It is widely stated that the scope of quantifiers is clause-bound (Chomsky 1977, May 1977, Farkas 1981, 1997, Fodor and Sag 1982, Aoun and Hornstein 1985, Beghelli 1993, Abusch 1994, Hornstein 1995, Fox and Sauerland 1997, and numerous others). This claim is based on the observation that (1a) has no reading in which reviewers covary with plays, while (2a) does.
A reviewer thinks every play will fail this season.
*[TP every playi [TP a reviewer thinks [CP ei will fail this season]]]
A reviewer attended every play this season.
[TP every playi [TP a reviewer attended ei this season]]
Current theories capture the contrast by making Quantifier Raising (QR), the covert syntactic operation that assigns scope to quantified noun phrases (QPs), clause-bound. Only in (2a), in which the universally quantified QP every play and the indefinite a reviewer are clausemates, can the universal QP raise to scope over the indefinite, yielding the Logical Form representation (LF) in (2b). This operation is prohibited for (1a) because the two NPs are not clausemates; hence, the LF in (1b) is illicit.
While this observation seems empirically well-grounded, its theoretical basis is less secure. Such clause-boundedness makes QR rather more restricted than one would expect a representative Ā-movement to be (see Reinhart 1997, Cecchetto 2004 for discussion). In what follows, I recap Fox’s (1995, 2000) theory of Scope Economy, which provides an explanation for QR’s clause-boundedness. I then introduce new data involving the interaction between QPs and certain instances of negation that are problematic for this approach. I conclude by sketching an alternative.
1 An Economy-Based Account of Quantifier Raising
Like many who research QR, Fox (1995, 2000) implicitly adopts what Beghelli and Stowell (1997) call Scope Uniformity: QR applies uniformly to all QPs and is not landing-site-selective. Any QP can be adjoined to any (nonargument) XP where it is interpretable. Further restricting this quite general assumption, economy considerations dictate that QR can apply only if it has an effect on semantic interpretation.1 QR cannot apply if the derivation without it would yield the same meaning.
Scope Economy (Fox 2000:23)
QR must have a semantic effect.
Fox (2000:62–66) proposes that the clause-boundedness of QR follows from Scope Economy. By (3), every application of QR must induce a change in semantic interpretation. At the same time, given that QR is an instance of Ā-movement, each application is subject to locality constraints on movement, which Fox formulates as Shortest Move.2
Shortest Move (Fox 2000:23)
QR moves a QP to the closest position in which it is interpretable.
The impossibility of cross-clausal QR follows from a tension between Scope Economy and Shortest Move. QR that does not obey Shortest Move is illicit, but QR that targets a clausal node, obeying Shortest Move, will not normally yield a new semantic interpretation, violating Scope Economy.
Returning to (1a), the two constraints derive the unavailability of the non-clause-bound reading of the universal QP in this example, repeated below as (5a). Two potential LFs for the wide scope reading of the QP every play are given in (5b–c). In (5b), every play raises directly to a position above the matrix subject; however, this violates Shortest Move since adjunction to the embedded clause is a closer interpretable position. In (5c), the QP every play targets the embedded clausal node to satisfy Shortest Move; however, Scope Economy is now violated because the move has no semantic consequence. As a result, the embedded QP has no extra, wide scope interpretation, as desired.
A reviewer thinks every play will fail this season.
*[TP every playi [TP a reviewer thinks [CP[TP ei will fail this season]]]]
*[TP every playi [TP a reviewer thinks [CP ei [CP[TP ei will fail this season]]]]]
2 Overriding Clause-Boundedness
Fox (2000:63) points out that the Scope Economy account makes a surprising prediction: QR’s clause-boundedness could be overridden if adjunction to CP (as in (5c)) had semantic motivation. Specifically, if the CP projection contained an element that the QP could scopally interact with, then Scope Economy would license cross-clausal movement.
Fox (2000:64) offers one set of data, from Moltmann and Szabolcsi 1994, that instantiates the configuration in (6) and seems to confirm the prediction. In (7), the needed scopal element is a wh-phrase in Spec,CP.
A reviewer knows when every play will fail.
[TP every playi [TP a reviewer knows [CP ei [CP whenj [TP ei will fail ej]]]]]
(7a), unlike (5a), is ambiguous and has a reading in which the embedded QP every play takes scope over the matrix subject: every play is such that some reviewer or other knows when it will fail. The corresponding LF in (7b) is permitted because the intermediate adjunction to CP forced by Shortest Move has the semantic effect of causing the universal QP to take scope over the wh-phrase in Spec,CP. At the same time, Moltmann and Szabolcsi (1994) and Szabolcsi (1997a) argue that cross-clausal QR is not the correct mechanism to derive the wide scope reading in (7). These authors propose an alternative ‘‘layered quantifier’’ analysis that respects clause-boundedness. The goal of this squib is to test Fox’s prediction in a domain that is not open to Moltmann and Szabolcsi’s objections.
