Inverse Linking and Extraposition

The term inverse linking describes the phenomenon whereby a DP that is embedded within a PP takes scope over the DP that seems to contain that PP (see May 1977, Larson 1985, Heim and Kratzer 1998, Sauerland 2005, Kobele 2010; see May and Bale 2006 for an overview). An example of a sentence with a salient inverse linking reading is given in (1), where the relevant interpretation is one where the embedded DP every Factory regular (call this DP1) takes wide scope with respect to a picture (DP2); that is, the sentence has a meaning paraphrasable as ‘Every Factory regular is such that Warhol painted a picture of them’, and it is compatible with a situation where Warhol painted pictures of numerous different individuals who were regulars at his Factory studio. Giving DP2 embedded scope would derive the interpretation where Warhol painted a single picture that depicted all the Factory-goers at once, a collective interpretation of sorts (the details of which I will ignore for the remainder of this squib).

The question that previous work has sought to address is how this inverse linking reading is derived. This is of interest since most analyses of the surface order of (1) take the PP to be a complement to the noun picture, and hence within the c-command domain of the indefinite determiner α; on the widely held assumption that the scope of a quantifier is its c-command domain, this makes inverse linking an instance of inverse scope. The proper analysis of inverse linking thus speaks directly to theories of inverse scope and scope-taking more generally.

In his original analysis, May (1977) argued that inverse linking readings are derived by Quantifier Raising (QR), an LF movement rule that moves DP1 to an IP-adjoined position from which it may c-command and hence scope over DP2. This QR rule is taken to be broadly similar to the one that May invokes to derive inverse scope for sentences like Someone likes everyone, where an object scopes over the subject. However, Larson (1985) notes a problem for this account, observing that it predicts that DP1 should be able to scope over additional higher quantifiers, for instance, the subject (DP3); that is, it predicts that an example like (2) should have a reading corresponding to the paraphrase ‘Every Factory regular is such that two famous artists painted a picture of them’. But (2) and similar examples like it lack this “split scope” interpretation. May and Bale (2006) call this Larson’s Generalization.¹

A number of different analyses have been proposed to account for Larson’s Generalization. Larson (1985) and Kobele (2010) propose that inverse linking involves the formation of a complex quantifier, utilizing additional machinery to get the semantics to work accordingly, and the machinery is such that it does not lead us to expect the split scope reading to be possible in general (i.e., there is no QR of DP1 to an IP-adjoined position). May and Bale (2006) revive the QR-based approach proposed in May 1977, 1985 by appealing to the islandhood of NPs, arguing that split scope readings are absent because DP1 simply cannot leave DP2.

Although they are quite distinct, these analyses are united in assuming that there is no role for overt syntax in deriving inverse linking; rather, they all invoke QR or equivalent mechanisms to get the inverse scope readings. In this squib, I argue that this is on the wrong track: although movement is indeed required to derive inverse linking, what is required is overt movement, and not QR or any other covert or purely semantic mechanisms (cf. Kayne 1998). As I will show, surface structure has more of a role to play in determining inverse linking than has been recognized up to now.

My starting point here is the new observation that the availability of inverse linking readings is sometimes conditioned by the order of the PP containing DP1 (call this PP1) and other postnominal material within DP2.² Consider the examples in (3). (3a) is a standard case where DP1 is contained in a PP complement to the head noun, where the inverse linking reading is readily available. (3b) is identical except that DP2 also contains a PP modifier, by Warhol, which occurs to the right of PP1, and yet in this example the inverse linking reading is unavailable, contrasting clearly with (3a). However, it is not the mere presence of a PP modifier that removes the availability of an inverse linking reading, because the reading becomes available once more if the PP complement occurs in an extraposed position to the right of the modifier, as in (3c).

This effect of PP order is systematic, as demonstrated for a few different configurations in (4)−(6).³ The (c) examples are not always perfect, but their inverse linking readings are always much more accessible than those of the (b) counterparts. Judgments on these examples seem to be stable, perhaps surprisingly so given the variable nature of scope judgments.

The contrast between the (b) and (c) examples indicates that word order has some role to play in determining the availability of inverse linking readings.⁴ This is contrary to what is expected by the approaches to inverse linking described above, which derive inverse linking by covert movement. If anything, the opposite pattern would be expected: if the (c) orders were derived by extraposition of PP1 to an adjoined position within the nominal, then the extraposed PP might be expected to be an island for subsequent QR of DP1 to its scope position, wherever that may be.

