Scope shift: an interface repair strategyTanya Reinhart, 2003

This is section 7 of chapter 2 from Interface strategies: Reference-set computation, to appear in MIT Press.

7.1. Minimize Interpretative Options.................................................................................................17.2. Applying the illicit QR as a repair strategy.................................................................................37.3. Complexity factors with indefinite numerals - the size of the reference set...............................7 References......................................................................................................................................19

[Note: In the previous sections on QR, I argued that it is, in fact, a much more restricted operation than standardly assumed. In the clearest instances of what appears as scope outside of the c-command overt domain, the relevant NP is indefinite (or an existential quantifier). However, these cases are captured, independently of QR, by a choice-function mechanism, proposed in Reinhart (1997), which interprets them in situ, so QR does not apply to generate the apparent scope shift. Nevertheless, there are cases of genuine scope shift, for which we still need QR. These are the subject of the present section.]

7.1. Minimize Interpretative Options

Though QR can be viewed just as a standard instance of a movement operation, it still poses conceptual problems. As I mentioned throughout this chapter, the problems were always there, but they are more acutely noticeable in the framework of the minimalist program. As we saw in chapter 1, the original theoretical goal in that framework was to allow movement (overt or covert) only for formal morphological reasons of checking features. That was captured by the econcomy condition (101) (discussed as (1) and (47) of chapter 1).

101) "If a derivation D converges without application of some operation, then that application is disallowed" (Chomsky 1992, p. 47)

Although it is possible, of course, to introduce some arbitrary feature that justifies QR, this goes against the spirit of the program, since there is no morphological evidence for such features. In the case of quantifier scope, this movement is motivated only by interpretation needs, and it is only witnessed at the inference interface.

As I mentioned in section 3 of chapter 1, it is not obvious that the strong restriction in (101) can be maintained for overt movement, because there is growing evidence that optional overt movement, not required for any morphological reasons is available across languages. Nevertheless, the basics of the minimalist program enable us to state the problem with free covert movement.

Recall (from the introduction), that the elementary requirement of the computational system is to enable the interface, what has always been stated as relating sound to meaning. The final outputs of the system can be viewed as pairs <p,i> of a phonological representation and an

interpretation representation. This relation is mediated by syntactic derivations. We may either assume that the relevant properties of these derivations are encoded in the phonological representations, as assumed in the theory of phonological phrases, or that in generating the <p,i> pairs, the computational system is operating on <p,d> inputs, of a phonological representation and a derivation, yielding <p,i> outputs. I will return to these questions in chapter 3. We may note now, that the more interpretations that can be associated with a given phonological representation, the more complex is the computation at the context interface - the computational system must generate more <p,i> pairs for each derivation, which is not necessarily problematic, but at the interface, only one such pair needs to be selected in the given context. The more there is to select from, the harder is adaptation to context.

There are several views regarding what economy considerations are (what is ‘economy’). A prevailing approach, which I examined in chapter 1, is that these considerations minimize computational effort within the computational system itself – the ‘least effort’ conditions. However, if we look at the problem from the perspective of the context interface, or more generally – of language use (communication) – a principle that would be extremely useful is to attempt at minimizing interpretative options associated with a given phonological representation.

It may appear that by this reasoning, a perfect computational system should allow no ambiguous phonological representations at all. But this is certainly not a possible conclusion. The crucial requirement is to meet the interface needs to begin with. There is no way to know that a system with no ambiguity would allow all that is needed for the inference and context systems – it may just be too poor, hence fail the interface requirement completely. In any case, we do know that the given human computational system allows ambiguity, just as it allows different derivations with the same interpretation.

But when it comes to covert movement, special attention is required to the context interface. This is a powerful mechanism that can associate with each single phonological representation several interpretations, obtained by movement not recoverable from the phonological representation itself. (Since QR is not clause bound, the number of possible scope-interpretations increases rapidly when the derivation includes one or more clausal complements.) This is an obvious area where an interface economy requirement to minimize interpretative options would be very useful.

The economy requirement (101) is of the type aiming at reducing the number of possible derivations out of a given numeration. In the case of overt movement, this has nothing to do (if it holds) with minimizing interpretative options, because overt movement changes also the phonological representation, so the number of <p,i> pairs per derivation does not increase, in principle, with applying as many overt operations as we want. (An accidental increase as an outcome of overt movement is possible, of course.) But if it applies to covert operations only, then it is a restriction on interpretative options, since covert operations of the QR type increase, in principle, the number of interpretations associated with a single phonological representation. Let us, then, restate (101) as (101').

101') If a derivation D converges without application of some covert operation, then that application is disallowed

(101') as well may turn out too strong as formulated. My crucial claim here is that some prohibition against covert operations that increase, in principle, the number of interpretative

options associated with a given phonological phrase must hold, if the computational system meets optimally the requirement of economy (efficiency) of the context interface.

(101'), on this view, is just a specific instantiation of the broader economy principle 'minimize interpretative options'. As I mentioned, the prevailing concept of economy has centered around the 'least effort' principle. Given that most arguments for such a principle came from syntax, and they no longer hold in current syntax , as we saw in chapter 1., it is appropriate to doubt whether such a principle is directly active at the interface. An interface instance where it has been previously assumed is the coreference restriction (Rule I), where variable binding was viewed, since Reinhart (1983), as a more efficient way to express anaphora than coreference. The 'least effort' view of this restriction is emphasized in Reuland (2001), who argues that computations applying at the interface (coreference) are always more costly than those applying at the CS (variable binding). However, I argued in Reinhart (2000) that there is a serious empirical problem with the 'least effort' approach to coreference, and suggested instead that the underlying economy principle is something like 'minimize interpretative options'. I turn to the way this works for coreference in chapter 4. Here let me just state a rough approximation of this principle.

