Negative Polarity Items (NPIs) that denote lower scalar endpoints, such as existentials like
According to a recent line of thinking (
(1) | a. | *Mary has ever been there. |
b. | *I read any book. |
Following Chierchia’s (
(2) | a. | [I read [any book][uσ]] |
b. | [EXH[σ] [I read [any book][ |
The question is of course why (2b) yields a contradiction. Following Chierchia, the uninterpretable feature [uσ] introduces all scalar and domain alternatives. The scalar alternatives are all elements on the scale <
The second factor behind the unacceptability of (2b) comes from the introduction of the exhaustifier. An exhaustifier that is applied to some proposition states that all stronger alternatives of that proposition are false. Chierchia (
(3) | [[EXH]] = [[ |
Now, suppose again that the domain quantification is the set of books {a,b,c}. Then [[I read any book]] denotes ∃x.[x∈{a,b,c} & read(I, x)]. Now, the domain alternatives of ∃x.[x∈{a,b,c} & read(I, x) are:
(4) | a. | ∃x.[x∈{a,b,c} & read(I, x)] |
b. | ∃x.[x∈{a,b} & read(I, x)] | |
c. | ∃x.[x∈{a,c} & read(I, x)] | |
d. | ∃x.[x∈{b,c} & read(I, x)] | |
e. | ∃x.[x∈{a} & read(I, x)] | |
f. | ∃x.[x∈{b} & read(I, x)] | |
g. | ∃x.[x∈{c} & read(I, x)] |
Apart from (4a), all domain alternatives in (4) are stronger than ∃x.[x∈{a,b,c} & read (I, x)]. That means that if EXH applies to ∃x.[x∈{a,b,c} & read(I, x)], all these stronger domain alternatives must be false.
(5) | [[EXH(I read any books)]] = |
[λp.p∧∀q∈Alt(p)[p ⊈ q → ¬q]](∃x.[x∈{a,b,c} & read(I, x)]) = | |
∃x.[x∈{a,b,c} & read(I, x)] & | |
¬∃x.[x∈{a,b} & read(I, x)] & | |
¬∃x.[x∈{a,c} & read(I, x)] & | |
¬∃x.[x∈{b,c} & read(I, x)] & | |
¬∃x.[x∈{a} & read(I, x)] & | |
¬∃x.[x∈{b} & read(I, x)] & | |
¬∃x.[x∈{c} & read(I, x)] |
But the conjunction of all negated stronger domain alternatives entails that there is no element, member of the set {a,b,c}, that has been read by me. This already follows from the three negated domain alternatives where the domain of quantification is a singleton set: ¬∃x.[x∈{a} & read(I, x)] & ¬∃x.[x∈{b} & read(I, x)] & ¬∃x.[x∈{c} & read(I, x)] ↔ ¬∃x.[x∈{a,b,c} & read(I, x)]. But then [[EXH(I read any books)]] must have the denotation in (6), which forms a logical contradiction.
(6) | ∃x.[x∈{a,b,c} & read(I, x)] & ¬∃x.[x∈{a,b,c} & read(I, x)] |
For Chierchia, following Gajewski (
However, if the NPI is embedded in a DE context, things change. To see this, take (7).
(7) | I didn’t read any book. |
Again, exhaustification of (7) will result in all stronger domain alternatives of (7) being false. But now, no domain alternative of (7), listed in (8), is actually stronger than (7). Apart from (8a), all of them are weaker, due to the fact that the negation reverses the direction of the inference.
(8) | a. | ¬∃x.[x∈{a,b,c} & read(I, x)] |
b. | ¬∃x.[x∈{a,b} & read(I, x)] | |
c. | ¬∃x.[x∈{a,c} & read(I, x)] | |
d. | ¬∃x.[x∈{b,c} & read(I, x)] | |
e. | ¬∃x.[x∈{a} & read(I, x)] | |
f. | ¬∃x.[x∈{b} & read(I, x)] | |
g. | ¬∃x.[x∈{c} & read(I, x)] |
Consequently, exhaustification in (7) applies vacuously: [[EXH(I didn’t read any book)]] = [[I didn’t read any book]] and the sentence just has the reading ¬∃x.[x∈{a,b,c} & read(I, x)] and is not unacceptable.
