'm being completely dense, but I don't see how he can treat definite descriptions as being in the same syntactic category as names, and indefinite descriptions as not. Definite descriptions and indefinite descriptions satisfy all the same syntactic substitution tests. That is you don't go from grammatical sentence to ungrammatical sentence by replacing one by the other. And Brandom explicitly states that such tests are all that creates syntactic categories (as someone who works in computationally friendly syntactic frameworks, I like this view, though I have to note that post X bar theory Chomskyans would probably disagree).
This is actually a huge problem. In Montague Grammar proper names and noun phrases such as definitite and indefinite descriptions have the same semantic type. Each takes something of the type of a predicate (if we're extensional <e,t>) and returns something of type t (a truth value). Making this work was one of the deep insights that made a recursive syntax-semantics interface possible, because the you don't have different semantic types for things that are the same syntactic type. The fact that Brandom loses this is a big mark against his theory then.
Assume that Bradom can deal with the issue of indefinite descriptions satisfying all the same syntactic distributional tests as definite descriptions and proper names. There's a bigger problem. If we start with a language that does not include negation, then proper names can yield asymmetric inferences. Assume that our language contains five predicates and three of them are true of John and two of those three are true of Billy. Then for all basic predicates Phi, Billy Phi's entails that John Phi's, and not vice versa. You have uniform asymetric substitutivity.
If you have negation in the language and understand any open sentence to define a predicate then it does not follow. Let's say that "is happy" is the basic predicate that holds of John and not Billy. Then "Billy is not happy" does not entail "John is not happy.
Isn't that a little bit weird though? On his account, logical operators are supposed to be making explicit what is already implicit in our inferential behavior. I'm not sure this is really what's going on when "Billy" is a proper name in a language with negation but a predicate in a language without. I guess the question is whether you need that category to make sense of negation in the first place. I need to reread Sections 2 and 3 with this in mind though. Brandom might just say that this second problem shows something deep about the gloriously holistic nature of language (that might be part of what Sections 2 and 3 of the chapter are getting at; I don't yet understand them).