(102) Minimize Interpretative OptionsUnless required for convergence, do not apply a procedure that increases the number of interpretations associated with a given single PF.

'Least effort 'is, of course, a very broad principle, that does not specify exactly what counts as effort. It is possible, therefore, to view (102) as spelling out an instance of this broad princi-ple. Increasing the number of interpretations associated with a given PF, increases also the effort required from the addressee (hearer) for identifying all interpretative candidates and se-lecting one in context. So having (102) as a principle that guides the application of interpre-tative procedures also conforms with 'least effort'.

7.2. Applying the illicit QR as a repair strategy.

By what I said so far, QR is not allowed at all, namely it is an illicit operation, ruled out by (101'). But, the whole point of this chapter was to argue that it is nevertheless needed in a restricted set of cases. On the approach outlined in chapter 1, illicit operations may still be used, in case the outputs of the computational system are insufficient for the interface needs of a given context. Thus, applying an illicit operation is a strategy used to extend the options permitted by the CS, and can be viewed as a repair mechanism. But its application still violates a condition of the CS. (In the case of QR, it increases the set of interpretations associated with the given PF). Therefore, their application comes at the cost of constructing a reference set to determine whether the illicit extension of the CS' limits is indeed justified. We may turn now to the view of QR as a repair strategy. The roots of this approach are in the view of QR as a marked operation.

The markedness approach, stated in semantic terms, was proposed by Keenan and Faltz (1978), who argue that lambda abstraction applies only to capture marked scope. I followed that idea within the LF framework in Reinhart (1983, chapter 9). The approach rests on the well motivated assumption, in the framework of generalized quantifiers, that to interpret quantified NPs, there is no need to ever raise them. The only motivation for movement is to obtain scope wider than their c-command domain at the overt structure. But this scope-shift is the marked case, and it is harder to obtain than the overt c-command scope. It is far from obvious, therefore,

that the computational system should be dramatically modified just to capture the marked cases. I proposed, instead, that the standard interpretation of quantified NPs is in-situ, namely their scope is their overt c-command domain. But QR may apply to create alternative scope construals. Scope outside the c-command domain, then, requires a special operation, which does not apply in the case of interpretation in situ. Interpretations derived by this operation then are more costly. This may explain why they are marked and harder to obtain1.

As mentioned in section 3 of chapter 1, the concept of markedness was always a bit vague, and the notion of a costly operation was not defined. However, the perspective of reference-set strategies at the interface enables us to give it more specific content. A marked operation is an illicit operation, which violates some principle of the computational system. Applying such operation requires checking that there is good reason to do this, namely that this is indeed the only way for a given derivation to meet the interface needs. Technically, checking this involves constructing and computing a reference-set of pairs <d,i>, of a derivation and its interpretation, all with the same input (numeration) and the same interpretation. If the set contains a derivation that does not use this operation, its application is ruled out. It is the fact that reference-set computation is required, then, which makes the operation costly.

The idea that QR is a marked and costly operation rested originally on the intuition that it is harder to obtain wide scope of universal quantifiers outside their c-command domain. This intuition found support in empirical studies of Gil (1982), where non-linguist subjects across languages were asked to identify scope construals of sentences. Gil found that although non-overt scope exists in such cases, the preferred reading (statistically) is overwhelmingly the overt one.

Nevertheless, such considerations are not sufficient to establish decisively the claim that QR is not a free operation, but rather a costly one. In principle, there could be all kinds of performance factors that determine why one interpretation is preferred over the other, and the decisions regarding the structure of the computational system should not, normally, be based on statistical frequency, or other performance considerations. Hence, there seemed to be no independent evidence that QR applies only when needed to obtain scope wider than overt c-command, and the debate concerning the status of QR seemed for years to be purely theory internalThe first direct evidence that QR does not apply freely was provided by Fox’ (1995, 2000) findings, which I surveyed in section 2 of chapter 1. A problem with covert movement is that we normally have no direct access to check how and whether it applies (since it has no effect on the phonological representation). However, Fox provided a way to do that, using ellipsis structures.

1  ?This statement of the underlying idea is from Reinhart (1983), p. 197-198. It still faces one empirical problem with quantified NPs which are complements of N, as in (ia). It was noted in Reinhart (1976) that this is the only structure which systematically goes against the generalization of overt c-command scope. The most available (perhaps even the only possible) scope construal is with the lowest QNP (inside the NP) taking widest scope. This is seen more clearly when there is further embedding, as in (ib).

i a) Some gift to every girl arrived on Xmas eve.b) Some gift to every girl in two countries arrived on Xmas eve.

I could only face these cases with an ad-hoc rule, and, indeed, May (1977) pointed out that these structures, which he labeled 'inverse linking', are the strongest argument for a QR view of scope. Within the view of QR as a marked operation, these cases should be interpreted in situ to yield this result. But I still have to leave the question how this happens open here.

Recall that the problem (noted by Sag (1976) and Williams (1977) was why the ambiguity of (103a) disappears when it is placed in the ellipsis context of (103b).