What the above pattern suggests is that extraposition of PP1 is what conditions the availability of inverse linking readings, since the order of PP1 with respect to PP2 is the only obvious difference between the (b) and (c) examples. If the modifiers are analyzed as NP-adjuncts,⁵ then the order in the (b) examples should diagnose a low position for PP1 and the order in the (c) examples should diagnose a high DP-adjoined position for PP1. As for the (a) examples with just one PP, these are in principle compatible with an analysis whereby PP1 has been extraposed string-vacuously to a DP-adjoined position, and this extraposition must be optional since the inverse linking reading is not forced. So, if it is extraposition that licenses inverse linking readings, it could be that the only difference between the (a) examples and the (c) examples is that word order allows us to “see” the effect on word order. Such an extraposition-based analysis makes sense if scope is determined by hierarchy: the landing site of the extraposed constituent can be analyzed as being located above the scope-taking determiner of DP2, either in a DP-external position or in some high DP-adjoined position within the nominal.⁶ Simplified versions of these two options are diagrammed in (7).

If we follow Pesetsky (1995) in assuming that PPs are transparent for c-command,⁷ then in both configurations DP1 will c-command some segment of DP2, and so we may expect DP1 to scope over DP2, as is required for inverse linking. We can quickly narrow our analytical options by considering examples such as (8) where the DP-external adjunction analysis in (7b) is not possible: when DP2 is in Spec,TP, extraposing PP1 to a DP-external position would put it in a postverbal position and so would be incompatible with the observed word order. The pair in (9) shows that the key contrast between cases with visible DP-internal extraposition and without it is maintained in the subject position as well.⁸

Thus, the fact that (8) and indeed (9b) have the inverse linking reading indicates that DP-external extraposition should be sufficient for deriving an inverse linking reading, and that the extraposition involved is not necessarily extraposition to VP.⁹ This does not rule out the possibility that some inverse scope readings are derived by extraposition to VP, but at least it indicates that extraposition to VP will probably not prove sufficient to account for the full range of data.¹⁰

An interesting wrinkle in the empirical picture appears when we consider the effect of relative clauses on inverse linking readings. While placing a PP modifier to the right of DP1 removes the inverse linking reading, placing a relative clause to its right does not always have this effect, as example (10) shows. The locative adjunct in the letters pages is construed as modifying the matrix VP, thus controlling for extraposition of the relative clause out of the DP.

This cements the claim made above that it is nothing about adding a modifier that restricts the inverse linking interpretation, since the relative clauses make a semantic contribution that is similar to that of PP modifiers. But why do they differ with respect to inverse scope? An answer is provided by the raising analysis of relative clauses, as in Kayne 1994 and much subsequent work. Such works argue that relative clauses may be derived by raising of the head nominal from the gap position within the relative clause; although the implementations in the literature differ in how they analyze the phrase-structural relation between the head nominal and the relative, they are united by the common assumption that the head noun starts out in the relative. Following Bianchi (1999), I furthermore assume that the nominal projection that is raised from within the relative may be large enough to contain quantificational items such as numerals; that this is possible is supported by the fact that a numeral on the head NP may scope below a quantifier located within the relative (Bianchi 1999).

If the relativized nominal can contain the projection hosting a numeral, then it should be possible to extrapose a PP complement to a position above that numeral prior to relativization; that is, the rightward position of the relative with respect to the head nominal is derived by leftward movement of that nominal, rather than by right-adjunction of the relative. Extraposing the PP and then fronting the nominal projection containing that PP would derive the inverse linking reading in (10), and it would allow us to maintain the claim that inverse linking readings are derived by extraposition.

One other issue to address, which was raised by a reviewer, is that the present account does not speak to the matter of how to explain Haddock’s Puzzle (Haddock 1987, Champollion and Sauerland 2011), which is the effect of restrictors on the interpretation of inverse linking sentences: (12) means that every basket that contains an apple contains a rotten apple, not that all baskets contain rotten apples.

However, I believe the explanation for this restrictor effect must lie elsewhere, as it is more general than inverse linking. To see this, consider the pair of sentences in (13). (13a) is provided by Champollion and Sauerland (2011), and they note that it is true in the context given by the picture in (14) (also from their paper). The observationhere is that the same holds with the sentence in (13b), whose structure is different.