An alternative instantiation of (6) that would be suitable for testing the prediction places a negative head in C0, what I will call CPNegation. As is well-known, negation introduces scope ambiguities and should thus be a prime candidate for licensing an application of QR adjunction to CP under Scope Economy.3 As above, in such a situation QR would obey Shortest Move and yield a semantically distinct interpretation, the wide scope reading of the QP with respect to CP-negation. Both of the LFs in (8) should be licensed—that is, whether QR applies or not. (The notation X > Y indicates that X takes scope over Y.)
The data to come show that QPs cannot take scope over CP-negation. The clause-boundedness of QR is in fact not overridden. This is problematic for the Scope Economy–based explanation.
3 Scope Interactions with Negation
It has become increasingly clear that not all QPs have the same scope options (Kroch 1979, Beghelli 1993, 1995, Liu 1997, Szabolcsi 1997b). Beghelli (1995) and Szabolcsi (1997b) identify four non-wh quantifier types:
Negative quantifiers: no
Distributive universal quantifiers: each, every
Group-denoting quantifiers: indefinites (a, some), bare numerals, partitives
Counting quantifiers: few, fewer than, more than, at most, at least, etc.
As Beghelli (1995:136–166) discusses, not all of these quantifiers interact equally with negation.4 In the crucial data to follow, I will use Beghelli’s counting quantifiers, which include complex numerical expressions such as at least three and at most two. They interact scopally with negation, as illustrated by the ambiguity in (10).
4 The Scope Data
There are a number of constructions in English in which negation, in the form of a contracted auxiliary like don’t, occurs in C0. I consider three: imperatives, declaratives with negative constituent preposing, and interrogatives. In all cases, we will see that a potential scope ambiguity between CP-negation and a QP is resolved in favor of a lone NEG > Q interpretation.
Beukema and Coopmans (1989) and I (Potsdam 1998) argue that negative inverted imperatives such as (11a–c) have the desired structure with don’t in C0 and the imperative subject in Spec,TP, as shown in (11d).
Don’t you eat the last piece of cake!
Don’t everyone go!
Don’t anyone tease him!
[CP[C′ don’ti [TP everyone ti [VP expect a raise]]]]
Negative inverted imperatives containing a QP are unambiguous, regardless of the position of the QP (see Schmerling 1982, Potsdam 1998, Moon 1999). (12a), for example, has only the interpretation in (12b), the wide scope reading of negation, and not the interpretation in (12c), the reading where the QP takes inverse scope.
We can sharpen the judgment by placing the example in a context that favors the inverse scope reading. In such a case, the example is infelicitous.
(13) All the student employees want to go away for spring break, but the library has to stay open for the week and at least five students are needed to staff the circulation desk—one for each day. More than four people have to not go on vacation so that the library can remain open. #So, don’t more than four people go on vacation!
The example in (14a) makes the same point in a different way. We can make sense of its infelicity because the only available meaning, the narrow scope interpretation of the QP with respect to negation in (14b), is pragmatically odd. One doesn’t normally place a lower bound on how many test questions someone shouldn’t skip. The inverse scope reading in (14c) is sensible but seemingly unavailable.
The same pattern appears with CP-negation in negative constituent preposing, illustrated in (15). This construction is widely analyzed using T0-to-C0 movement (see Koster 1975, Emonds 1976, Progovac 1994, Haegeman 1995, Rizzi 1996).
Never have we seen such a mess.
Only under duress will Joey share his chewing gum.
[CP never [C′ havei [TP we ti [VP seen such a mess]]]]
An inverted negative auxiliary in this construction also obligatorily takes wide scope with respect to clause-internal QPs.
(17) provides a context that favors the inverse scope reading, but the example is infelicitous. [pa
(17) John is an incredibly difficult professor. Usually, everyone who takes his class fails. This semester, miraculously, Albert took his class and passed it. Everyone else still failed. #Thus, only this semester didn’t John fail at least one student.
Paraphrases with clause-internal negation are acceptable in this context, (18), because the QP can scope over internal negation.
John didn’t fail at least one student this semester.
Only this semester did John not fail at least one student.
