Quexistentials and Focus

Many languages have words that can be used either as question words or as existential indefinites (e.g., Ultan 1978, Haspelmath 1997, Bhat 2000, Haida 2007). We call such words quexistentials (question + existential). An example is the Dutch word wat, which can mean either ‘what’ or ‘something.’¹

It has been claimed (see, e.g., Haida 2007:47, 51, 169, 182, and many references cited there) that the presence or absence of focus typically determines whether a quexistential is interpreted as a question word or as an existential indefinite. In particular, it has been claimed that in many languages, possibly universally, quexistentials are interpreted as question words if and only if they are focused. We will refer to this generalization as the quexistential-focus biconditional (QF biconditional for short). For instance, the Dutch quexistential wat can only be interpreted as a question word in (3), where it is focused, and can only be interpreted as an existential indefinite in (4), where it is not focused.

The fact that quexistentials are always focused on their interrogative use should be seen as a particular instance of a more general fact: namely, that interrogative words (quexistential or not) are always focused. We propose to account for this fact by generalizing the common view on contrastive focus in a way that incorporates both an external and an internal notion of contrast. On the other hand, we will show that the issue of the (non)focusability of quexistentials on their existential use hides many complications.

The article is organized as follows. Section 2 provides some general background on quexistentials; section 3 lays out the basic empirical facts on how quexistentials interact with stress and focus; section 4 explores in more depth how focus relates to the interrogative use of quexistentials, and to question words more generally; and section 5 explores in more depth how focus relates to the existential use of quexistentials, and to existential indefinites more generally. It also argues in favor of reinterpreting the Dutch facts so that they do not form a counterexample to the QF biconditional. Finally, section 6 concludes.

In English and many other languages, interrogative words look different from existential indefinites.

In other languages, existential indefinites are morphologically composed from interrogative words, as in Greek.²

The paradigm is completely productive in Greek, as illustrated in (3).

What we call quexistentials are words that can be used either as question words or as existential indefinites, without any additional overt morphology. We have already shown one example of a quexistential: the Dutch word wat. Another is the Russian word kto, which can function as interrogative ‘who’ or as existential ‘someone’.

One might wonder why we use the term quexistential given that a few related terms are already in use. For instance, Kuroda (1965) coined the term indeterminate pronouns for certain lexical items in Japanese that, like quexistentials, participate in both interrogative and existential constructions. This term has been used in much subsequent work for similar items in other languages. We do not use it, however, because there are morphosyntactic differences between the interrogative and existential uses of indeterminate pronouns. Japanese indeterminate pronouns are accompanied by the particle ka both on their existential and on their interrogative use. However, on the existential use the particle must appear locally on the indefinite noun phrase, while on the interrogative use it must appear in clause-final position. Moreover, on the interrogative use, in matrix questions the particle is optional and can only appear in the presence of a politeness marker (Miyagawa 1987, 2017, Uegaki 2018). On the other hand, on the existential use the particle’s presence is obligatory and not dependent on the presence of a politeness marker.

Such differences between the two uses set indeterminate pronouns in Japanese apart from the kind of lexical items that we call quexistentials. In the case of quexistentials, there is no difference in spell-out between the existential and the interrogative use.

We do not adopt the term wh-indefinite (e.g., Bruening 2007) either, because it is used to refer only to the existential use of items that also have an interrogative use (in this case, the item is a quexistential) or to indefinites that are morphologically based on interrogative words with additional morphology (as in the Greek examples above).

Nor do we take over the term ignorative, coined by Karcevski (1941:70), which is meant to indicate that the speaker lacks knowledge of the referent when using a quexistential. Since there are languages in which quexistentials can also be used for referents known to the speaker, this term is not fully appropriate either.

Thus, we use the term quexistentials to refer to lexical items that permit existential and interrogative uses without any differences in spell-out. We refer to the interrogative reading of a quexistential as the qu of quex and to the existential reading as the ex of quex. The latter two terms are names for interpretations, while the term quexistential is used for the lexical item itself. In glosses, we use QUEX, regardless of the meaning the sentence ends up having.

