3.1 Preverbal sentential negation

The movement analysis of wide scope for modals is particularly well-suited to English, since there are good reasons to believe English modals are in a higher position than their base-generated position: they typically scope below negation, which is taken to be below T, but they show up in T, above negation. However when we look at a wider range of facts from other languages, we see that the position of sentential negation seems not to matter, as root necessity modals may take scope over negation from various positions. We review a number of different subcases here.

First, there are languages in which the modal verb seems to stay particularly low, such as Russian and Slovenian. In Russian, verbs do not seem to exhibit V-to-T movement, since the finite verb follows adverbs (Bailyn 1995 ⁷), and negation also precedes the verb. The root necessity modal dolžn-⁸ still can scope over negation, even though it seems not to raise over it, as shown in (11).⁹ The same is true for Slovenian, given in (12), which also has preverbal negation and is claimed to lack V-to-T on the basis of adverb order facts (Ilc & Sheppard 2003).¹⁰

Then, there are languages such as Norwegian and Swedish, in which negation is a phrasal adverb (see e.g. Holmberg & Platzack 1995, 17) and the finite verb precedes it in main clauses but follows it in embedded clauses, due to the clause type-dependence of V2. Norwegian has a necessity modal må which translates as “must” and which scopes over clausemate negation in main and embedded clauses, irrespective of its position.¹¹ We provide an embedded example involving a relative clause, since these strongly resist embedded V2.

It seems not to matter for the scope of the modal in Norwegian or Russian that the modal verb stays low.

There are also languages in which the verb does seem to raise and negation seems to be situated in a higher head position which still precedes the verb. Greek, which we saw in the introduction, is one such language, and Spanish and Italian are similar. These languages show independent evidence for V-to-T movement, since the finite verb precedes adverbs (see e.g. Belletti 1990), but sentential negation is a preverbal negative marker. Must-type modals scope over this preverbal negative marker in these languages too.¹²

We note that overt verb raising past negation is consistently impossible in these languages and their varieties, even though they allow verb raising to C in the absence of negation (see Zanuttini 1997 for extensive discussion).

A somewhat different kind of high preverbal negation is to be found in the Celtic languages, such as Scottish Gaelic, in which sentential negation is expressed not with a clause-internal operator but instead with a complementizer which precedes the verb and all other material within the TP.¹³ Although most modal expressions involve non-verbal predication in this language, it has a verbal deontic necessity item feumaidh/fheum¹⁴ which translates as “must” and which occurs in T like other lexical verbs. This modal’s scope with respect to a higher negation is subject to variation: while most speakers only get a reading where the modal scopes below negation, for some speakers the modal scopes above negation.¹⁵

The fact that the modal may take wide scope with respect to negation, at least for some speakers, is quite surprising in light of the fact that no other quantifiers may outscope negation; for instance, universal quantifiers, whether in the subject or object position, may only take narrow scope.¹⁶

Comparable facts are to be found in other languages with high negation as well, such as Tongugbe Ewe.¹⁷ Ewe has bipartite clausal negative which is composed of a preverbal negative particle m- and a clause-final negative marker o (Collins et al. 2018). There are reasons to believe that the sentence-final component of negation is as high as the CP-layer: it is in complementary distribution with other overt complementizers, it obligatorily occurs to the right of TP-level adjuncts such as time adverbials, and negation obligatorily take scope over quantificational subjects, for instance universal quantifiers, which precede the preverbal component of the bipartite negation.

We conclude (as do Collins et al. 2018) that the second part of this bipartite negative marking ought to as high as the CP-layer, and thus just as high as the negative complementizer in Scottish Gaelic.¹⁸ At the very least, the semantic scope of the bipartite negation is high enough in the clause to scope over the subject, and so the situation is comparable to that which we saw with Scottish Gaelic (and also what we see with Russian, Italian, Greek and Spanish, as discussed in section 3.2 below). To come back to the interaction with modal scope: in Tongugbe Ewe, deontic necessity is encoded by a form of be followed by a finite clausal complement, and this modal takes wide scope with respect to the matrix-level negation, as we see in (19).

To summarize, we find that root necessity modals outscope negative heads that precede them in a wide range of languages, in a variety of structural configurations. This includes cases where the verb is particularly low, as in Russian and Norwegian, and where negation is particularly high, as in Scottish Gaelic and Ewe.

Zooming out and taking a broader typological view, we are not aware of any generalizations regarding the kinds of clause structures which are conducive to wide scope root necessity modals. The availability of such modals seems to be somewhat arbitrary: Russian and Slovenian have such modals, but Bosnian-Croatian-Serbian does not; standard Dutch has one, but northeastern Dutch does not (see I&Z p. 530 fn.3); some Scottish Gaelic speakers have one, but others do not. The syntax of sentential negation seems not to be a relevant conditioning factor, since modals can scope over higher and lower sentential negatives, whether they have head status (as with Russian, Greek and Scottish Gaelic) and ones which have phrasal adverb status (as with Norwegian). The availability of wide scope seems to be a lexical property of individual modals, and subject to lexical variation. This makes the tie between movement and the extension of a modal’s scope look tenuous, in particular in light of the fact that negation, in particular head negation, typically blocks verb raising across languages (Zanuttini 1997, Zeijlstra 2004). Cases such as English seem to show us that there is no absolute ban on raising verbs past negation, at least at PF, but it is clear that we would expect some interaction between the crosslinguistic syntax of negation and modal scope if their interaction was in fact syntactically determined.

3.2 High negative operators

In this section we present data that show that wide scope of the modal is available with a variety of negative operators which are in a position higher than sentential negation: negative quantifiers in preverbal position, high covert negative operators in negative concord languages, negative inversion constructions and negative coordinators.