Finally, subject-auxiliary inversion in English interrogatives is standardly analyzed in terms of T0-to-C0 movement (e.g., Koster 1975,, Koopman 1984, Chomsky 1986). As above, a QP obligatorily takes narrow scope with respect to CP-negation (Rupp 1998:154, citing Andrew Radford, pers. comm.).
The Scope Economy–based approach to QR clause-boundedness wrongly predicts the above examples to be ambiguous. To illustrate, (20b) is the available LF corresponding to the unavailable interpretation of (12), repeated as (20a).
Don’t more than four people go on vacation!
[CP more than four peoplej [CP[C′ don’ti [IP tj ti [VP go on vacation]]]]]
Raising more than four people from the subject position to an adjunction position above negation satisfies Shortest Move and Scope Economy since it yields an interpretation distinct from the derivation in which it does not apply; nevertheless, the MORETHAN 4 > NEG interpretation is not possible.5
I suggest that the above data are representative of a larger pattern, the CP-Negation Scope Generalization.
The CP-Negation Scope Generalization
CP-negation takes wide scope with respect to QPs in its clause.
Scope Economy derives the unexpected clause-boundedness of QR; however, it does not capture (21) and overgenerates readings in examples with CP-negation. It remains to be determined whether the theory can be modified to avoid these results.6
The inability of a QP to take scope over CP-negation suggests that CP is not a possible target adjunction site for QR, a stipulation made by a number of researchers (e.g., May 1985, Cecchetto 2004). If we assume this, then clause-boundedness may follow in combination with an independently needed theory of successive cyclicity. A core result of research in bounding theory within the Government-Binding tradition and phase theory within the Minimalist Program is that CPs are cyclic nodes for cross-clausal movement (but see Rackowski and Richards 2005 and Den Dikken 2009).7 If CP is simply not a possible adjunction site for QR, then a QP will not be able to raise out of its clause without violating Subjacency or the Phase Impenetrability Condition. We have an alternative answer to the clause-boundedness independent of Scope Economy. If such an approach is on the right track, it nonetheless remains to be explained why adjunction to CP is not a possible landing site for QR.8
1 An exception is that QR is obligatory for semantic type considerations. QR must apply to move a QP from within VP to a position where it can be interpreted, sister to a clause-denoting expression of type t (Fox 2000:23). Thus, the first possible, and required, adjunction site for QR is VP.
2 Cecchetto (2004) uses the more current Phase Impenetrability Condition (Chomsky 2001) as the relevant movement locality constraint.
3 I follow Ladusaw (1988) in assuming that the scope of negation is fixed by its surface position in C0. There is no Neg-Raising or Neg-Lowering at LF. In particular, negation in C0 does not reconstruct to T0. If CP-negation could reconstruct, it would only increase the likelihood of the grammar allowing the unavailable scope readings in (12c), (14c), (16c), and (19c) in which negation has narrow scope with respect to a QP.
4 The negative quantifier no and the distributive universal quantifier each are degraded to varying degrees with negation.
Every-QPs are grammatical with negation, but for many speakers they cannot take inverse scope over c-commanding negation: (iia) is unambiguous for these speakers and does not have the inverse scope reading in (iic). Other speakers allow both readings. Every is standardly taken as the prototypical quantifier, but I will not use it for this reason. See Horn 1989, Hornstein 1995, and Mayr and Spector 2010 for some discussion of every and negation.
Group QPs such as indefinites and bare numerals do interact scopally with negation; however, such QPs also allow a specific reading that has unlimited upward scope (e.g., Fodor and Sag 1982, Heim 1982, Ruys 1992, 2006, Abusch 1994, Beghelli 1995, Farkas 1997, Liu 1997). Fodor and Sag (1982) point out that the specific reading of group QPs can escape scope islands, such as conditional clauses. This specific reading is not equivalent to the inverse wide scope reading and arguably results from a different mechanism than QR (Reinhart 1997, Kratzer 1998). Group QPs thus also need to be avoided in the crucial data to follow because an apparent wide scope reading may appear that is in fact the difficult-to-distinguish specific reading.
5 An anonymous reviewer offers an example in which a clause-internal QP does scope over CP-negation.
(i) Only on Monday didn’t some representative from every city come to the workshop.
The inverse-linking example (i) has an interpretation in which only on Monday, for every city, there was some representative from it who didn’t come to the workshop. In this interpretation, EVERY has scope over NEG ; however, the derivation of the EVERY > NEG interpretation does not require QR of every city over CP-negation. May (1985) argues that the every-QP embedded in the subject moves by QR only as far as the edge of the subject noun phrase and no farther.