According to Chierchia’s proposal, the combinatorial properties of [uσ], the introduction of domain alternatives, and the exhaustification requirement ensure that any existential quantifier or other element denoting low-scale endpoints that is equipped with such a feature [uσ] is an NPI. At the same time, even though this has not been explicitly claimed within the framework, Chierchia’s proposal also predicts that any universal quantifier that carries such a feature should be a Positive Polarity Item (PPI). To see this, take the non-existing word
(9) | a. | I read pevery book. |
b. | [EXH[σ] [I read [pevery book][ |
Now, the exhaustifier in (9b) applies vacuously. The reason is that none of the domain alternatives of
(10) | a. | ∀x.[x∈{a,b,c} → read(I, x)] |
b. | ∀x.[x∈{a,b} → read(I, x)] | |
c. | ∀x.[x∈{a,c} → read(I, x)] | |
d. | ∀x.[x∈{b,c} → read(I, x)] | |
e. | ∀x.[x∈{a} → read(I, x)] | |
f. | ∀x.[x∈{b} → read(I, x)] | |
g. | ∀x.[x∈{c} → read(I, x)] |
However, things are different with the negated counterpart of (9):
(11) | a. | I didn’t read pevery book. |
b. | [EXH[σ] [I didn’t read [pevery book][ |
The semantics of (11b) yields a logical contradiction, for the very same reason as (2b) does. The reason is that all domain alternatives of ¬∀x.[x∈{a,b,c} → read(I, x)], listed in (12), entail ¬∀x.[x∈{a,b,c} → read(I, x)].
(12) | a. | ¬∀x.[x∈{a,b,c} → read(I, x)] |
b. | ¬∀x.[x∈{a,b} → read(I, x)] | |
c. | ¬∀x.[x∈{a,c} → read(I, x)] | |
d. | ¬∀x.[x∈{b,c} → read(I, x)] | |
e. | ¬∀x.[x∈{a} → read(I, x)] | |
f. | ¬∀x.[x∈{b} → read(I, x)] | |
g. | ¬∀x.[x∈{c} → read(I, x)] |
Then the meaning of (11b) then is again contradictory, and should render the sentence unacceptable:
(13) | [[EXH(Ididn’t read pevery book)]] = |
[λp.p∧∀q∈Alt(p)[p ⊈ q → ¬q]](¬∀x.[x∈{a,b,c} → read(I, x)]) = | |
¬∀x.[x∈{a,b,c} → read(I, x)] & | |
¬¬∀x.[x∈{a,b} → read(I, x)] & | |
¬¬∀x.[x∈{a,c} → read(I, x)] & | |
¬¬∀x.[x∈{b,c} → read(I, x)] & | |
¬¬∀x.[x∈{a} → read(I, x)] & | |
¬¬∀x.[x∈{b} → read(I, x)] & | |
¬¬∀x.[x∈{c} → read(I, x)] = | |
¬∀x.[x∈{a,b,c} → read(I, x)] & | |
∀x.[x∈{a,b} → read(I, x)] & | |
∀x.[x∈{a,c} → read(I, x)] & | |
∀x.[x∈{b,c} → read(I, x)] & | |
∀x.[x∈{a} → read(I, x)] & | |
∀x.[x∈{b} → read(I, x)] & | |
∀x.[x∈{c} → read(I, x)] |
The universal counterpart of NPI
Some answers may suggest themselves. For instance, it may be the case that, for some reason, polarity effects may appear only among existential quantifiers. In this way, the
First, the existing analyses for the explanation of the
In Section 2, I first demonstrate that at least certain universal modals that are PPIs are PPIs for the very same reason that under Chierchia’s approach NPIs are NPIs. In Section 3, I show that the exact implementation of this approach predicts that such universal quantifier PPIs may actually surface under negation, as the exhaustifier whose presence they trigger may scopally intervene between the negation (or any other anti-licenser) and the PPI itself. I argue that, consequently, universal quantifier PPIs are fine under negation as long as they appear under negation at surface structure, but may not reconstruct under negation when they appear above negation at surface structure. In Section 4, I present several cases of such universal quantifier PPIs, showing that universal quantifiers, albeit in disguise, can indeed be attested, both in the domain of quantifiers over possible worlds and in the domain of quantifiers over individuals. Section 5 focuses on different kinds of PPIs (in particular strong vs. weak PPIs) and shows how their differences follow from a small and independently motivated amendment of Chierchia’s proposal for NPI-hood. Section 6 concludes.
As has been pointed out by Israel (
(14) | a. | She must not leave. | ☐ > ¬ |
b. | She should not leave. | ☐ > ¬ | |
c. | She ought not to leave. | ☐ > ¬ |
Iatridou & Zeijlstra (
(15) | a. | She doesn’t have to leave. | ¬ > ☐ |
b. | She doesn’t need to leave. | ¬ > ☐ |
(16) | a. | She cannot leave. | ¬ > ◊ | ||
b. | She may not leave. | ¬ > ◊ |
In fact, in the domain of deontic modals, all existential modals scope under sentential negation.
Empirical evidence for the PPI-status of universal modals that outscope negation comes from two facts. First, other polarity-sensitive verbs/auxiliaries have been attested in the domain of modals as well. English
(17)
a.
John need*(n’t) leave.
b.
Hans
Hans
braucht
needs
*(nicht)
not
zu
to
gehen.
go
‘Hans doesn’t have to go.’
c.
Jan
Jan
hoeft
needs
*(niet)
not
te
to
vertrekken.
leave
‘Jan doesn’t have to leave.’
Given that generally PPIs surface in domains where NPIs appear, it is likely to expect that modal PPIs can be attested as well.