First, consider negative subjects. Iatridou & Sichel (2011) show that NegDPs in subject positions interact scopally with root modals in exactly the same way as sentential negatives in English. Thus possibility and necessity modals can, may, have to, need to scope below both subject NegDPs and -n’t, while necessity modals must, should and ought to scope over them both (must can also scope below, at least for some speakers, as reported in Iatridou & Zeijlstra (2013)¹⁹). The same facts hold in a number of the languages with NegDPs and wide scope necessity modals, such as French,²⁰ Norwegian, Dutch,²¹ where the wide scope of the necessity modal is available. The examples below illustrate this fact (a narrow scope interpretation also seems to be available in all languages).

Iatridou and Sichel argue that these facts follow from an approach to NegDPs where the scope of their negative component is determined by the same syntactic element as sentential negation. We do not get into the details here, but they predict that the scope of NegDPs will always be identical to that of sentential negation, and so it accounts for their generalization straightforwardly, and without recourse to reconstructing semantically negative determiners (which they show to have numerous problems, arguing against Lasnik 1999).

Our contention here is that it is not correct to say that NegDPs always have the same scope as sentential negation, as there are cases involving operators other than modal verbs where we see differences between the two negatives. Consider the case of probably, a ‘high’ adverb which is shown by Nilsen (2004) to be a PPI. In non-negative clauses, probably can occur before or after the finite auxiliary (after is typically preferred), but in negative clauses with -n’t it can only occur before the sentential negation.

If NegDP subjects scoped in the same position as sentential negation, we would predict that probably should be possible in a pre-verbal position but following a NegDP. However this is not borne out, as (24a) shows, and the contrast with (24b) makes clear that there is no unexpected lexical incompatibility between negation and probably, and they can appear in the reverse order, with its corresponding semantic scope.²² (24c) shows that the ungrammaticality of (24a) is not due to probably appearing after a quantifier.

Similar facts obtain in French with sûrement, with the difference that it always occurs after the finite verb.

These facts indicate that the negation of NegDPs is not identical to sentential negation, but rather is higher, presumably as high as the subject position. This result dovetails with proposals in Zeijlstra (2011) and Collins & Postal (2014), who argue for NegDPs as semantically negative elements which encode negative scope from the subject position, rather than non-negative indefinites with special licensing conditions.

Evidence for a high position of negation with subject negative DPs is found more transparently in non-strict negative concord languages, like Spanish and Italian. These languages allow a negative DP in a preverbal position without an accompanying overt sentential negative, as opposed to postverbal DPs which must co-occur with one. To account for this pattern, Zeijlstra (2004) and Penka (2011) argue that in such languages, postverbal NegDPs must be licensed by the overt sentential negation, but preverbal NegDPs can’t because they are not c-commanded by it, so a covert negative operator is merged in a higher position to license them. We observe that the availability of wide scope of necessity modals is not affected by this higher merge position for semantic negation. Indeed it is available whether the subject NegDP is before the verb (without sentential negation, as in (26)) or after the verb (with sentential negation, as in (27)).

In strict negative concord languages, the sentential negation marker must co-occur with any negative DP, whether preverbal or postverbal. Zeijlstra (2004) captures this fact by saying that the semantic locus of negation in strict negative concord languages is always a covert operator in the left periphery. Indeed Zeijlstra (2004) shows that strict and non-strict negative concord languages differ with respect to the scope of overt sentential negation, where in strict negative concord languages, it obligatorily scopes over a wider range of quantifiers in subject position. Nevertheless, in these languages, wide scope of necessity modals is observed; we show examples again with preverbal NegDPs, as these are arguably the ones which most clearly have a high covert negation (although if Zeijlstra is right the argument extends to any negation-containing sentence in these languages). The following demonstrates this with data from Russian (28a), Greek (28b)²³ and Ewe (28c).

Thus, for all these NegDP configurations, if I&Z are right in accounting for the data in terms of covert movement, the relevant movement rule must be able to move the modals quite high, as high as the upper regions of the left periphery.

Another construction where negation takes high scope is negative inversion in English (see Emonds 1976; Haegeman 2000; Collins & Postal 2014). The fact that negation takes particularly high scope in negative inversion is shown by the following examples. (29) demonstrates that the fronted negative operator licenses subject NPIs, and the triplet in (30) shows that because-clauses may outscope sentential negation and NegDP subjects, but not fronted negative operators in negative inversion.

The high scope of negation in negative inversion is discussed in more detail in Potsdam (2013). Potsdam observes that quantificational arguments are actually unable to take scope over the negation of negative inversion constructions, on the basis of data such as (31). He also shows that the same holds for inverted negation in negative imperatives and negative questions, and concludes that inverted negation generally takes wide scope in CP or FocP.

However, as Francis (2017) notes, must is surprisingly still able to scope above negation, in contrast with other scope-taking elements.

Therefore, if the modal undergoes head movement – specifically, some covert step of head movement to a higher position than its landing site after T-to-C movement – it must do so to a projection above the FocP or CP, depending on the analysis, and such a movement must be forbidden for phrasal categories such as because-clauses, which must scope below negation in this construction.

Finally, consider negative connectives, i.e. neither…nor and its equivalent in other languages. We observe that wide-scoping modals such as English must, French devoir can produce a wide scope interpretation when present in negative coordinations.