103 a) A doctor will examine every patient. (Ambiguous)b) A doctor will examine every patient, and Lucie

will [ ] too. (Only narrow scope for every patient)

104 a) Every patient1 [a doctor will [VP examine e1 ]]b) and Every patient1 [Lucie will [VP examine e1 ]]

The scope construal of (103a) which disappears in the ellipsis context is that obtained by raising every patient covertly, as in (104a). Since we know that this construal is possible for (103a), in isolation, the explanation for the ellipsis context must rest on what happens in the elided conjuncts. The parallelism requirement on ellipsis determines that the scope construal in both conjuncts should be identical. Hence, to derive the reading (104a) in this context, the elided conjunct should have the structure (104b), where every patient raises covertly, in the same way. Fox argues that this construal is illicit, because the movement has no effect on the interpretation - (105a), where this movement applies covertly, is precisely identical in interpretation to (105b), where it does not.

105 < a) <Every patient1 [Lucie will [VP examine e1 ]] For every patient x, Lucie will examine x>

b) < Lucie will [VP examine every patient] For every patient x, Lucie will examine x> >

As we saw, the way this is computed, technically, is that applying QR requires the construction of a reference set consisting of pairs <d,i> of a derivation and its interpretation. So the reference set for (104b, 105a) is (105). Since this set contains the pair (105b) with the same interpretation but with a simpler derivation, (105a) is ruled out.

If QR applies freely, there can be no difference between (104a) and (105a). In both, the operation applies to (the same) quantified object. Thus Fox provides a proof that QR is, in fact, not free, and it needs to be checked against the interpretative effects it produces. This example is particularly interesting, since there is even some context pressure to allow QR to apply here. If it does, it would allow the conjunction (103b) to have the interpretation (104), which is not obtainable if we do not apply QR in the second conjunct (104b). However, Fox points out that affecting the interpretation of a neighboring derivation does not count as a sufficient reason to apply an operation illicitly. It is only if this operation produces a new interpretation for the given derivation itself, that it is allowed.

As I mentioned in chapter 1, Fox coaches his analysis in terms of the Minimal Link Condition (–MLC). He still assumes that QR is an obligatory operation for all quantified DPs. Hence it does apply also in (105b), but VP internal arguments are constrained by the MLC to move only to a VP- initial position. If they move further, as in (105a), the MLC would allow this longer link only if it has an interpretative effect. However, this assumption that QR is obligatory has no empirical basis, and it rests only on theory internal considerations. Recall that what is at stake here is the question whether the interpretation of quantification requires obligatorily an operation like QR. On the standard QR view, QR is an obligatory operation which is assumed to be necessary, e.g., in order to create the variable bound by the Q operator, regardless of

whether the final scope is isomorphic to the overt c-command domain, or not. On the alternative view, QR is not required for the interpretation of quantification, but it is only an optional operation for obtaining scope-shift. Whatever is needed for the interpretation of generalized quantifiers can be captured directly at the stage of assigning a semantic representation to sentences, as done in the Montague, or generalized quantifiers, tradition. (It is not necessary to assume that each lambda operator required in the semantic representation corresponds to a variable in the syntactic representation.)

The least we can conclude is that precisely the same results obtained in Fox’ analysis, are obtained in a system where QR is an illicit operation, which never applies at all, unless forced by relevant interface needs. We saw in chapter 1 that in recent developments of the minimalist program, the reference-set MLC, as originally stated, has no other evidence or use in the computational system. Forcing an otherwise superfluous QR movement, just so it can obey this otherwise unneeded condition, does not seem to be an optimal move.

We should note another implication of the MLC view of QR, which may have empirical consequences. As stated, this view entails that reference-set computation is required for every derivation that contains a quantified argument (and a two place verb). Since in such cases QR should apply obligatorily, we have to consult the MLC to determine the landing site of the moved argument. The MLC, in the version under consideration, involves constructing a full reference set of <d,i> pairs in each case. Thus, consider again the derivation of the sentence under consideration, repeated in (106), but this time with no specified context.

106) Lucie will examine every patient.

107 < a) <Every patient1 [Lucie will [VP examine e1 ]] For every patient x, Lucie will examine x>

b) < Lucie will [VP every patient1 [VP examine e1]]] For every patient x, Lucie will examine x> >

The sentence contains the quantified DP every patient. This DP has to undergo QR during the derivation. In principle, it could adjoin to either VP or IP. To decide where it should go in practice, we need to construct the reference set in (107). Since the interpretations are identical, and (107b) is the shorter link derivation, (107b) will be selected as the only possible derivation. Note that this is the logic of the system –reference set computation must apply just to decide which is the correct landing site. If reference-set computation comes with a visible processing load, as I argued in section 3 of chapter 1, this means that (106), and all (relevant) sentences with a quantifier, are harder to process then the same sentence with a referential argument. In other words, all sentences with (a two place verb and) a quantifier are equally marked, in the sense described above, since they all involve the costly reference-set computation, regardless of which scope construal is selected. Though this has not been empirically tested, I do not expect to find this as an actual result.

Under the alternative view I proposed here, a reference set needs to be constructed only if we are considering applying the illicit QR. Only when this happens, there would be a computational cost. And normally, we expect this to happen only if there is a contextual reason to want to do that. Otherwise, condition (101') (no covert movement for needs other than convergence) will apply and block this option from consideration.

This example illustrates a general difference between the view of reference set computation as applying freely in the syntax, and reference set computation as a repair strategy at the interface. The first is the standard case in optimality theory. In that framework, even the simplest derivation is a selection from a set with worse competitors. Hence, as I explained in chapter 1, optimality theory entails that the parser cannot be transparent, and in actual language use, the phonetic inputs are computed by algorithms that bypass the computational system. In a mixed system like the early minimalist program assumed by Fox, the parser may be still be transparent, with the isolated cases of reference-set computation as the exception.