The key point is that neither of these sentences gives rise to a presupposition that there is only one square in the context described, and so neither gives rise to a presupposition failure in the context of (14). This means that they show the same effect on the restrictor that is seen in (12) (narrowing of the restriction of the embedded nominal), and so are within the purview of Haddock’s Puzzle. However, in (13b) the lower nominal is embedded in a relative clause, and relative clauses are typically scope islands for strong quantifiers; that is to say, (12) contrasts with (15) in that (15) lacks the inverse linking reading (and is strange as a result). This is unsurprising for an extraposition analysis, since relative clauses are islands for extraposition; see (16).

The fact that the domain-restricting effect of Haddock’s Puzzle effects is seen in contexts where inverse linking is not available constitutes evidence for treating Haddock’s Puzzle effects as coming about via mechanisms distinct from those that derive inverse linking. The fact that extraposition gives no means by which to understand the domain restriction effect is thus not a problem for my analysis of inverse linking.

In the foregoing discussion, I have argued that restrictions on the availability of inverse linking readings are best explained if these readings are derived by extraposition. What about QR? If QR were available to derive inverse linking readings, then none of the observed restrictions would be expected: Larson’s Generalization would be unexpected,¹¹ as Larson (1985) originally noted, and the effect of modifiers noted above would not be expected either. We might conclude, then, that QR is not capable of giving an embedded quantifier scope over a c-commanding quantifier within DP. This ought not to be surprising in the wider context of inverse scope facts. While QR can clearly reverse the scope of two quantifier arguments, there are many situations where it cannot—for instance, in double object constructions (Bruening 2001) and various other constructions where the higher quantifier unambiguously c-commands the lower one (Elliott and Thoms 2015). QR is clearly able to give objects scope over subjects; it is only able to do so when the subject reconstructs (Hornstein 1995), even though it can be shown with independent evidence that QR can give object DPs high scope above IP-level modifiers (Johnson 2000). Taken together, these facts suggest that the characterization of QR as a free adjunction rule is on the wrong track, and that to the extent that it is available at all, it is restricted by the presence of other intervening nominals.

One other point to take away from this discussion is that the mechanisms that have been posited in the literature for deriving “complex quantifiers” should either be excluded from the theory or restricted from applying within DP. Kobele (2010) shows that inverse linking readings can be derived with the compositional rule of function composition, which has been proposed independently in the literature. But if this rule were indeed part of the grammar, then we would not expect these readings to be unavailable in the cases with additional modifiers noted above. The general picture that emerges, consonant with work such as Kayne’s (1998) and Fox and Nissenbaum’s (1999), is one where there is more isomorphism between surface syntax and interpretation than has been recognized, at least once we take into account the role of extraposition.

There are many more issues that require resolution here. One issue is how the structures I have sketched are to be interpreted semantically: at a first pass, it seems that interpreting an extraposed quantifier that is DP-adjoined will require some type-shifting (see, e.g., Büring 2001,¹²). An anonymous reviewer makes the insightful observation that it is possible that inverse linking still crucially requires QR of both DP1 and DP2, and notes that the role of extraposition could be to move DP1 to an “escape hatch” from which it may undergo QR to a higher scope position.¹³ As for the specifics of the role of extraposition, I have sketched a quite simplified view of extraposition as right-adjunction, with fairly conservative assumptions about DP structure and clause structure. It may prove fruitful to reassess these simplifications in subsequent work; to mention one briefly, the analysis just sketched is not readily recast in the manner of Kayne 1998 (where rightward movement is analyzed in terms of leftward remnant movement) in conjunction with Kayne’s (1994) view of antisymmetry.¹⁴ Finally, a reviewer notes that inverse linking readings are typically not available when downward monotone quantifiers are involved.¹⁵

The proper analysis of cases such as these, and the broader question of why different determiners might show different scope interactions in general, must also be put off for another time. What seems clear is that there are many empirical issues that remain to be explored in the domain of inverse linking and quantificational interactions within DP.

For discussion and other input, I thank the LI reviewers, Klaus Abels, Sam Alxatib, Chris Barker, Chris Collins, Nigel Flower, Stephanie Harves, Caroline Heycock, Andrew Nevins, and Craig Sailor.