Second, it is a well-known fact that PPIs may take scope under negation under special circumstances (cf.
(18) | a. | She must not marry him because he looks smart (but because he is a good linguist). |
‘It is not because he is smart that she has to marry him.’ | ||
b. | I mustn’t always take the garbage outside. (Many times my son does that.) | |
‘It is not always the case that I have to take the garbage outside.’ |
The second test (after
(19) | a. | Few students mustn’t leave. | few > not > must |
‘There are few students who don’t have to leave.’ | |||
b. | Only John mustn’t leave. | only > not > must |
|
‘John is the only one who doesn’t have to leave.’ |
If modals like
To see this, take (20), where the modal does not reconstruct below negation. Let’s assume that the modal base of (20a) consists of the worlds w1, w2, w3. The semantics of
(20) | a. | She must not leave. |
b. | [EXH[σ] [she must[ |
(21) | a. | ∀w.[w∈{w1, w2, w3} → ¬ leavew(she)] |
b. | ∀w.[w∈{w1, w2} → ¬ leavew(she)] | |
c. | ∀w.[w∈{w1, w3} → ¬ leavew(she)] | |
d. | ∀w.[w∈{w2, w3} → ¬ leavew(she)] | |
e. | ∀w.[w∈{w1} → ¬ leavew(she)] | |
f. | ∀w.[w∈{w2} → ¬ leavew(she)] | |
g. | ∀w.[w∈{w3} → ¬ leavew(she)] |
Now suppose that uσ]-leave] and therefore (22b) has the semantics in (23). But (23) is a contradiction, as it states that not in all worlds w1, w2, w3 she leaves, and at the same time that she leaves in all worlds w1, w2, w3. This proposal thus correctly predicts that
(22) | a. | She mustn’t leave. |
b. | [EXH[σ] [she |
(23) | ¬∀w.[w∈{w1, w2, w3} → leavew(she)] & |
¬¬∀w.[w∈{w1, w2} → leavew(she)] & | |
¬¬∀w.[w∈{w1, w3} → leavew(she)] & | |
¬¬∀w.[w∈{w2, w3} → leavew(she)] & | |
¬¬∀w.[w∈{w1} → leavew(she)] & | |
¬¬∀w.[w∈{w2} → leavew(she)] & | |
¬¬∀w.[w∈{w3} → leavew(she)] = | |
¬∀w.[w∈{w1, w2, w3} → leavew(she)] & | |
∀w.[w∈{w1, w2} → leavew(she)] & | |
∀w.[w∈{w1, w3} → leavew(she)] & | |
∀w.[w∈{w2, w3} → leavew(she)] & | |
∀w.[w∈{w1} → leavew(she)] & | |
∀w.[w∈{w2} → leavew(she)] & | |
∀w.[w∈{w3} → leavew(she)] |
One caveat should be made, though. The toy model used in (21)–(23), contains only three possible worlds. In more realistic models, the number of worlds is of course much bigger (and can even be infinite). More importantly, the alternatives will not reduce down to singleton sets, as there is never enough information for a speaker/hearer to narrow down the domain of worlds into singleton sets. Note, though, that for this approach to yield the contradiction it is only necessary that the domain alternatives are partitioned and that the union of all domain alternatives is already the same set as the original domain of quantification. For instance, in (23) the contradiction would also be yielded without any singleton alternatives. In fact, if there is already a partition with two subdomains, with, for some proposition p, one subdomain consisting of all and only all p-worlds and the other subdomain consisting of all and only all not-p-worlds, the contradiction is yielded. Both subdomain alternatives would then be stronger, whereas the union of these subdomains of quantification is still identical to the original domain of quantification.
The fact that modal PPIs can be analysed along the lines sketched above does, however, not entail that they have to be analysed as such. It could very well be the case that the source of their PPI-hood lies elsewhere. However, there are good reasons to analyse them along the suggested lines.
First, Chierchia’s approach builds upon the idea, originally proposed by Kadmon & Landman (
(24) | a. | I don’t have potatoes. |
b. | I don’t have any potatoes. |
And even though the judgements are subtle, it seems that similar effects are attestable in the case of
(25) | a. | She must leave; in fact, she has to leave. |
b. | She has to leave; in fact, she must leave. |
(26) | a. | She must leave. |
b. | She has to leave. |
However, the idea that all NPIs are domain wideners has been criticised (see, e.g.,
Second, an alternative way to evaluate the suggested analysis is by comparing it to other competing analyses. One potential alternative that comes to mind, though, is that certain modals like
Third, the strongest piece of evidence, however, comes from the hitherto unreported observation that PPIs under this approach should be able to “self-intervene” (though see
Under Chierchia’s approach, every NPI that is exhaustified gives rise to a logical contradiction unless some DE operator intervenes between the exhaustifier and the NPI:
(27) | EXH > DE > NPI |
All other scopal configurations of EXH, DE and NPI than (27) give rise to either a feature-checking violation (when the uninterpretable feature [uσ] remains unchecked) or give rise to a logical contradiction. However, in the domain of PPIs, things are different. Whereas (28) is a scopal configuration that yields ungrammaticality, other scopal configurations between EXH, a DE operator and a PPI are fine:
(28) | *EXH > DE > PPI |
One such configuration that is fine is the one where the DE operator appears under the scope of the PPI (as in (29)), which we saw was the scopal configuration that emerges when the modal does not reconstruct (in the case of
(29) | EXH > PPI > DE |
But another licit scopal configuration that has not been discussed so far is the one in (30).