These facts are especially problematic for a movement account of the modal’s wide scope. We show in particular that a widespread analysis of neither..nor as a negative disjunction is strikingly incompatible with modal movement to derive its wide scope. To see this, consider how negative coordinations are analyzed. For two propositions p and q, the meaning of a negative coordination can be decomposed as one of two truth-conditionally equivalent possibilities: a conjunction of negative elements (¬p) ∧ (¬q), or a negation of a disjunction ¬(p ∨ q). Most prominent analyses of negative coordinations involve a negated disjunction (Gonzalez (2020) for French, Gajić 2016 for BCS and Jeretič 2018; 2022a for Turkish). In such an analysis, for the modal to outscope negation, it must raise above the entire coordination, resulting in an LF of the type □¬(p ∨ q). This LF, however, does not correspond to the intended reading, since the modal only applies to one of the disjuncts; there is no way of achieving the desired reading by any movement of the modal, whether it be head movement or something else. Otherwise, if negative coordinations were conjunctions, contra the claims in the above-cited papers, we would have to assume a final LF of the type (¬p) ∧ (□¬q), which is in violation of the Law of Coordination of the Likes, and raises issues on how close does negation have to be to the conjunction to license the neither..nor coordination. Note that the alternative approach presented in section 5, in contrast, naturally accounts for the wide scope interpretation of the modal in a negative coordination, regardless of its underlying semantics.

For all of the cases described in this section, deriving wide scope via head movement requires movement of the modal to some position above TP or higher. In all cases, this movement must be covert, since the negative operators are higher than the overt position of the modal. In the case of Negative Inversion, the modal’s surface position is already a derived one, yet is expected to scope below negation, so the modal would have to undergo further covert movement above it. As for negative connectives, the wide scope interpretation is particularly problematic for a movement account, as it is logically incompatible with the common analysis of negative connectives as disjunctions; otherwise, under the already less popular conjunctive analysis of negative coordinations, a movement account of modal scope leads to adopting a number of shaky assumptions.

3.3 Embedded modals

A question that does not arise with English must, but which can be asked using data from other languages, is whether a must-type root necessity modal may scope over a clausemate negation even if it is embedded under another auxiliary. In this section we show that modals in such configurations still scope over negation, even though the modal is c-commanded by another verbal head.

First, consider the case of French. In simple cases, French verbs move to T (Pollock 1989). French has several necessity modals that can take scope above negation. In particular, falloir takes obligatory wide scope, as shown in (34) (similar facts and arguments presented in this section hold for devoir, that takes optional wide scope).

Following an analysis of the I&Z type, the wide scope of falloir is achieved by head movement of the modal to T, above the negation marker pas (though still below the second, optional negation marker ne). However, we show that these modals can also be used in constructions that clearly don’t have movement to T, i.e. in infinitival constructions, as in (35a), and in compound tenses, as in (35c). Wide scope of the modal is still available in these cases, despite the lack of overt head movement.²⁷

The strong challenge here comes from (35b) and (35c),²⁸ where the modals are dominated by another auxiliary; if we were deriving the wide scope by head movement, this would require quite an unusual type of non-local head movement that is not recognisable from French grammar.

Before we move on, we will show that modals that are embedded under another auxiliary in this manner can scope over higher negations in other languages as well. As discussed in the previous section, Spanish tensed verbs undergo V-to-T, as they appear before adverbs, despite appearing after negation. However, they appear after adverbs when in their nonfinite forms, e.g. the near future, (36a), and conditional, (36b). As in French, these involve a finite verb in T which embeds the modal. Despite the fact that T is filled and the modal is embedded well below NegP, the modal can still take scope over negation.

Dutch modals also have non-finite forms that can be embedded under other auxiliaries. (37a) shows cases where the necessity modal moeten is embedded under zullen ‘will’ and had ‘had’ (past perfect). In these cases, the modal scopes over negation, just like it does in simpler cases where it is finite.²⁹

Finally, there is actually a case to be found in English, namely supposed (to). As noted by Homer (2011), supposed to is a necessity modal which takes wide scope with respect to negation, despite always occurring below it.³⁰

The argument from supposed requires a bit more argumentation than the other cases reviewed so far, since one might claim that the locus of the construction’s modal force is the be which it typically occurs with; such an analysis might lean on comparison with the modal is to construction (as in John is to be here by five), which also scopes over negation (I&Z p. 530). But we can provide support for the claim the locus of modal force in this construction is supposed by considering examples such as (39), where the supposed occurs without a verb in a small clause construction but still contributes the same modal interpretation and still scopes over negation.

Given that supposed is embedded under a finite be in T in examples such as (38), it would seem to pose the same sort of challenge as the other case.³²

4.1 Classical head movement

Let us first consider the case of classical head-to-head movement (for a recent defense see Roberts 2010). We will consider two implementations with fairly conventional phrase structure: (i) the modal raises covertly over the NegP to some higher (semantically vacuous) head X, skipping the Neg head completely, as shown for finite modals in (41a); (ii) the semantically interpreted negation is a phrasal specifier of NegP and the modal moves through its semantically vacuous head to a higher (also vacuous) X position, as shown in (41b) for finite modals.³⁴

These diagrams involve the high NegP above TP, and so would be applicable to Spanish and Greek. For languages such Scottish Gaelic, negation would be in some higher C position immediately above the highest head in the inflectional layer (cf. Bennett et al. 2019 on Irish), and there would need to be covert head movement to some X which would be a higher complementizer in the CP layer.

For both of the analyses above, we must assume some type of interpretable covert head movement of the modal. One immediate problem with this is that there is little to no empirical evidence for covert head movement independent of the proposal at hand. Covert head movement features prominently in early Minimalist work such as Chomsky (1995), but there was little in the way of empirical motivation for this component of the theory, and none of this was retained in subsequent developments of the framework (e.g. Chomsky 2001). Arguably, the burden of proof for covert head movement should be set particularly high, since there is as much demand for the elimination of covert movement as there is for the elimination of head movement (see e.g. Chomsky 1995; Kayne 1998). Moreover the addition to the theory of technology such as Agree (Chomsky 2001), which does much of what covert movement did in early Minimalism,³⁵ renders covert head movement suspiciously redundant. In addition, a related problem is that covert head movement of modals, so construed in line with I&Z’s proposal, would be markedly different from QR of DPs, since DPs can often QR for no reason other than to take wide scope (Fox 2000), while covert head movement would only be permitted to rescue a polarity clash. Recall that the default for non-PPI modals is to scope below negation obligatorily, so allowing optional covert head movement of modals (without obligatory reconstruction) would lead to overgeneration. It’s not clear why covert head movement would differ from covert phrasal movement in this way.

