Scope shift: an interface repair strategyTanya Reinhart

This is section 2.7 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.....................................47.3. Complexity factors - the size of the reference set.........................11

[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 Options

Unless 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 principle. Increasing the number of interpretations associated with a given

PF, increases also the effort required from the addressee (hearer) for identifying all in-

terpretative candidates and selecting one in context. So having (102) as a principle

that guides the application of interpretative procedures also conforms with 'least ef-

fort'.

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.

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).

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

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.

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 internal.

The 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. 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

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

7.3. Complexity factors - 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)

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.

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 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 buildings

b) 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)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.

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 different 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 different 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 different 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, different, 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:

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

quantifier 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 represent the interpretation.) Since the interpretations are distinct,

nothing rules out (119b). In this case, the evaluation of whether QR is permitted re-

quires 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 ad-

mitted. Obtaining this scope shift in (120) requires precisely the same steps and refer-

ence 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 isolation, 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 buildings

b) [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 different 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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