(30) | DE > EXH > PPI |
Nothing in (30) violates any rule of grammar. The PPI’s uninterpretable feature [uσ] has been checked by higher EXH; application of EXH over its (propositional) complement does not give rise to any contradiction (as no DE operator is embedded in the complement of EXH); and, finally, since exhaustification applies vacuously, nothing forbids the DE operator to take scope over its own complement that contains the vacuously exhaustified PPI. Since no further EXH is included, (30) can underlie acceptable sentences.
To see this, take (31a) again, repeated from (11), but now with the logical form in (30)/(31b):
(31) | a. | I didn’t read pevery book. |
b. | [not [EXH[σ] [I read [pevery book][ |
Now, the exhaustifier in (31b) applies vacuously. The reason is that
(32) | a. | ∀x.[x∈{a,b,c} → read(I, x)] |
b. | ∀x.[x∈{a,b} → read(I, x)] | |
c. | ∀x.[x∈{a,c} → read(I, x)] | |
d. | ∀x.[x∈{b,c} → read(I, x)] | |
e. | ∀x.[x∈{a} → read(I, x)] | |
f. | ∀x.[x∈{b} → read(I, x)] | |
g. | ∀x.[x∈{c} → read(I, x)] |
Hence, the meaning of [EXH [I read [pevery book]]] is the same as the meaning of [I read [pevery book]] (both mean ∀x.[x∈{a,b,c} → read(I, x)]), which can subsequently be negated without any problem (yielding ¬∀x.[x∈{a,b,c} → read(I, x)]). Hence, a universal quantifier PPI can actually take scope below negation, provided the logical form is one where negation does not take scope in between the (higher) EXH and the (lower) PPI.
The only difference between unacceptable (28) and acceptable (30) concerns the position of the covert exhaustifier. The question thus arises as to what determines the position of a covert operator in a sentence. In this we follow Zeijlstra (
(33)
a.
Nessuno
neg-body
ha
has
telefonato
called
a
to
nessuno.
neg-body
‘Nobody called anybody.’
b.
[OP¬[iNEG] [nessuno[uNEG] [ha telefonato [a nessuno[uNEG] ]]]]
One might wonder what the nature of the principle is that states that covert operators must be assumed to be present in a position c-commanding the highest overt marker of them. There are two ways to think about that. First, the mechanism can be derived from Chomsky’s Merge-over-Move constraint. Inserting an abstract operator below an element that marks this operator (i.e. that stands in an Agree relation with it), requires an additional step of movement. To see this, take (33) again. If Op¬ were inserted below highest
(34) | a. | [nessuno[uNEG]i [OP¬[iNEG] ti ha telefonato [a nessuno[uNEG] ]]] |
b. | [OP¬[iNEG]i [nessuno[uNEG] ti ha telefonato [a nessuno[uNEG] ]]] |
Since a competing derivation, (33b), lacks these extra movement steps, (34a–b) can be ruled out under Merge-over-Move.
Alternatively, one can also conceive the principle that posits the abstract operator in a position above the highest overt agreeing marker as an extra-grammatical constraint on grammatical structures. Under such a conception, all derivations that contain an abstract operator in some position where it can check off the relevant uninterpretable features and that do not give rise to semantic anomalies are grammatically fine, but are not parsable. It is the parser that includes the abstract operator the moment that the parser detects its marker; so the only sentences that are both parsable and grammatically correct are the ones where the operator is higher than its highest agreeing marker. Such extra-grammatical constraints are not unfamiliar in grammatical theory. For instance, Ackema & Neeleman (
As for now, I remain agnostic about how exactly EXH-inclusion is constrained, but, in full analogy to the inclusion of abstract negative operators, I take the following to hold:
(35) | In any sentence with an NPI/PPI that needs to be checked by a covert exhaustifier, this exhaustifier must be present in a position where it c-commands the NPI/PPI at surface structure. |
We are now in a position to determine which scopal configurations are fine for exhaustified PPIs and which ones are not. The question at stake is when a scope configuration like (30), repeated in (36) below, is licit. After all, when (30)/(36) would reflect a possible LF, it shows that PPIs may indeed appear under the scope of their anti-licenser, provided that the exhaustifier they induce acts as an intervener. The answer to this question is now straightforward: if a PPI is in a position lower than its anti-licenser, EXH may c-command the PPI under the DE operator, provided that the complement of EXH is propositional. Then, the PPI can take scope under its anti-licenser:
(36) | DE > EXH > PPI |
If, however, the PPI c-commands its anti-licenser at surface structure, the exhaustifier must be in a position c-commanding both the PPI and the DE anti-licenser:
(37) | EXH > PPI > DE |
Note that both (36) and (37) are acceptable scope construals. However, a consequence of this is that any sentence where the exhaustifier that checks off the uninterpretable feature [uσ] of a PPI that c-commands a DE operator at surface structure would forbid the PPI to reconstruct below the DE operator, even in cases where non-PPIs would be allowed to reconstruct. The reason is that, then, this PPI would end up in the illicit scope configuration (38) that yields a logical contradiction.
