Scope shift with numeral indefinites - syntax or processing?

To appear in L. Tasmowski & S Vogeleer (eds), Indefiniteness and Plurality, Linguistik Aktuell/Linguistics Today Series, Benjamins. It has been argued extensively that numeral indefinite plurals cannot scope out (Ruys (1992), Beghelli and Stowell (1997), Kamp and Reyle (1993) Szabolcsi (1997)). E.g. it is virtually impossible to interpret Four guests sleep in two rooms as involving eight guests in the reported sleeping event, as would be the case if two rooms receives wide distributive scope. In several approaches, this strong effect is built into the Computational System (syntax), as restrictions on the operation of QR, or more complex feature specification of the syntactic projections that correspond to different quantifiers. But I argue that there are several problems with this line. E.g. in the minimally different Four guests sleep together in two rooms, scoping out of the numeral (eight guests) is substantially easier. More broadly, it turns out that the restrictions on the scoping of numerals are not absolute, but depend on the relations of the given derivation to other possible derivations or interpretations. On the view proposed in Fox (1995, 2000) and Reinhart (1995, 2006), scope shift is an interface repair strategy that is permitted only when it generates a reading that could not be obtained otherwise. This entails that when QR applies, a reference-set must be constructed to determine whether this is indeed the case. The need to construct and compare a reference-set is costly in terms of processing, as it requires holding two or more full derivations in working memory. An aspect of the computational cost that deserves attention is the size of the reference set. In the easier instances of QR (e.g. Some student read every book), the reference set contains only two members - with and without -QR. This is a cost that at least adult speakers can bear. (I argue elsewhere that children cannot.) But when two plural numerals are involved, a careful listing of all members of the reference set reveals five such members. It appears that a reference set with five members is beyond what even adults can hold in working memory, so the computation required to license the scope shift derivation cannot be completed. By contrast, when the subject cannot be interpreted distributively, as in the four guests slept together example, only three members must be activated, which is still within the limits of what can be processed. What has appeared to be a syntactic restriction on scope shift with numerals, is thus, better explained as a processing failure.