In any case, under the view that reference set computation is involved in each derivation containing a quantified expression, it is not possible to explain why derivations with scope-shift are harder to obtain, or more marked then derivations with no such shift. In both cases, the selection of an interpretation requires the same costly computation. 2

7.3. Complexity factors with indefinite numerals - the size of the reference set3

Another potential indication of the costly nature of the scope-shift operation is the vast disagreement on the data in the linguistic literature. We noted already in passim some of the history of such disagreements. Thus, in the seventies, it was debated whether sentences like (108), allow indeed wide scope construal of the object quantifier.

108) Some tourists visited every museum.

I argued in Reinhart (1976) that "in spite of earlier reports in the literature” sentence like (108) could not be ambiguous and “the universal cannot have scope over the subject” (p. 193). I later retracted this position in favor of a marked QR operation. But the same type of categorical verdict surfaced again in the nineties with other problems of scope-shift. In 1992, Ruys argued that "in spite of earlier reports in the literature, which may have been founded on simple extrapolations from data with strong quantifiers, rather than on actual intuitions, it seems to be impossible for the object in [109a] to be interpreted with scope over the subject [in the distributive construal]”. (Ruys (1992), p.106-107)

109 a) Three men lifted two tables.b) X (two (X) & tables (X) & X Dλz (Y (three (Y) & men (Y)) & y lifted z))

Under the distributive wide scope construal of two table, represented in (109b), the sentence means something like Two tables were each lifted by three men. This construal can be true in a situation where six men were involved in the lifting of the tables. It is, indeed, virtually

2 The same question arises for approaches building QR into the numeration, as in Chomsky (1995), which I discussed in chapter 1. On that view, some feature like 'QUANT' must be included in the numeration, to license QR . This functional feature will be allowed into the numeration only if it has an effect on the output, namely, if the interpretation obtained is not identical to what will be obtained without this movement. If this is so, there is, in fact, no concept of markedness. When an operation like QR is needed for interpretation, it ends up indistinguishable in status from any other economical operation. Thus, we have no obvious explanation for the fact that quantifier scope outside the c-command domain was found, empirically, to be harder to obtain, and less common.

3 I thank Eddie Ruys for intensive discussions and comments on this section.

impossible to associate sentence (109a) with such a model.

The conclusion Ruys drew from this fact (which was first noted in Verkuyl, 1988) is that plural numeral indefinites can never have wide distributive scope. This view has been widely accepted in the nineties, and was built into the theory of Ben-Shalom (1993), Beghelli and Stowell (1995), Kamp and Reyle (1993) and Szabolcsi (1996). In these approaches, it is assumed that scope-shift of universal, or all strong quantifiers, is fully free and productive. But in the case of numeral plural indefinites, it is not allowed, either because such DPs cannot undergo QR, as proposed by Ruys, or because the distributive operator is too low to allow the subject to be in its scope, which is, roughly, the spirit of the analysis in Beghelli and Stowell (1995).

Although the judgment of (109) is pretty robust, we should still note that judgments of scope shift are known to vary with contexts. Thus, what eventually settled the previous debate regarding the status of (108), was that much more convincing examples were found, which show the existence of scope-shift with universal quantifiers. Typically, they are found where the overt scope results in a contextually weird interpretation. In the case of covert universal scope, one such example is (110), discussed by Hirschbuhler (1982) in a different context. The overt scope would yield here the reading that one flag was stretching over all buildings, which is highly unlikely.

110) An American flag was hanging in front of every building.

111 a) An American flag was hanging in front of two building.b) A guard stood in front of two buildings.

As noted already in section 4., in the same context, numeral indefinites can be interpreted with wide distributive scope, as in (111). (111a) can clearly mean that there were two buildings such that in front of each, an American flag was hanging, and this, in fact, is the interpretation that would first come to mind. Namely, this is the wide scope distributive reading of two buildings. The same construal is found also in (111b). If numeral indefinites cannot scope out, which would explain the unavailability of wide distributive scope for two tables in (109), it should also not be available for two buildings in (111). But the fact of the matter is that the sentences in (111) do have the distributive reading.

It appears that the state of the arts regarding covert scope-shift remains as already described in Ioup (1975): Its availability varies dramatically with contexts and with the individual quantifiers. As long as we do not reach clearer generalizations, beyond mere lists, there is no reason to take one of the contexts as more representative of the behavior of scope-shift than the others. Theoretically, we may as well take (111) as the representative example, and leave open the question why it is so difficult to obtain the same reading in (109). A more ambitious task would be to search for generalizations that may explain this dramatic variation. Let us pursue here the line that is opened by the view of QR as an illicit operation.

There appear to be two completely independent factors that determine the ease of obtaining scope shift. One, which we already noted, is the strength of the contextual need to apply QR. Under the present view, QR does not apply, unless there is an interface need that requires it. A strong need of this sort is consistence with world knowledge. As noted above, following Winter (1997), when the overt scope is inconsistent with world knowledge, it is easier to perceive the scope-shift reading.

112 a) A flag was hanging in front of twenty buildings.b) A bomb blew up five monuments across the world.

113 a) A police truck towed away twenty cars.b) A student read every book.