(38) | *EXH > DE > PPI |
So, a particular prediction that I take the application of Chierchia’s (
Now strikingly, all modal PPIs in English appear above the negative marker:
(39) | a. | She mustn’t leave. |
b. | She oughtn’t leave. | |
c. | She shouldn’t leave. | |
d. | She isn’t to leave. |
Also, several other languages discussed in Iatridou & Zeijlstra (
(40)
Zij
she
moet
must
niet
not
vertrekken.
leave
☐ > ¬
‘She mustn’t leave.’
(41)
Sie
she
soll
should
nicht
not
gehen.
go
☐ > ¬
‘She shouldn’t go.’
The other languages involving modal PPIs discussed in Iatridou & Zeijlstra (
(42)
Dhen-prepi
not-must
na
to
it
kanume
do
afto.
this
☐ > ¬
‘We must not do this.’
(43)
Juan
John
no-debe
not-must
ir.
leave
☐ > ¬
‘John must not leave.’
Both Greek
Hence, all modal PPIs attested so far appear either above negation or form a morpho-phonological complex with it. This is already strongly in line with the proposed analysis. But even more evidence can be provided. Dutch is a language that exhibits V-to-C movement in main clauses, but not in embedded clauses. Modal auxiliaries, being verbal in nature, thus appear above negation in main clauses, but below negation in subordinate clauses. Consequently, Dutch
(44)
Zij
she
moet
must
niet
not
vertrekken.
leave
EXH > MUST > DE
‘She mustn’t leave.’
However, in embedded clauses, two scopal orderings should be fine: one where EXH intervenes between the negation and the modal, and one where EXH takes widest scope:
(45)
… dat
… that
zij
she
niet
must
moet
not
vertrekken
leave
EXH > MUST > DE
DE > EXH > MUST
‘… she mustn’t leave’ / ‘… she doesn’t have to leave’
Example (45) is thus predicted to be ambiguous, unlike (44), a prediction that is indeed born out:
(46)
a.
*Zij
she
moet
must
niet
not
vertrekken,
leave,
maar
but
het
it
mag
may
wel.
‘She mustn’t leave, but it is allowed.’
b.
Zij
she
moet
must
niet
not
vertrekken,
leave,
omdat
because
het
it
verboden
forbidden
is.
is
‘She mustn’t leave, because it is forbidden.’
(47)
a.
Ik
I
weet
know
dat
that
zij
she
niet
not
moet
must
vertrekken,
leave,
maar
but
dat
that
het
it
wel
mag.
may
‘I know that she doesn’t have to leave, but that it is allowed.’
b.
Ik
I
weet
know
dat
that
zij
she
niet
not
moet
must
vertrekken,
leave,
omdat
because
het
it
verboden
forbidden
is.
is
‘I know that she mustn’t leave, because it is forbidden.’
The fact that the Dutch pattern shows exactly the predicted behaviour can be taken as a piece of evidence in favour of the proposal that takes PPI modals to be universal quantifiers that introduce domain alternatives and that require covert exhaustification. But it gives rise to a new question as well: why have universal quantifier PPIs only been attested in the domain of modal auxiliaries and never in the domain of quantifiers over individuals?
Nothing in this proposal on the PPI status of modals hinges on the fact that they are quantifiers over possible worlds. In fact, the approach to NPI-hood has even been developed for quantifiers over individuals. Hence, nothing in the approach should forbid the existence of universal quantifiers over individuals that are PPIs (for the same reason). However, no such PPI has been attested so far.
