Caveat Lector! What follows is wonkier than what I have posted heretofore.
Chris Barker has a remark in the recent issue of LI where he presents, what seems to me, pretty convincing evidence that quantificational binding (of a pronoun) does not require c-command, wider scope suffices. More particularly, he adopts Safir’s scope requirement:
(1) A quantifier must scope over any pronoun that it binds.
and operationalizes scope with (2):
(2) A quantifier can take scope over a pronoun only if it can take scope over an
existential inserted in the place of the pronoun.
The test in (2) conceptually divorces ‘scope’ from ‘c-command’ and allows one to investigate whether the two move in tandem, i.e. whether a scopes over b iff a c-commands b. The data Barker presents shows pretty clearly that though c-command is a sufficient condition for scope, it is not obviously necessary.
Barker’s interesting discussion serves a (perfectly reasonable) PR function. He has another way of doing binding/scope that fits well with the conclusion that it is not tied to c-command. He does not argue in detail against theories that have tried to save the Scope/C-command generalization, but his congeries of counter-examples certainly suggests that defenders of the orthodox have their work cut out for them (including an earlier counterpart of me should I/he be tempted to defend (2)). Though I could quibble with some of the data (there are a lot of cases involving ‘each,’ which is known to be recalcitrant in many ways, e.g. WCO effects with ‘each’ are quite attenuated (his1 mother considers/believes each boy1 to be perfect/His1 mother yelled at each boy1 to stop shouting), I found weight of data and Barker’s and conclusion based on it pretty convincing. At the very least, he has made a good case to re-open our minds about the relation between c-command and scope.
This said, I want to point out another consequence of Barker’s argument should his conclusion prove correct. It suggests that UG does not concern itself with quantifier scope and that QR, the grammatical vehicle for adjusting phrase structures in order to bring scope and c-command together, is not a rule of grammar. This view has a pedigree. Tony Kroch’s thesis argues that the grammar does not regulate variable Q-scope. In fact, it was Chomsky’s work on WCO and the noted parallel between (3a,b) that prompted taking quantifier scope to be a species of A’-movement:
(3) a. *Who1 does his1 mother love t1
b. *His1 mother loves everyone1
(3a) resists a paraphrase as whose mother loves him and (3b) is infelicitous as everyone’s mother loves him. Chomsky’s very reasonable point was that the facts in (3) could be collapsed if WCO were an LF fact and (3b) was covertly transformed via QR into a structure analogous to that in (3a).
Soon enough, other facts arose that supported this view (the curious can look at chapter 1 of my book Logical Form for a review of some of this). However, Barker’s paper suggests that this data is not representative and that the grammar does not regulate scope via QR at all. The paper cites examples where quantifiers scope out of subject islands, relative clauses, subject sentences and adjuncts. If these data are more or less accurate, then it suggests that QR is not a rule of grammar. More exactly, QR seems unregulated by the kinds of locality conditions we expect movement operations to be subject to.
There remains a way of finessing this conclusion. Maybe covert movement is not subject to locality restrictions of the kind we see for overt movement. This is a venerable assumption. Those predisposed to single-cycle theories of syntax (that’s you minimalists out there) might find this assumption challenging. I suspect that there are ways around this (e.g. treating islands as effectively PF linearization phenomena) but that too will take some work. At any rate, Barker’s conclusion, if correct, has interesting consequences.
I end this rambling with a question: Why were we so easily convinced that binding required c-command? First, because we understood LF as the input to semantic interpretation and took difference in truth conditions to be sufficient indication of difference in LFs. Thus, if (4) is ambiguous, it must have at least two different LFs. QR delivered two different LFs.
(4) At least one boy kissed every girl
Second, as May emphasized, QR was the perfect fix for the regress problem that ACD constructions appeared to present.
The first assumption was now far less attractive, at least to me. There is no reason to assume that the grammar alone determines semantic interpretation. Being one factor among many leaves LF/CI interface issues plenty interesting. The second reason stands. If Barker is right, then it looks like we need to rethink the analysis of ACDs. Some have started doing so, attributing ACD licensing to something like extraposition (Baltin, Fox-Nissenbaum), or ‘afterthoughts’ (Chomsky). At any rate, the free ride that the QR analysis of ACDs enjoyed by piggy backing on the “independently motivated” rule of QR is probably over.
I confess that I have always found QR a bit unsavory. It didn’t really function like other A’-movement operations (too many landing sites), it really was hard to find overt versions of it (something unexpected if analogized to Wh-movement), it enjoyed different properties than other forms of A-movement (it doesn’t require obligatory reconstruction for if it did it could not license ACDs, but quantified RCs cannot generally drag their sentential parts along for the covert ride for if possible principle C would be systematically violated) etc. Barker’s paper suggests that we need to rethink not only the c-command condition on binding and scope but the standing of QR as a grammatical operation.
 Dave Kush (p.c.) noted that the sufficiency of c-command for scope is quite interesting. Why should it be that a’s c-commanding b is sufficient for a to scope over b. One can imagine systems where the two notions are entirely divorced and that some c-commanding elements cannot scope over elements they c-command. Interestingly, one of Reinhart’s tests for bound variable readings of pronouns does seem sensitive to c-command:
(i) John loves his mother but Bill doesn’t (sloppy ok)
(ii) John’s father loves him but Bill’s mother doesn’t (no sloppy)
(iii) Everyone from NYC loves its subway. Does everyone from Boston? (no-ish sloppy)
I find the sloppy readings in (ii) and (iii) marginal at best, though I can be convinced that I am wrong about this.
 Earlier work in the mid 80s by George Wilson and Jeff King treats certain cases of bound pronouns as flagged variables in a natural deduction system. This approach also dissociates binding and scope from c-command.
 May’s subsequent work also proved influential.