In (112), world knowledge discards as unlikely the overt scope reading and scope shift is preferred. But in (113), there is nothing in the world to determine which of the two scope construals is more likely. Under the present view, applying scope shift is always costly, because it requires reference set computation. Given that there is nothing in the context that forces opting for scope shift, the preferred option would be to assign the sentence the overt scope interpretation. This explains the experimental findings in Gil (1982), where the overt scope construal was overwhelmingly the preferred interpretation, regardless of the type of quantifier used. It is important to note, though, that we are examining here sentences in isolation. Uttered in a discourse context, there are many other interface needs that may force a scope shift even in sentences like (113). Among these contextual factors are topic and focus considerations, and the fact that specific indefinites resist scope dependence. It is also known since Ioup (1975) that some quantifiers (like each) may force a preference for distributive wide scope even when it involves scope shift.

However, such contextual considerations are not sufficient to explain the full range of the facts examined above. In (113) it is possible to construct, with the appropriate context, a scope-shift interpretation, but in (109), repeated, it is much harder to imagine a context that would enable that. It remains virtually impossible to take (109) to mean that up to six men were involved in lifting the relevant two tables.

109) Three men lifted two tables.

Furthermore, Beghelli and Stowell (1997) point out that even in contexts like (111) and (112), cited in Reinhart (1995) as examples for the availability of scope shift with numeral indefinites, this shift is not always possible. If we replace the singular subject with a plural numeral indefinite, scope shift becomes as difficult as in (109).

114 a) Three flags were hanging in front of two buildingsb) Five guards stood in front of twenty buildings.

The sentences in (114) have a funny air. The only reading that can be obtained is the one inconsistent with world knowledge (same five guards are simultaneously in front of twenty buildings).

There must be some internal properties of the sentences in (109) and (114) that restrict the option of scope-shift. But what can these be? The standard approach, as we saw, has been to search the answer in the computational system itself, specifically within the internal properties of the moved constituent. These approaches view QR as part of the computational system, and search for restrictions on its operation, stipulating e.g. that plural numerals cannot undergo QR. This has a theoretical cost - QR can no longer be viewed as just a free application of the move operation, because special restrictions are needed on which constituents can move and where. This requires stipulating various abstract features corresponding to different quantified DPs, and functional projections that host these features.

Still, with this massive enrichment of the machinery of the computational system, this approach cannot, anyway, explain the difference between (112) and (114).

Beghelli and Stowell (1997) propose an enrichment of the computational system that does capture this difference. First they assume that the distributive operator (their "silent each") has a fixed position lower then the external subject position ("between AGRS-P and AGRO-P"). It is only up to that position that the internal indefinite can move. Thus, to begin with, the subject is not in the scope of the moved indefinite and its distributive operator. To enter this scope, the subject needs to reconstruct to its original theta position (in Spec VP). In (112) this reconstruction takes place, so a flag in (112a) ends up in the (distributive) scope of two buildings. But the subject cannot always reconstruct. Beghelli and Stowell argue that only "simple indefinites" which they define to be singular indefinites and bare plurals can do so. All other indefinites, like the plural numeral subjects in (109) and (114), or Generalized Quantifiers indefinites (like less then three guards) must be interpreted in their surface position. Hence, the relevant scope shift cannot be obtained in (109) and (114).

The insight underlying Beghelli and Stowell's analysis is that it is not just the properties of the VP internal DP that determine its ability to take wide distributive scope, but the properties of the subject have an effect as well. However, the question remains whether their implementation of this insight is on the right track. More generally, the question is whether this is a problem of the Computational System or of the interface.

Note again the cost to the computational system, if enriched the way Beghelli and Stowell propose. Along with all the previous features and functional projections that govern the movement of quantified DPs, we now need some mechanism restricting reconstruction. It is far from obvious that reconstruction should be governed by feature compatibility at all. But if it does, it is not clear what independent property distinguishes precisely these two instances of "simple indefinites" from all other indefinites, namely, which feature is coded.

But the crucial question is empirical - Is it indeed possible to approach the problem with a list of the DP subjects that prevent scope-shift (or cannot reconstruct)? Turning to this empirical question, we may note the judgments of examples in this section may appear subtle, and many of them have not been previously discussed or judged in the literature. To verify my intuitions, I tested all examples (in Hebrew) with a couple of non-linguist informants, using a method specified in a footnote4.

4 Linguists may have biased judgments on sentences that have an established judgment in the theory, but the sentences under consideration lend themselves easily to testing with non-linguists, because they can be followed with questions about the number of objects or people participating. In examples like (i)-(iii), the topmost number allowed for the set denoted by the subject, if QR applies is given in parenthesis. Presenting a sentence like (ia), I asked: Assuming that there are 5 tables, how many table-cloths there are?. For (iib) the question would be: How many doctors will examine patients? If the informant gives the narrow scope answer - one, the next question would be: Could there be more, e.g. 10 doctors?

(i) a. A tablecloth covers every table. (Up to as many tablecloths as tables)b. A doctor will examine every patient. (Up to as many doctors as patients).

(ii) a. A tablecloth covers two tables. (Up to two tablecloths)b. A doctor will examine ten patients. (Up to ten doctors)

(iii) a. Two doctors will examine ten patients. (Up to twenty doctors)

Let us look at the minimal pair in (115), where (115a) repeates (114a).

115) a) Three flags were hanging in front of two buildings.b) Three identical flags were hanging in front of two buildings.

Unlike (115a), (115b) can be easily interpreted as asserting that in front of each of two buildings, three identical flags were hanging. While in (115a) the interpretation allows for only three flags (which makes it difficult to imagine the situation described by the sentence), in (115b) the preferred interpretation is that there were all together six flags. The DP three identical flags is not "simple indefinite" by Beghelli and Stowell's definition, and still, in their terms, it can reconstruct. To make sure this is not some peculiarity of the specific linguistic context in (115), let us examine other contexts.