In this section, I argue that the reason why only universal PPIs have been attested among quantifiers over possible worlds and not among quantifiers over individuals, again, lies in the fact that universal quantifier PPIs may actually scope under negation, and therefore do not appear to be PPIs. To see this, take again the scopal ordering of a universal quantifier with a feature [uσ], negation and the covert exhaustifier that gives rise to the logical contradiction, the ordering in (48):
(48) | *EXH > NEG > ∀ |
If negation intervenes between the exhaustifier and the universal, a contradiction arises. But, as argued above, nothing requires that a universal quantifier with a feature [uσ] (henceforward ∀[uσ]) has its exhaustifier scope higher than the negation: the feature [uσ] only requires that the exhaustifier c-commands the ∀[uσ] and therefore has scope over it, but does not require that it has immediate scope. An alternative underlying syntactic configuration for such a universal quantifier carrying a feature [uσ] is (49):
(49) | NEG > EXH > ∀ |
But (49) does not give rise to a logical contradiction. As shown in (31)–(32), the proposition
(50) | ¬∀x.[x∈{a,b,c} → read(I, x)] |
Universal PPIs (or to be more precise: universal quantifiers that obligatorily introduce domain alternatives that must be exhaustified) are fine in negative/DE contexts as long as the exhaustifier takes scope in between the anti-licenser and the universal quantifier itself. Universal quantifier PPIs may appear under negation without being unacceptable and therefore are unrecognizable as such.
How do we know, then, if such PPIs that are universal quantifier over individuals exist in the first place? As discussed before, we can only do so on the basis of examples where a universal quantifier negation appears above a morphologically independent negative marker at surface structure. In that case the surface scope order would be EXH > ∀ > NEG. Under such a configuration, the universal quantifier that is equipped with a feature [uσ] cannot reconstruct below negation (as this would give rise to a logical contradiction), but a universal quantifier that is lacking [uσ] would be able to reconstruct below negation.
Interestingly, variation between universal quantifiers that may and that may not reconstruct under negation when appearing above it at surface structure has indeed been attested (and never been properly explained). In the remainder of this section, I argue that the only distinction between such quantifiers is the presence or the absence of a feature [uσ] on ∀. Following this line of reasoning, it can actually be established that English
In English and most other languages (cf.
(51) | Everybody didn’t leave. | ∀ > ¬;¬ > ∀ |
However, for a small number of languages this is not the case. For most speakers of Dutch (and several Northern German varieties), this reconstructed reading is not available (cf.
(52)
Iedereen
everybody
vertrok
left
niet.
not
∀ > ¬;*¬ > ∀
‘Nobody left.’
(53)
Kul
all
t-tulaab
the-students
ma
not
mashu.
walked
∀ > ¬;*¬ > ∀
‘No student walked.’
(54)
Zen’in-ga
all-
sono
that
testo-o
test-
uke-nakat-ta.
take-not-
∀ > ¬;*¬ > ∀
‘Nobody took that test.’
This observation has never received a satisfactory explanation, but directly follows once universal quantifiers in Dutch, Northern German, Levantine Arabic and Japanese are taken to be PPIs. Focusing here on the Dutch example, if
However, how can we independently investigate whether Dutch
(55)
Speaker A:
Iedereen
everybody
gaat
goes
de
the
kamer
room
uit.
out
‘Everybody leaves the room.’
Speaker B:
Nee,
no,
onzin.
nonsense.
Iedereen
everybody
gaat
goes
niet
not
de
the
kamer
room
uit;
out;
alleen
only
Jan
Jan
en
and
Piet.
Piet
‘No, nonsense. Not everybody leaves the room, only John and Piet do.’
Second, PPIs can take scope under clause-external negation. Again, this applies to
(56)
Ik
I
zeg
say
niet
not
dat
that
iedereen
everybody
vertrekt;
leaves;
alleen
only
Jan
Jan
vertrekt.
leaves
‘I’m not saying that everybody leaves; only John leaves.’
Third, PPIs can scope under negation if a proper intervener scopes between the PPI and its anti-licenser. In a way, we already saw that this is the case for those PPIs that appear under the surface scope of negation (since EXH then acts as an intervener), but more examples of intervention effects can be attested (see (18)). Example (57) can be true in a situation where it is not always the case that everybody leaves the room. Note that this reading is facilitated by adding extra stress on
(57)
Iedereen
everybody
gaat
goes
niet
not
altijd
always
de
the
kamer
room
uit.
out
‘It is not always the case that everybody leaves the room.’
Finally, Szabolcsi (
(58)
Het
it
verbaast
surprises
me
me
dat
that
iedereen
everybody
niet
not
blijft.
stays
‘It surprises me that not everybody stays.’