A related empirical problem comes directly from the case of Scottish Gaelic in particular. Recall from section 3.1 that sentential negation in Scottish Gaelic is encoded by a negative complementizer, and that in at least some varieties the root necessity modal may scope over this negative element. The analyses above would necessitate an analysis where the modal moves covertly to some position above this negative complementizer. The trouble with this is that this instance of covert movement would need to be unique in the language, as other quantifiers are not able to scope over sentential negation, as shown in the sentences in (17), where universal quantifiers in subject and object positions scope below negation, even though QR is otherwise available (for object>subject scope). Similar facts are found in Ewe, as shown in (18), which also has a particularly high syntactic negation.

These facts are arguably part of a more general pattern, discussed in section 3.2, whereby negation in the CP-domain obligatorily takes scope over QPs in the clause that the C embeds (Potsdam 2013). Accounting for data in I&Z’s terms would require us to say that covert head movement is able to target some position above the CP-negation, but covert phrasal movement is not. This is a further step in the direction of a disunified analysis of quantificational scope-taking, and it is not clear what it would derive from.

An additional problem for the structures in (41a)–(41b) is that they involve multiple violations of the Head Movement Constraint (Travis 1984). First, consider the structure in (41a): the HMC is violated in this structure because the modal crosses Neg without adjoining to it. It is shown by Zanuttini (1997) and Zeijlstra (2004) that negation of the Greek/Italian type is a head in the clausal spine; in this respect, it is different from the negation of languages such as Norwegian, which behaves like a phrasal category (i.e. an adverb) with respect to a number of other independent diagnostics. One of the head-like properties that negation shows in these languages is that it blocks (overt) verb raising to C, for instance in questions or imperatives where the verb would normally raise in the absence of negation (see especially Zanuttini 1997 on these issues). Such facts are expected in the context of the HMC. Given the analysis of Greek/Italian negation as a head, and the fact that verbs (including modal verbs) do not move overtly past negation in any case in these languages, the claim that the modal moves over covertly on an analysis such as (41a) is somewhat surprising.

The analysis in (41b) avoids the HMC problem that troubles (41a), but does so at the cost of an empirically unsuccessful account of the syntax of negation, since it involves analysing the overt negative element as a phrasal specifier. As noted above, Zanuttini (1997) and Zeijlstra (2004) provide a number of empirical arguments for analysing the overt negators in Greek/Italian type languages as heads, distinguishing them from the adverb-like negatives of languages such as Norwegian and Dutch. These properties would need to be reconsidered one-by-one if we were to adopt the analysis in (41b). In addition, Zeijlstra (2004; 2008) argues that the availability of negative concord across languages can be accounted for, and indeed explained, on the basis of the division of languages into head negation vs non-head negation languages (i.e. Italian vs Dutch). By adopting the analysis in (41b), we would have to give up on this as well, since it would effectively collapse this distinction.

The HMC problems only multiply once we consider the specifics of the embedded modal cases discussed in section 3.3. In all cases, the modal occurs in some low position below negations of different kinds (high negation in Spanish, most likely low negation in the others), and so in order for these modals to scope over negation they must be undergoing covert head movement to some higher head position above the NegP projections. (42)shows how this might work for French, where T is occupied by an auxiliary such as avoir, which has moved from some lower position where it embeds a constituent containing the modal (which we represent as ModP here).³⁶ Spanish would be broadly similar.

Movement of the modal incurs at least two violations of the HMC: one by crossing the base-generated position of the auxiliary, and one by crossing T. The landing site for movement of the modal must be some higher head position, since T is filled by avoir. In addition, the identity of the X projection is not evident, and it is unclear whether we would expect it to always be available, for instance in cases like (39), where there is no apparent TP layer at all.

These considerations taken together, (42) looks like quite an unlikely analysis for the wide scope reading of the modal. A similar cluster of problems besets the analyses for the data from Spanish, French and English, and adopting a version of the analysis in (41b), where the modal raises through negation, would not improve matters, since the modal would still need to cross both the higher auxiliary’s trace and its derived position where it is adjoined to T. Stepping back from the technicalities for a moment, it seems fair to say that the kind of head movement that is required to derive (42) would be quite unlike anything else that is familiar from the overt syntax of these languages. Its status is suspicious at best.

A potential way out in the case of the embedded modal data is to confront the HMC head-on (Harizanov & Gribanova 2017), in light of cases in other languages where it seems not to apply. One class of cases which is particularly relevant is the so-called long head movement (LHM) construction, where we see a participle moving over a local auxiliary to some higher position in the same clause (see e.g. Rivero 1991; 1994). LHM is found in southern and western Slavic, Balkan languages and in Old Romance, and it is illustrated for Bulgarian in the following example, in which the participle occurs to the left of the auxiliary.

A possible analysis of the embedded modal facts is to say that the covert syntax of these modals is the same as the overt syntax of LHM, with the only difference being in patterns of pronunciation.

While this line of reasoning is familiar, and in principle capable of accounting for some of the data, it is still limited, since LHM is much more restricted than whatever mechanisms are involved in providing embedded modals with wide scope. One restriction on LHM is that it only applies in finite matrix clauses, much like V2 movement in Germanic (Rivero 1991). If wide scope for modals was derived by LHM, then we would incorrectly predict no wide scope in the French example (35a), in which the modal occurs in a non-finite embedded subject clause, as well as English (39). The insensitivity of the availability of these modals’ wide scope to clause structure, unexpected if derived by movement, echoes the more general cross-linguistic and cross-structural pattern we uncovered in the previous section. A second restriction that often applies to LHM, which is particularly relevant here, is that it is often blocked by negation. Rivero (1991) discusses this at length and shows that in languages such as Bulgarian, LHM is impossible in negative clauses.