116 a) Two simultaneous questions confused fifteen subjects in the experiment. (The others did fine with two simultaneous questions.)b) Ten matching answers brought two couples to the final round [in a televised couples-contest].c) Two subsequent meetings took place in three offices.

In (116a) it is not necessarily the case that the same simultaneous questions confused all thirty subjects. Similarly, in (116b), there is no reason to assume that the two couples got the same matching answers, namely, the wide scope distributive reading where each of the two couples got ten (possibly different) matching answers is readily available. In (116c), each office could host a different set of two subsequent meetings, namely there could be up to six meetings in these three offices.

What the sentences in (115b) and (116) have in common is that they disfavor a distributive interpretation of their subjects. Roughly, this is because the property of being simultaneous, identical, subsequent or matching does not distribute among members of the set. (The set of subsequent meetings is not a set each of whose members is a subsequent meeting.) Given this observation, we can also note that this is, in fact, the property shared by Beghelli and Stowell's set of "simple indefinites". Singular indefinites obviously cannot have a distributive interpretation, and for bare plurals, this interpretation is extremely difficult to get.

Nevertheless, having found a shared property of the subjects that do allow scope shift of the object does not mean we can define the relevant set of DPs that can reconstruct in terms of their internal properties, say, the set of 'non distributable' DPs. Any numeral DP can be disambiguated to allow only the collective interpretation by using an adverb like together. It turns out that in this case, scope shift is allowed, regardless of the internal properties of the subject:

b. Three men lifted two tables. (Up to six men)

For (ii), I was able to solicit a yes answer to the second question in all my informal testing. For (iii), it was impossible to convince the informants to consider the option that there were twenty doctors or six men involved. The same method was used in the examples to follow below. Although my testing was in Hebrew, the area of semantic judgments of quantifier scope is not, to my knowledge, subject to variations between Hebrew and English.

117 a) Four guests sleep in two rooms.b) Four guests sleep together in two rooms.

118 Three Canadian flags were hanging together on two buildings.

(117a) is the standard case where object scope shift is impossible - the sentence can only be understood as involving four guests. However, in (117b) it is possible to construe the situation as involving eight guests, namely in each of the two rooms four guests are sleeping together. Similarly, in (118) it is possible to construe the depicted situation as involving six flags. These construals can only be obtained if the objects have wide distributive scope.

The descriptive generalization seems to be that if in a given derivation the subject could (potentially) be interpreted distributively, scope shift of the object is not allowed. But, Crucially, we are concerned here with the potential of the subject to be distributive, not with the question whether it in fact is. In the derivations where scope shift was found impossible, like (117a), (114) or (109) (Two men lifted three tables), the subject is indeed of the type that can be distributive, but it is not actually interpreted distributively in the derivation under consideration. Namely, the scope shift derivation is ruled out even if we interpret the subject collectively. Why should scope shift of the object depend on whether the subject could, in principle, be interpreted distributively in another LF derivation?

Generally, when properties of the derivation are not absolute, but depend on its relations to possible other derivations or interpretations, this is an indication that reference-set computation is at work. Let us turn now to what could explain the pattern under consideration within the interface view of QR, which involves such computation.

Even a brief checking of the problematic derivations above (like (117a) reveals that the reason that scope-shift is ruled out cannot possibly be that the same interpretation is obtainable without QR. QR is the only way to obtain the relevant reading, and furthermore, we saw that there is a very good contextual reason to want to apply QR here. But I will argue that the reason why the relevant readings cannot be derived, despite this fact, is that the computation involved in deciding the matter is too costly. The need to construct and compare a reference set is costly to begin with. However, in all cases considered so far, this is a cost that at least adult speakers can bear. (In chapter 5, I argue that children cannot.) An aspect of the computational cost that we have not considered so far is the size of the reference-set. There may be a limit to how much even adults can hold in their working memory while attempting to satisfy the interface requirements.

To see this, let us first review briefly again the procedure of constructing a reference set. When the option of applying the illicit covert movement operation is considered, we need to construct a <d,i> pair of the intended derivation. We then need to find out whether the same i(nterpretation) is not available without applying QR, namely whether the same interpretation cannot be associated with the overt derivation. Strictly speaking, the only way to find that out is by running through all the interpretations of the overt derivation. This task is sometimes relatively simple, as in the case of (119)

119 a) A flag was hanging in front of every building.f (CH (f) z (building (z) f(flag) was hanging in front of z))

b) [every building] [a flag was hanging in front of e] z (building (z) f (CH (f) f(flag) was hanging in front of z))

120) A student read every book.

In (119a), the only scope construal possible at the overt structure is with the universal quanti-fier in the scope of the existential. What is under consideration is applying QR, to obtain (119b), in which their scope is reversed. The two <d,i> pairs considered, then, are (119a) and (119b). (Nothing hinges in this discussion on the choice-function mechanism used to rep-resent the interpretation.) Since the interpretations are distinct, nothing rules out (119b). In this case, the evaluation of whether QR is permitted requires considering a minimal number of just two <d,i> pairs. This is a standard cost of reference-set computation. Whether scope-shift is easy to obtain in such derivations depends only on the contextual needs. Since in (119) world knowledge disfavors the overt scope construal, the reference set is constructed and the scope-shift construal admitted. Obtaining this scope shift in (120) requires precisely the same steps and reference set. However, as we saw, since there is nothing in the context that would lead us to attempt a scope shift to begin with, the option would not arise in isola-tion, which accounts for the feeling that it is harder to obtain in this case. (As mentioned, there may be also other contextual factors that effect the ease of obtaining scope-shift).