So, Dutch
So far, we have not distinguished between PPIs of different strength. As Iatridou & Zeijlstra (
(59) | a. | Few students should leave. | should > few; *few > should |
b. | Few students must leave. | must > few; few > must |
(60) | a. | At most five students should leave. | should > at most five; *at most five > should |
b. | At most five students must leave. | must > at most five; at most five > must |
(61) | a. | Only John should leave. | should > only; *only > should |
b. | Only John must leave. | must > only; only > must |
The distinction between strong and weak PPIs is reminiscent of the distinction between strong and weak NPIs. For instance, English
(62) | a. | *I have seen him in years. |
b. | *Somebody has seen him in years. |
(63) | a. | I haven’t seen him in years. |
b. | Nobody has seen him in years. |
(64) | a. | *Few people have seen him in years. |
b. | *At most five students have seen him in years. | |
c. | *Only John has seen him in years. |
By contrast, English
(65) | a. | *I ever saw him. |
b. | *Somebody ever saw him. |
(66) | a. | I didn’t ever see him. |
b. | Nobody ever saw him. |
(67) | a. | Few people ever saw him. |
b. | At most five students ever saw him. | |
c. | Only John ever saw him. |
As noted by Collins & Postal (
(68) | a. | *I don’t travel in order to have seen him in years. |
b. | *I don’t say that I have seen him in years. |
Again, weak NPI licensing is not subject to such syntactic locality constraints and may apply across locality boundaries:
(69) | a. | I don’t travel in order to ever see him. |
b. | I didn’t say that I ever saw him. |
Gajewski (
Let’s illustrate this for
(70) | If few students pass the exam, the department is faced with budget cuts; this year no student passed the exam, so the department will face budget cuts. |
If
This solution, however, faces two serious problems. First, it is unclear how it can be a property of an NPI that its exhaustifier must (not) consider the pragmatics of its licenser. And second, it is unclear how the locality conditions fit in. The latter is actually a problem for understanding weak NPI licensing in the first place, for how can it be possible that in (69), repeated below as (71),
(71) | a. | [EXH[σ] I don’t travel [in order to ever[ |
b. | [EXH[σ] I didn’t say [that I ever[ |
In order to circumvent these problems, I suggest, slightly speculatively, to make the following amendments to Chierchia’s theory, based on these NPI facts. Later on, I demonstrate that they make very precise and correct predictions in the domain of PPI-hood.
Let’s assume that there are two ways in general to trigger the presence of an exhaustifier: one way is by syntactic agreement (as has been shown in this article at various places); another one would be the result of a pragmatic mechanism that states that if there have been introduced some (domain) alternatives in the sentence and they have not been applied to by any operator that applies to alternatives, as a last resort, the entire clause is exhaustified. Implicitly or explicitly, such mechanisms have been suggested in the literature before (cf.
(72) | a. | Syntactic exhaustification: | - is triggered by agreement; |
- is subject to syntactic locality constraints; | |||
- may apply at any position in the clause, provided its complement is of the right semantic type; | |||
b. | Pragmatic exhaustification: | - takes place as a last resort operation; | |
- is not subject to syntactic locality constraints; | |||
- may apply at the CP level only (given that it is a last resort operation applying at propositional level). |
Now, the strict vs. non-strict distinction among NPIs may naturally follow: both types of NPIs obligatorily introduce all scalar and domain alternatives, but strict NPIs must syntactically agree with the exhaustifier; non-strict NPIs are subject to pragmatic exhaustification. But if strict NPIs are exhaustified by a different exhaustifier than non-strict NPIs, nothing forbids that these two exhaustifiers may have different semantic properties. This opens up ways to understand the weak-strong distinction and its correlation with the strict-non-strict NPI/PPI distinction. Since weak NPIs are subject to pragmatic exhaustification, it seems plausible to assume that the pragmatic exhaustifier has the same properties that we assigned thus far to EXH. In this sense, EXH functions like a classical Neo-Gricean operation. However, if syntactic exhaustification always considers the implicatures of the licenser as well it makes rather sense to assume that this is a different type of exhaustifier, call it EXH+, which also considers the implicatures generated in its entire complement.
As sketchy as the above may be, it provides a solution for the two problems addressed before. First, it predicts that all weak NPIs, unlike strong NPIs, can be licensed by a licenser outside their syntactic domain. Second, it is now possible to syntactically encode the difference between weak and strong NPIs by postulating that all NPIs obligatorily introduce domain alternatives (which is what renders them NPIs), but that only strong NPIs carry an uninterpretable feature [uσ] that triggers the presence of EXH+ that they agree with; weak NPIs are simply subject to the pragmatic exhaustification requirement (given that they obligatorily introduce domain alternatives). Note that an additional advantage is that what underlies NPI-hood under the exhaustification approach boils down to only one requirement (obligatory introduction of domain alternatives) and not two (obligatory introduction of domain alternatives and the presence of a [uσ]-feature on the NPI).
This solution also makes predictions for the domain of PPI-hood. If the presence or absence of an uninterpretable feature [uσ] is what distinguishes weak from strong existential NPIs, this should also be behind the distinction between strong and weak universal PPIs, again in the reverse configuration (as weak NPIs and strong PPIs have a distribution described in terms of downward entailment, whereas strong NPIs and weak PPIs have a distribution described in terms of anti-additivity): whatever makes a weak NPI a weak NPI, makes a strong PPI a strong PPI, and whatever makes a strong NPI a strong NPI, makes a weak PPI a weak PPI. Both weak and strong PPIs introduce domain alternatives, but only weak PPIs carry a feature [uσ] (and trigger EXH+ rather than EXH).