This restriction does not apply to all LHM languages however, as Slovak differs from Bulgarian in allowing LHM in negative clauses if the negative marker attaches to the fronted participle.

Rivero shows that the possibility of LHM in negative clauses correlates with the type of negation, such that it is impossible in languages with ‘high’ negation (where NegP occurs above TP, Zanuttini 1991, Zanuttini 1997) but possible in languages with ‘low’ negation (‘English-type’ languages, according to Rivero). These are the kinds of interactions between negation and head movement that we might expect to find, but we did not find any such interactions in our overview of wide-scoping modals in the previous section, and so this makes LHM and modal scope seem quite distinct. In particular, it is hard to see how invoking covert LHM would derive wide scope for the embedded modals in Spanish, given that it is a ‘high’ negation language. We conclude, then, that invoking LHM of the Slavic/Balkan type is unlikely to provide us with a means by which to understand the ability of embedded modals to scope over clausemate negatives, and so the problems outlined above still stand.

Of course, it is possible to draw another, perhaps more nihilistic conclusion from the LHM phenomenon, namely, that the HMC is not a real restriction on syntax at all, and that any argument for or against specific analyses of head positions that is built on the HMC is doomed from the start. This would strip our argument in this section of much of its potency, and so we should acknowledge it. But any move in that direction would leave unaccounted for a great number of restrictions on rules that affect heads, and it would ultimately constitute an abandonment of much of the empirical base of syntactic theories of head movement, thus making it look decidedly less syntactic. This doesn’t seem to be a productive move for defenders of syntactic head movement to make.

Finally, one could consider the possibility that only overt head movement is subject to the HMC, while covert movement is not so restricted. This strikes us as undesirable, for at least two reasons. First, if anything we would expect the covert version of head movement to be the more restricted one, given that covert phrasal movement seems to be more restricted than overt phrasal movement. Second, if we assume that there is no postsyntactic LF-movement but rather that covert operations simply involve pronouncing the lower copy of a movement chain, as is quite typical in contemporary work (see e.g. Bobaljik & Wurmbrand 2012), then this proposal would suggest that the HMC is not syntactic in nature, but rather it would be a PF-phenomenon. But if this is the case, then the case for a syntactic analysis of head movement would be weakened significantly, only lending support to non-syntactic alternatives.

In summary, the data reviewed in section 3 is difficult to account for in terms of an account where modal scope is determined by classical head movement. Simply put, if the scope of modals is determined by syntax, then it should interact with syntax in a meaningful way. This is not what we see crosslinguistically.

4.2 Head movement a la Matushansky (2006)

Although our primary target in this paper is classical head movement of the head-head adjunction type, another implementation of head movement to discuss is the one in Matushansky (2006). Matushansky’s proposal is intended to solve the various theoretical problems with classical head movement that were raised by Chomsky (2001). Although it has proven somewhat influential in certain areas of the literature (see e.g. Jenks 2014, Kramer 2014, Harizanov 2014; 2019), as far as we know it has not been subjected to many detailed critiques.

The starting point for Matushansky’s article is the list of problems identified by Chomsky (2001) as motivating the move towards a non-syntactic account of head movement. First, there is the claim that is always semantically vacuous, the claim that we are engaged with assessing here. Second, in the context of Chomsky’s probe-goal framework, there is the question of how one can force a probe to attract just a head X and not the XP that it heads; this seems to require introducing some diacritic for distinguishing heads and phrases, an unwelcome move in the context of Chomsky’s theory. We can call this the Attraction Problem. Third, Chomsky lists a bunch of other properties of head movement which seem to distinguish it from phrasal movement and which, for Chomsky, render head movement’s theoretical status particularly suspect.

These problems are also discussed insightfully by Roberts (2011) and Dékány (2018).

Matushansky’s proposal aims to address most of these problems by analysing head movement as an instance of very local head-to-specifier movement which is combined regularly with the morphological readjustment rule of m-merger (Marantz 1988). On this analysis, which is situated in the Distributed Morphology framework (Halle & Marantz 1993), the syntax derives structures such as (47a), where X moves to the specifier of an immediately dominating YP, and then when the structure is spelled out, here conceived as shipping the structure from syntax to a distinct morphological component, the m-merger rule readjusts the terminals to produce the structure in (47b), where X and Y form a complex head which will feed Vocabulary Insertion.

This analysis immediately solves the c-command problem and the countercyclicity problem, and it captures the “snowballing” property of head movement (it passes through and picks up all other heads on its way to its final landing site) by positing that spellout and thus m-merger apply at every maximal projection. As for the Attraction Problem, Matushansky analyses head movement as being driven by an uninterpretable c-selection feature on the attracting head, X above, and it attracts just the head of the lower projection YP because this is the minimal element that it can attract and satisfy the attractor’s requirements. Matushansky argues that phrasal movement is simply an instance of pied-piping, which applies when moving only the head is unavailable, and she claims that this holds whenever the attracting X and the attracted Y are not in an immediately local relation, due to a condition which she calls the Transparence Condition (p. 48):

This predicts that head movement and phrasal movement should always be in complementary distribution, and it predicts that head movement will always be strictly local, as required by the HMC. Note finally that Matushansky’s approach requires that every maximal projection be a phase, since m-merger is cast as a morphological operation which applies after every step of head movement, and so every maximal projection will need to be sent to spellout in order to ensure that m-merger applies to every step of head movement.

How could Matushansky’s account be used to account for the modal scope data? Matushansky does not discuss covert head movement in her paper. The desired outcome is one where Matushansky-style head movement may apply freely and unconstrained by locality when it is covert. Syntactic and morphological restrictions conspire to derive the locality of head movement in this account – in particular, the combination of the c-selection trigger and the obligatory application of m-merger in each maximal projection – so it makes sense to look to the morphological component of this analysis as a means by which to set covert head movement free, since covert movement ought not to feed morphological operations.