But let us now look at the computation that scope shift requires in a derivation with two plural numerals, such as (121a), which has been the problem under consideration here.

121 a) Two flags are hanging in front of three buildingsb) [three buildings] [two flags were hanging in front of e]

We are considering whether the QR derivation (121b) is allowed. For this, it is necessary to check whether the interpretation it would generate is not available also without applying this illicit operation. In order to determine this, all scope construals possible in (121a) need to be listed and checked. It turns out there are quite a few of those. For ease of presentation, I will represent them only informally here.

First, there is the choice function (collective) interpretation of both indefinites, which is summarized in (122a). (In fact, (122a) stands for two equivalent representations, a point I return to it directly.) In this construal the situation involves two flags and three buildings.

122 a) Choice functions: There is a set x of two flags and a set y of three buildings, such that x is hanging in front of y. (two flags, three buildings)

Distributive subject:b) There is a set of two flags, such that for each flag x in this set, there is

a set y of three buildings, and x is hanging in front of y. (two flags, six buildings)

c) There is a set of three buildings y, and a set of two flags such that each flag x in this set is hanging in front of y. (two flags, three buildings)

Next, the overt derivation (121a) allows also a distributive interpretation of the subject,

where each member of the two flags set is considered. Recall that in the present view, this option requires no further covert movement. Distributivity is just an interpretative procedure that applies to the overt structure. So it is one of the interpretations of (121a) that need to be considered. The internal three buildings can only be interpreted via a choice function (collectively). But the existential closure of the function variable can be either inside or outside the scope of the distributive subject. There are, thus, two scope construals under the distributive interpretation of the subject. In the narrow closure in (122b), the situation involves six buildings. The wide closure in (122c) ends up equivalent to (122a), but to see that, it had to be listed and computed.

With all these interpretative options activated and stored, we may turn to evaluate the output of the illicit QR in (121b). In principle, the moved three buildings in (121b) could be interpreted collectively, via a choice function. This <d,i> pair, however, would be filtered out, because the interpretation is equivalent to what could be obtained without QR, in (122a), or (122c). But the interpretation that could motivate QR here, is (123b), in which three buildings is distributive.

123 a) [three buildings] [two flags were hanging in front of e]b) There is a set of three buildings such that for each building x in this set, there

is a set y of two flags, and y is hanging in front of x (six flags, three buildings).

This interpretation is indeed distinct from all the others. It is the only one that allows the situation associated with the sentence to involve six flags. So, applying QR here is very well motivated, and the derivation should be allowed.

But while in the case of (119) concluding that QR is allowed required holding and comparing two <d,i> pairs, here the same procedure requires holding four such pairs (in fact, five, as we shall see directly). This may be just too much for the human processor. The difference in the processing load imposed by (119) and (121) is substantial enough to suggest that the problem with obtaining scope shift in (121) is a problem of processing. Since the reference set required for (121) is too big, the computation cannot be completed, so scope shift cannot be approved.

The crucial complexity factor is the availability of the distributive interpretation of the subject, combined with a plural-numeral internal argument, of the choice-function type. This combination always adds two members to the reference set. All the facts we discussed above now follow: If the subject is a singular indefinite, as in (112) no distributive interpretation is possible, so these two extra members are not generated. The same is true when the distributive construal is otherwise not easily available, as with bare plural subjects, or the examples of (115) -(116) with three identical flags, or two subsequent meetings.

It is also clear why subjects that can in principle be distributive cause a problem in such configurations regardless of whether they are in fact interpreted distributively. The logic of the system is that to determine whether scope shift is allowed, all scope construals in the derivation must be checked, to verify that the desired interpretation is not already available without QR. There is no other way to formally verify this, but running through all scope interpretations of the given derivation. The only case a derivation is exempt from this construal is when it is clear that in this specific derivation the subject cannot have the distributive reading. The other instance of such exemption that we observed was (117),

repeated.

117 a) Four guests sleep in two rooms.b) Four guests sleep together in two rooms.

The derivation in (117a) follows the steps examined for (121), and scoping out two rooms is blocked for the same reason of a processing load too heavy to determine. But in (117b), with precisely the same subject, the distributive option is ruled out by the collective adverb together. The fact that the subject could be distributive in another derivation, without this adverb, is not relevant, because what we need to consider is the set of possible scopal interpretations of the given derivation. While the distributive interpretation of the subject is in the set for (117a), it is not in the set for (117b).

It is important to note that considering the full set of possible scopal interpretations is only required when one contemplates applying QR. Recall that, as discussed in section 7.1, QR never applies just to interpret derivations, and given the choice function mechanism, it also does not apply just for standard (collective) wide scope of indefinites. All scope construals except for scope-shift are obtained without QR. Under this view, the fact that (121a) and (117a), allow four scope construals, or that it is (two way) ambiguous, is not relevant when the derivation is normally used at the interface. Disambiguating, or selecting the interpretation appropriate to context, is an altogether different procedure. There is no need to assume that the full set of options needs to be considered. Thus, what I said here does not entail that (121a), without QR, is more complex or difficult to process than (119) (with a singular indefinite subject and a universally quantified object). The only entailment is that the QR interpretation is relatively easy to process in (119), but it cannot be processed in (121) and (117a).

The comparison of (119) and (121) represents two edges of a spectrum of possible reference-sets for QR. A two member-set is relatively easy; a set with four or five members is unprocessable. In between there are other options, where the situation may be less clear.

Thus, let us compare the computation involved in (119), repeated, with (124), where a plural indefinite replaces every building.

