Here's how things stood before the break on Wednesday.
     1.  We distinguished concepts themselves' being compositional (which no one seriously contests) from their possession conditions' being compositional.  Fodor, of course, claims both.
     2.  There seem to be counterexamples to the latter:  Possession conditions that take the form of stereotypes; those that are recognitional, if Jerry is right; those that are informational in Jerry's sense, if Horwich is right.
     3.  That suggested to Dorit that possession conditions are never compositional.  So she tentatively concluded that Fodor's article is misleading, in that it isn't really about recognitional concepts in particular.  If she's right, it's worse than that:  Not just that Fodor has proved (if anything) something more general than he meant to, but that he's proved something that he himself begins by denying.  For he insists that possession conditions are compositional, and for any alleged type of possession condition that does not compose, there is no concept that has that possession condition.  Thus, if possession conditions never compose, there are no concepts at all!
     4.  But Dorit did not give an argument for the thesis that possession conditions are never compositional, i.e., a general argument rather than just a few examples of noncompositional types of possession condition.

     Now, here's a counter-argument, for the claim that all possession conditions are compositional.  Its main premise (MP) is the Schiffer-Horwich-Grandy-(?)Horgan thesis that we possess complex concepts simply by knowing how to compose them.  (That is, we possess each of the atomic component concepts, and we know the distinctive way(s) to stick them together.)
     OK, suppose I possess each of C¹, C² and C³; I satisfy each of their own respective possession conditions.  And suppose I do know the way to stick them together to get C¹⁺²⁺³.  Then by MP, I automatically possess C¹⁺²⁺³.  "C¹"-"C³" were arbitrarily selected concepts, so this shows that all possession conditions compose, QED.
     That argument doesn't show that compositionality for possession conditions is (anything like) analytic, because MP is a substantive thesis.  But if MP is a fairly basic fact about us, then it's fair to conclude that possession conditions are compositional, in that if I possess a complex concept's atomic components and know the way to stick them together, I automatically possess that concept.
     Now, I think a weaker version of Dorit's contrary thesis is correct:  Possession conditions of a distinctive kind K (stereotypical, recognitional, informational,...) will not normally compose into a complex possession condition of kind K.  (Some still will:  The possession conditions of truth-functional connectives probably compose.)
     Is there anything wrong with the Schiffer-Horwich-Grandy-(?)Horgan thesis?  Not that I can see, but I invite further discussion.