The analysis does not predict that head movement should be completely free, because the Transparence Condition ensures that pied-piping will occur in any case where a probe attempts to attract a head X when it is contained in its XP. However, if the head X is first extracted covertly to the specifier of the immediately dominating YP, and m-merger fails to apply, then that X should be visible to any attracting head above. Thus in (49), if Z or B bear a [uX] probe (which is not necessarily a c-selection feature) then they should be able to attract X, unconstrained by the Transparence Condition, since X has been extracted from XP and thus its accessibility is not at stake.³⁷ But given that every phrase is a phase on this account, movement to BP would need to proceed via ZP, since B could only find elements at the edge of the ZP phase.

Thus to derive long-distance head movement of X to Spec,BP, there would need to be three features implicated: a c-selectional feature that attracts X from within XP, an “edge” feature which attracts X to a non-terminal landing site, and a feature which attracts X to its (criterial) scope position. Although it is somewhat baroque, a derivation of this kind ought to get the desired result: moving modals covertly would be free of HMC restrictions. Thus the difficult case of Spanish embedded modals could be derived from a (simplified) structure such as (50), where the modal moves covertly via all available specifier positions all the way to Spec,XP, a position above the high NegP projection.

Here we review reasons to be skeptical about this analysis of covert head movement in particular, and Matushansky’s theory in general.

Most of the problems that we see come from the assumption that every phrase must be a phase, which is necessary to avoid allowing overt head movement to derive widespread excorporation. The claim that every phrase is a phase is shared by much work in Nanosyntax (Starke 2009; Baunaz et al. 2018), and is also adopted in other work (Bošković 2002, Müller 2010). However a sustained and careful argument against this outlook is developed by Abels (2012: ch.2), who shows that there are various empirical phenomena which suggest that movement paths are punctuated (stopping off at some but not all projections) rather than uniform (stopping off at every projection). One example comes from reconstruction in Norwegian. Abels shows (p. 27–29) that there are fewer scope reconstruction possibilities for moved subjects than one would expect if moved subjects could stop off at various positions in the clause on their way to Spec,TP. Pairs such as (51)–(52) demonstrate this: while (51) allows for a reading where the subject scopes below the adverb sannsynligvis “probably”, but above the modal må “must”, such an intermediate scope reading is not allowed in (52), where the subject binds into the PP which occurs between the two elements; rather, the subject must take wide scope if it binds into the PP. If movement paths were uniform, then there ought to be some intermediate trace position t″ to which the subject can be reconstructed, which would derive the relevant reading.

Other arguments against the every-phrase-is-a-phase outlook are to be found in Fox & Pesetsky (2005), Richards (2011), Bošković (2014) (see also van Urk 2020 on the matter of identifying positive evidence for phase domains). Matushansky’s theory runs counter to this broad tradition in work on phases, and the rethinking of how to handle locality phenomena that are normally captured in terms of punctuated movement paths is far from trivial.

Another problem comes up when we consider how Matushansky’s theory captures the “snowballing” character of head movement. Consider (47) again, and in particular the next stage of the derivation where another head A is merged, shown below.

It is vital for Matushansky that m-merger applies to the moved head X and its host Y prior to merge of a next-higher head A, because if that doesn’t happen, A will only attract Y (the head it c-selects) and X will not be pied-piped with it, deriving something akin to excorporation. What this means is that spellout must make X-Y into a syntactically opaque complex head prior to any further syntactic operations applying, and so m-merger/spellout must feed syntax. This requires an “interleaving” of cycles of syntax and morphology which seems to be in direct violation of basic principles of modularity (see Preminger 2020 for critical discussion). In addition, it is not clear what kind of theory of phases is assumed to make this work. In the derivation of (53) the YP must have been spelled out prior to A merging. But it is widely assumed that when a domain is spelled out, its internal content cannot be affected by any subsequent syntactic operations (see e.g. Collins & Stabler 2016, 67); in the words of Uriagereka (1999), the spelled-out domain is “like a giant lexical compound” (p. 256). How can the internal contents of that domain be accessible to A? And even if the domain can somehow remain accessible and A can trigger copying of Y into Spec,AP, how can some subpart of that domain, the lower copy of Y, then be deleted following movement, if it has already been spelled out as part of the YP domain? There is a deep conflict here, one which seems to require a total rethink of how phases and spellout work. The combination of this problem, the modularity issue and the empirical problems with the every-phrase-is-a-phase outlook seems to us to be reason enough to reject the Matushansky approach to head movement.

This outlook also creates problems for the analysis of modals in particular. Recall that the outlook defended in I&Z was one where head movement of a modal would only be semantically non-vacuous if it had an effect on interpretation, for instance if it was to take a PPI-modal out of the scope of a c-commanding negation. This was necessary to capture the fact that non-PPI root modals typically scoped below negation unambiguously, across many languages. The claim in I&Z’s analysis was that any instance of modal head movement which did not have such an effect on movement would obligatorily undergo total reconstruction; we can understand this as involving deletion of the interpretable features of the higher copy which would feed semantic interpretation, subject to economy considerations (cf. Nunes 2004). But given the every-phrase-is-a-phase model, deriving a structure such as (50) would require multiple instances of modal movement which would have no effect on the interpretation of the PPI modal, and which would obligatorily reconstruct going by I&Z’s reasoning. Thus reconstructing the first step of movement from XP to Spec,YP would result in the head copy X failing to bear any of the semantic features which would be responsible for deriving semantically non-vacuous movement, and so any subsequent operation that targets and copies that X will also be semantically vacuous. It is not clear, then, how successive-cyclic head movement could be semantically non-vacuous in this system if it did not have an effect on interpretation at each cycle (as is required for covert phrasal movement by Fox 2000).³⁸

Taking these issues into consideration, we conclude that Matushansky’s theory of head movement is also unlikely to provide a satisfying account of the clause structure-insensitive nature of modal scope with respect to clausemate negation.