119 a) A flag was hanging in front of every building.f (CH (f) z (building (z) f(flag) was hanging in front of z))

b) [every building] [a flag was hanging in front of e] z (building (z) f (CH (f) f(flag) was hanging in front of z))

124) a) A flag was hanging in front of two buildings.fi (CH (fi) (fj (CH (fj) ( fi(flag) was hanging in front of fj(building)))fj (CH (fj) (fi (CH (fi) (fi(flag) was hanging in front of fj(building)))

b) [two buildings] [a flag was hanging in front of e]

125 a) There is a flag x, such that there is a set of two buildings y and x was hanging in front of y.

b) There is a set of two buildings y such that there is a flag x and x was hanging in front of y.

In (124a) both arguments are interpreted with a choice function. Technically, this means that the overt derivation allows two scope construals, depending on where existential closure is applied. This is only a matter of which closure is in the scope of the other, as given in (124a). For convenience, an informal representation of the two options of existential closure is given in (125). The two construals are equivalent, of course, but strictly speaking, if the reference set must include all scopal interpretations of the overt derivation, both options need to be checked. The QR derivation in (125b) would be filtered out if two buildings is interpreted collectively, but here it is interpreted distributively, so the derivation is allowed.

The upshot is that while the reference set for (119) includes two <d,i> pairs, the one for (124) includes three such pairs. (This is also the reason why the reference set for the three flags and two buildings example in (121) includes five members, and not four as assumed above, for brevity. The collective construal of the DPs corresponds to two representations.) Does this difference have a processing effect? It seems impossible to trace any difference regarding the ease of obtaining scope shift in these sentences. But this is also the context where world knowledge strongly favors scope shift. Recall that the theoretical verdict in the literature we started with (following Ruys 1992) has been that plural numeral indefinites cannot scope out at all, namely, independently of what the subject is. This must have been based on observing some actual difficulties with scoping them out also when the subject is a singular indefinite. If we move to a context that does not force an interpretation so strongly, there seems to be a difference in the ease of scoping out between the two types of DPs.

126 a) A tablecloth covers every table.b) A tablecloth covers two tables.

127 a) A doctor will examine every patient.b) A doctor will examine twenty patients.

In an informal checking with non-linguists, my informants interpreted (126a) as involving a separate tablecloth for each table. But the first interpretation of (126b) was with one tablecloth for both tables (though it was possible to convince them that there could also be two separate tablecloths). This is a context that still has a slight preference for the scope-shift construal (since it is more common for tables to be covered with individual tablecloths). In the context of (127b), with no preference imposed whatsoever, it is much harder to imagine the situation as involving more than one doctor. It is not completely impossible, as it is in the two numerals examples, but it takes lots of efforts to construct a context that would enable that interpretation. (E.g. that in the emergency room patients were first examined and screened by interns, who decided that 20 patients require a doctor's attention.) Thus, there seem to be indeed a slightly greater difficulty with scoping out numeral indefinites, and I cannot offer more regarding why it is sometimes more difficult then at other times.

Another indication that it is the size of the reference set that determines the ease of scope-shift, rather then the internal properties of the moved DP comes from examining the complex numerals like more then five, less then five, or at least five. In the literature surveyed (e.g. Beghelli and Stowell (1995)), these are considered the most radical instances of unmovable DPs. It is believed that they are even harder to scope out then the bare plural numerals. In fact, it seems to be the other way around (based again on informal checking with non-

linguists).

128 a) A tablecloth covers two tables.b) A tablecloth covers at least two tables.

129 a) A doctor will examine twenty patients.b) A doctor will examine less then twenty patients.

While in (128a) the preferred interpretation involved one tablecloth, in (128b) my informants preferred the construal with at least two tablecloths, namely the scope shift reading. In the context of (129), which does not impose contextual preferences, it is much easier to perceive the scope shift reading (not necessarily the same doctor) in (129b), then in (129a).

Recall (from section 6.4) that in the present analysis, complex numerals are not interpretable by choice functions. (Kamp and Reyle (1993) argue that they are interpretable only as generalized quantifiers.) For this reason, they do not have multiple scope construals in situ. For the bare plural numerals, like two tables different scopes can be obtained by applying closure at different projections, without moving the DP. But for generalized quantifiers, scope wider then their overt position can be obtained only by movement. This means that when considering their covert movement, the reference set would be identical to the cases of (119), with an internal universal quantifier. It contains only two members - the scope construal in situ, and the scope construal after movement. Hence their ease of scoping out should be identical to that of universal quantifiers, which appears to be the case.

Returning to reference sets with three members, they are found also when a generalized quantifier is scoped over a bare numeral indefinite subject. This is because the subject has in this case two construals - collective and distributive, so the overt derivation comes with two members already in the reference set. One such example is (108), repeated. I am admittedly biased regarding this sentence. In Reinhart (1976) I used it to argue against the idea of QR, claiming that there is no scope shift reading in this sentence. I still find this reading difficult to get (harder than with a singular indefinite).

108) Some tourists visited every museum.

Nevertheless, we should not attach too much significance to the difference between a two-members reference set and a three-members set. There may be a slightly greater processing difficulty associated with the second, but it is also obvious that a three members reference set is not beyond the processing ability of adults, and many other contextual factors may have a bigger effect on the ease of obtaining scope shift in this case, then the size of the reference set.

The crucial distinction we observed in this section is that between the five-members sets (with two or more bare numeral indefinites) and the reference sets with two or three members. The first mark a real limitation of the human processor, so contextual factors can do very little to save scope shift in such cases.

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