Now, the presence of EXH+ no longer causes non-anti-additive DE operators to give rise to a contradiction when they scope over universal PPIs. As we saw, a plain DE operator like
So now we may assume that English
(73) | NEG > EXH+ > PPI | – Possible under syntactic exhaustification; |
– Impossible under pragmatic exhaustification. |
(74) | EXH(+) > NEG > PPI | Possible under both syntactic exhaustification and pragmatic exhaustification |
Now, for English, given the fixed position of modal auxiliaries in the clause, this may be hard to test, but other languages exhibit constructions that can be used to evaluate these predictions. As said before, Dutch exhibits V-to-C movement in main clauses only. We already established that whereas Dutch
(75)
a.
Weinig
few
mensen
people
moeten
must
vertrekken.
leave
few > must; must > few
‘Few people must leave.’
b.
Hoogstens
at most
vijf
5
mensen
people
moeten
must
vertrekken.
leave
at most 5 > must;
must > at most 5
‘At most 5 people must leave.’
c.
Alleen
only
Jan
John
moet
must
vertrekken.
leave
only > must; must > only
‘Only John must leave.’
This is in line with our predictions. But Dutch also exhibits a universal modal PPI meaning ‘should’ (of the form
(76)
a.
Weinig
few
mensen
people
zouden
would
moeten
must
vertrekken.
leave
*few > should;
should > few
‘Few people should leave.’
b.
Hoogstens
at most
vijf
5
mensen
people
zouden
would
moeten
must
vertrekken.
leave
*at most 5 > should;
should > at most 5
‘At most 5 people should leave.’
c.
Alleen
only
Jan
Jan
zou
would
moeten
must
vertrekken.
leave
*only > should;
should > only
‘Only Jan should leave.’
(77)
a.
Wenige
few
Leute
people
sollen
should
gehen.
go
*few > should;
should > few
‘Few people should go.’
b.
Höchstens
at most
fünf
5
Leute
people
sollen
should
gehen.
go
*at most 5 > should;
should > at most 5
‘At most 5 people should go.’
c.
Nur
only
Hans
Hans
soll
should
gehen.
go
*only > should;
should > only
‘Only Hans should go.’
Now, the final prediction is that in an embedded clause (both Dutch and German exhibit V-to-C movement in main clauses only), these stronger PPIs, being pragmatically exhaustified only, still must outscope negation. The pragmatic exhaustifier EXH can only be introduced at clausal/CP level. And, indeed they do:
(78)
… dat
… that
Jan
Jan
niet
not
zou
would
moeten
must
vertrekken
leave
*not > should; should > not
‘… that Jan shouldn’t leave’
(79)
… dass
… that
Hans
Hans
nicht
not
gehen
go
soll
should
*not > should; should > not
‘… that Hans shouldn’t go’
Hence, the evidence presented so far shows that when applied to the domain of PPI modals the suggested amendment to Chierchia’s theory that was independently necessary given the different syntactic and semantic behavior of weak and strong NPIs again makes correct predictions for the treatment of universal PPIs. Finally, note that this predicts that Dutch
To conclude, universal quantifier PPIs do exist, both in the domain of quantifiers over individuals and in the domain of quantifiers over possible worlds, as is predicted by Chierchia’s (
The observation that many NPIs are licensed in DE contexts goes back to Ladusaw (
Note, though, that
Note that for Chierchia, following Gajewski (
Chierchia’s approach is not uncontroversial or uncontested, and has been criticised by Geurts (
An alternative approach would be to say that PPIs are not the mirror image of NPIs (as claimed by, e.g.,
The domain of epistemic modals is richer in terms of polarity effects than that of deontic modals, in the sense that various existential modals also exhibit NPI- or PPI-effects when used epistemically, but not when used deontically. For instance, epistemic
Note that
Even though Giannakidou & Mari (
Agreement with respect to negative features always requires the interpretable feature to c-command the uninterpretable one(s) (cf.
Naturally, the question arises as to whether Levantine Arabic and Japanese also allow the inverse scope readings to emerge under DE predicates such as
Another question that may arise is why there are so few universal quantifiers over individuals that are PPIs. I presume that this has to do with the fact that, even though they can be detected (and thus acquired), the cues that signal their PPI-hood are more obscure. Note that this is different for the discussed modals, where their PPI-hood is easier to detect (and thus to acquire), and whose number is significantly larger.
To capture the difference between the two scopal construals, take a scenario where we know of two (out of twenty) students, namely Mary and Suzanne, that they ought to leave. In such a scenario,
Earlier versions of this work have been presented at the Amsterdam Colloquium 2013 and at workshops or invited lectures at MIT, UPF Barcelona and the universities of Cologne, Frankfurt, Jerusalem, Osnabrück and Vienna. I am grateful to the audiences for their useful feedback. Also, I would like to thank my colleagues with whom I discussed this work, most notably Gennaro Chierchia, Cleo Condoravdi, Regine Eckardt, Anastasia Giannakidou, Sabine Iatridou, Clemens Mayr, Andreea Nicolae, Paula Menendez-Benito and Johann Schedlinski.
The author has no competing interests to declare.