4.3 A phrasal movement account of PPI modals

If head movement is not the right way to derive wide scope for necessity modals, what about phrasal movement? Phrasal movement is a suggestion that Homer (2011; 2015: pp. 31–32, and Appendix III) briefly entertains to account for wide scope modals. For Homer, the ModP undergoes phrasal movement to a position above negation, if and only if it is ungrammatical below negation. He doesn’t give any particular details about the structure, but we infer that it would be something like (54), where the ModP moves to a position above the Neg head, say Spec,NegP.

Such an analysis predicts that the embedded vP should scope over negation as well, and there are cases that show this is not correct. Consider an example with supposed: while the modal scopes over a higher negation, the vP it embeds does not, as shown by the scope facts below, where know from the embedded vP must scope below negation.

The same point can be made with cases where there are NPIs in the embedded clause. These ought to be unlicensed if the predicate they are contained in is moved covertly out of the scope of negation (see Wagner 2006 for concrete evidence for effects of this kind), yet in (56) there is no problem with the NPI, so long as negation is present.

This indicates that the vP would reconstruct back to its original position, where it can compose with negation, leaving Mod in its derived position, which later composes with and scopes above the negated vP.

This seems to require an exotic species of partial predicate reconstruction, for example a version of the remnant movement-based account of Kayne (1998). However we bring up further points which cause trouble for any movement-based account, which may even include an imaginative implementation of Kayne’s theory.

A general point we take issue with is the existence of polarity-driven phrasal movement of PPIs, which is what Homer invokes in this analysis. There are other instances of polarity items that cannot undergo movement to rescue their grammaticality. For example, we saw that probably is ungrammatical under negation, as seen in example (23b), repeated below:

One could argue that since overt movement is available to rescue the grammaticality of this sentence, covert movement cannot be (cf. Bobaljik & Wurmbrand 2012). However, there are other instances in which overt movement is not available, yet movement does not save the grammaticality of a polarity-sensitive item. One is in a sentence containing negation, an NPI, and an intervening element blocking the NPI’s licensing – i.e. a configuration that violates Linebarger’s (1980) Immediate Scope Constraint. We give a known example of such a configuration with anything in (58), and one with the NPI modal need in (59a).

The grammaticality of these sentences would be rescued if the NPIs anything and need moved between negation and always, where they would satisfy the Immediate Scope constraint. However, we do not observe this. Why then can must move to satisfy its polarity requirements, but not need?

More generally, as argued in previous sections, wide scope readings of modals are subject to different conditions than more well-known instances of phrasal movement like typical quantifier raising. Movement of modals is restricted to specific necessity modals, while typical QR is available to all types of nominal quantifiers. Movement of modals is not restricted to any syntactic configurations, while typical QR is restricted to certain languages and syntactic configurations (Bobaljik & Wurmbrand 2012); in fact, we have seen specific cases in which QR of nominal quantifiers above negation is not available, while wide scope readings of certain modals are (as in Scottish Gaelic and Ewe with their complementizer negation, and in English negative inversion constructions).

We conclude that the sketched phrasal movement account of Homer (2011; 2015) faces a variety of problems that make it no better off than the more developed head movement-based account of I&Z.

4.4 The invalidity of the argument from de dicto indefinites

There is one argument that both I&Z and Homer use to back the movement analysis of modal scope: de dicto (or non-specific)³⁹ readings of indefinites that are meant to diagnose wide scope readings of modals. They note that the movement approach predicts the availability of non-specific readings for indefinites which scope above negation, since the modal has moved to a higher position where it may scope over the subject as well as negation. Indeed, if a subject scopes below a necessity modal and above negation, then we can be quite sure that the modal has undergone movement. I&Z and Homer argue that this prediction is borne out. In (60) and (61), the DPs may be interpreted as non-specific, which is a diagnosic for an intensional operator outscoping them. In these sentences, the only apparent possibility for this intensional operator is the necessity modal must.

These indefinites are not interpreted below negation, therefore, the only scopal construal that achieves the desired interpretation is one in which the modal has moved from below negation to above the indefinite.

We claim, following the same line of reasoning as in Jeretič (2021a), that this argument is invalid. This is because non-specific readings of indefinites are available even in cases in which they cannot scope below a modal. We construct examples that involve modals that scope below negation, but indefinites that still scope above. Consider the following examples, in which the modals can and need scope below negation.

In these three different scenarios, there is a clear available non-specific reading of the subject indefinite. Strikingly, this reading cannot be achieved by manipulating the scope of the three elements. The modals (can or need) all have unambiguous narrow scope with respect to negation (neg>mod), and the subject indefinites all unambiguously scope above negation in these scenarios. This means we end up with the only possible scope construal to be subj>neg>mod. However, this configuration is at odds with the non-specific interpretation of the indefinite to correspond to a narrow scope of the indefinite with respect to the modal.⁴⁰

We take this to be evidence that there must be a mechanism to achieve the non-specific reading of the indefinite other than having it scope below the modal. Examples (62) and (64) are generic statements: a high scoping generic operator can thus provide the source of the non-specific reading, allowing the modal to stay below the indefinite. In (63), the statement holds of the (near) future, which can also be analyzed intensionally. We do not make any claims about what the final analysis for these sentences is, only that the source of the non-specific reading may be different than scoping below the modal, and thus it cannot be used as a diagnostic for movement of the modal in any of these sentences.

