It should be pointed out that Fodor (surprisingly, I think, given how opposed he is to analyticity) thinks compositionality must be a
conceptual, not contingent matter - it can't just depend on our psychology.  Thus Fodor would not be happy with 'mere' contingent
compositionality of possession conditions.

     Textual evidence: on p. 6 (Villanueva) Fodor says: "Somebody who is good at recognizing that trouts are fish and that puppies are pets is
*not thereby good at recognizing that goldfish are pet fish*.  The capacity for recognizing pet fish as such is *not conceptually, or
linguistically, or semantically connected* to capacities for recognizing pets as such or fish as such.  The connection is *at best* contingent,
and it's entirely possible for any of these recognitional capacities to be in place without any of the others. (Second emphasis mine.) He goes
on: "This doesn't, of course, show that the semantics of PET FISH are uncompositional.  What it shows is that recognitional capacities aren't
possession conditions for the concepts that have them.  If recognitional capacities were possession conditions, PET FISH would not inherit its
satisfiers from those of PET and FISH.  So if recognitional capacities were possession conditions, PET FISH would fail premise P.  So
recognitional capacities aren't possession conditions.  So there are no recognitional concepts."

     In light of this, I could revise my point as follows.  *If*, with Fodor, we insist that the compositionality of possession conditions is a "conceptual", and not merely contingent matter, then (I conjecture) on no view of what it is to possess a concept will it turn out that possessing component concepts non-contingently guarantees possessing the complex concept.  If we add the claim (that Fodor seems to endorse) that the compositionality of concepts *should* be something that is conceptually guaranteed, we get a general argument of the sort I had in mind, i.e.:

             (P1) Concepts compose as a matter of conceptual necessity
             (P2) Possession conditions compose at best contingently
             So, Concepts cannot be constituted by possession conditions.

(This may need some cleaning up.)  The idea is that this argument doesn't impugn recognitional concepts specifically, but rather drives a wedge between possession conditions and concepts.  Or something like that.  So Fodor misadvertizes his main point.