5.1 A scaleless implicature analysis for wide scope necessity modals

Jeretič (2021a; b) proposes a no-movement analysis of wide scope necessity modals. On this analysis, root modals take semantic scope below negation, but may achieve a wide scope interpretation by triggering a scaleless implicature, which is a semantic enrichment that arises from the effect of an exhaustivity operator. In other words, a negated necessity expression will have as its base meaning the expected narrow scope interpretation of the modal ¬ > □ given by the syntax, which, after application of the exhaustivity operator, is strengthened to a meaning equivalent to the wide scope □ > ¬. Crucially, this meaning is achieved without the modal having to move.

The analysis is implemented in a grammatical framework for scalar implicatures, such as Fox (2007) or Bar-Lev & Fox (2020). Scaleless implicatures are predicted when a quantifier Q projects subdomain alternatives (expressions that are obtained from replacing the domain of quantification of Q with each of its subsets), and no scalar alternative (a quantifier expression that stands in an entailment relation with Q).

For example, English necessity modal must can be analyzed as a scaleless implicature trigger. As written in (65), we take must to be a universal quantifier over a set of worlds M, which corresponds, following standard Kratzerian modal semantics (Kratzer 1989), to the best worlds of a modal base according to a contextual ordering source. For simplicity, we ignore modal base and ordering source in the notation for the meaning of must, and simply name the domain of quantification M.

We assume that must’s set of alternatives lacks a scalar alternative, which would correspond to a possibility modal, i.e. an existential quantifier over the same domain M. Jeretič (2021a) argues that scalematehood must include a full match in semantic properties modulo force,⁴¹ however there is no possibility modal in English that is a perfect match for must. In particular, among the most plausible candidates, can differs from must in its temporal properties, and may can’t express teleological and pure circumstantial flavors, which are covered by must (see Jeretič 2021a for details). Therefore, can and may cannot be scalar alternatives to must, nor can any other possibility modal in English. Furthermore, we assume that must is lexically specified to project subdomain alternatives, which are obtained by replacing the modal’s domain of quantification by its non-empty subsets, as shown in (66).

It is assumed that when an utterance has alternatives, an exhaustification operator applies to strengthen the utterance by excluding these alternatives from the meaning of the utterance, or including them. In (67) is the definition of the exhaustifier proposed by Bar-Lev & Fox (2020). This operator is designed to first exclude all the ‘innocently excludable alternatives’ (IE) – those which can be non-arbitrarily excluded without yielding a contradiction, as defined in (68a), and then include any remaining ‘innocently includable alternatives’ (II) – those which can be non-arbitrarily included without yielding a contradiction, as defined in (68b).

We assume this operator can apply at the TP or CP levels, and must apply if it globally strengthens the utterance.

Now, take a negated root must utterance in (69a) before exhaustification. Its LF is given in (69b), where, crucially, negation is above the modal (mismatching the higher PF position of must in T). Its translation in predicate logic is in (69c).

Following (66), the set of alternatives of S is shown in (70).

To clearly present the derivation of the scaleless implicature, we simplify the domain of quantification M to a mere two worlds {w₁,w₂} (the end result is generalizable to an infinite domain). The sentence with the simplified domain of quantification and its associated set of alternatives are given below.

Using this simplified domain, we now derive the set of innocently excludable alternatives (IE) and that of innocently includable ones (II). The alternatives of the type ‘you must_{w1} not go’ and ‘you must_{w2} not go’ are not IE alternatives, because excluding them from the utterance yields a contradiction, as shown in (72).

Including them yields no contradiction: all alternatives are therefore II. The exh operator then applies (merging at the TP or CP level), as shown in (73a). Since all alternatives are II, no alternative is excluded, and all alternatives are included. A scaleless implicature is derived; the resulting meaning, shown in (73b), corresponds to the equivalent to the wide scope of the modal with respect to negation.

Thus we can see that under a scaleless implicature analysis, LF movement of the modal above negation is not necessary to achieve the observed wide scope reading.

5.2 Its insensitivity to syntactic diversity

The exhaustification operation responsible for the strengthening to a wide scope reading is in principle not affected by the syntactic status or position of the negation or the modal. Analyzing wide scope interpretations of modals in this way allows us to capture their insensitivity to the variability of syntactic configurations covered in this paper. In contrast, what may affect the computation of an implicature are intervening semantic elements which affect the result of the exhaustification procedure.

We here name the types of syntactic options for negated modals discussed in this paper, and show how the scaleless implicature computation remains largely unaffected by them. Keep in mind that a scaleless implicature analysis need not (and arguably, should not) explain all instances of wide scope readings of modals mentioned in this paper. Here we just show that such an analysis is applicable in and insensitive to the variety of relevant syntactic configurations.

5.3 Further predictions

5.4 Summary

We have presented an alternative analysis to the wide scope interpretations of necessity modals, which does not rely on movement, but rather on a semantic strengthening mechanism. This analysis, and semantics-based analyses more generally, is predicted to be largely insensitive to the variety of syntactic configurations of negations and modals, and therefore wide scope interpretations are expected to be observed across these cases, provided there is no intervening semantic operator preventing exhaustification.

The scaleless implicature analysis outlined above is however by no means the only available in situ analysis, and arguably shouldn’t apply to all cases of wide scope modals. A related but different analysis, also present in Jeretič (2021a), involves an underlying possibility modal as a scaleless implicature trigger. In unembedded, unnegated contexts, it is strengthened to a necessity reading. Under negation, no implicature is triggered, and it retains its possibility reading; a negated possibility meaning ¬◊ is equivalent to a wide scope necessity □¬, thus accounting for the basic behavior. Such analyses can be found in Staniszewski (2020) for English should and Jeretič (2021a) for several modals including Ecuadorian Siona ba’iji. Non-scaleless implicature analyses are available as well, e.g. modals can be analyzed as pluralities of worlds that are homogeneous and exhibit a neg-raising behavior (see Jeretič 2021a: Ch6 and Agha & Jeretič (2022) for such an analysis for weak necessity modals, like English should).