As far as we have seen, all languages that have quexistentials also have dedicated question words and dedicated existential indefinites. Dutch, for example, has only one quexistential, wat (interrogative ‘what’/existential ‘something’). It does not have a quexistential that can mean both ‘who’ and ‘someone’. Rather, it has a nonquexistential interrogative wie meaning ‘who’ and a nonquexistential indefinite iemand meaning ‘someone’. German has many more quexistentials than Dutch but still has purely interrogative words and purely existential indefinites as well.³

The main mystery about quexistentials is how one and the same word can yield an interrogative or an existential interpretation. Several answers to this question have been proposed. Some of them treat quexistentials as variables (e.g., Cheng 1994, Postma 1994, Bruening 2007), others as expressions generating Hamblin alternatives (e.g., Yanovich 2005), and yet others as existential quantifiers with obligatory domain alternatives (Liao 2011, Chierchia and Liao 2015). On the first two approaches, the ex of quex arises when the variable or the alternative set generated by the quexistential is bound by an existential closure operator, and the qu of quex arises when it is bound by a question operator. On the third approach, the ex of quex arises when the domain alternatives generated by the quantifier are evaluated by an exhaustification operator, and the qu of quex arises when they are evaluated by a question operator. The pros and cons of these proposals are discussed in some detail in Hengeveld, Iatridou, and Roelofsen 2019. For present purposes, however, it does not matter by which mechanisms the two readings of a quexistential arise. All that matters are the final products of these mechanisms, the two readings. It is the interaction of these two readings with focus that we are concerned with here.

In Hengeveld, Iatridou, and Roelofsen 2019, the languages that have quexistentials are divided into three groups depending on the licensing conditions of the ex of quex:⁴

• •

  Polarity-sensitive languages. In these languages, the ex of quex is possible only in environments that can be roughly characterized as ones licensing negative polarity items (NPIs). This group has been argued to include Mandarin (e.g., Huang 1982, Cheng 1994, Lin 1998, 2004, Chierchia and Liao 2015, Liu and Cui 2019), Russian (Yanovich 2005), and Vietnamese (Tran and Bruening 2013).

• •

  Undique languages (from the Latin word meaning ‘everywhere’). In these languages, the ex of quex is licensed everywhere except in the fronted position where interrogative words move to if the language has overt wh-movement. This group includes Passamaquoddy (Bruening 2007, Bruening and Tsai 2009) and Korean (Yun 2019).

• •

  Topological languages. We will distinguish a third category here, assuming for the moment that Postma (1994) is correct that there are languages in which the ex of quex is licensed only inside the VP (but see ^{footnote 39}). This group would include Dutch and German, according to Postma (1994).

Below we illustrate the distribution of the ex of quex in one language from each of these groups (Russian, Passamaquoddy, and Dutch).

Russian is in the polarity group, which means that in this language the ex of quex is not possible in affirmative episodic sentences.

The ex of quex is possible in Russian in yes/no questions, provided that the quexistential is not fronted, because then it is interpreted as an interrogative word.

The ex of quex is also possible in the antecedent of a conditional.

But it is not possible in the consequent (one would have to use a nonquexistential indefinite).

Finally, in Russian, wh-questions do not license the ex of quex.

In Russian, then, the ex of quex is polarity-sensitive, just as it is in Mandarin according to Huang (1982), Cheng (1994), and Lin (1998), among others, and in Vietnamese according to Tran and Bruening (2013).⁵

Compared with Russian, Passamaquoddy has a much more unconstrained distribution of the ex of quex. Bruening (2007) cites the following sentences:

As is obvious, none of the constructions in (17) would be possible in Russian, since the ex of quex does not appear in a polarity environment here, and the Russian ex of quex is polarity-sensitive.

Our own fieldwork on Passamaquoddy adds the following cases, which would not be possible in Russian either:⁶

These cases confirm the observations reported by Bruening (2007) with respect to the broad availability of the ex of quex.

Unsurprisingly, even though the Passamaquoddy quexistentials do not need negation (or any other downward-entailing environment) to appear in the ex of quex reading, they are fine in such environments.

According to our consultant, (19) can only have the translation shown and cannot be taken to mean ‘There is something that Piyel did not eat’. This is consistent with Bruening’s (2007) argument that the existential interpretation of the Passamaquoddy quexistential always takes narrow scope.

Thus, Passamaquoddy belongs to the undique group.

As mentioned in section 1, Dutch has one quexistential, wat, which can mean either ‘what’ or ‘something’.

The ex of quex is clearly not polarity-sensitive in Dutch, as it can appear in positive past episodic sentences such as (20b).⁸

The go-to article for quexistentials in Dutch (as well as German) is Postma 1994. Postma argues that Dutch and German quexistentials are variables at birth. When the syntactic conditions for question formation are met (e.g., movement to the left periphery), the variable is bound by an interrogative operator. When the quexistential stays inside the VP, the variable is bound by an existential closure operator, as proposed in Heim 1982 and Diesing 1992 for indefinites in general (not specifically for quexistentials).⁹ Specifically, Postma follows the proposal in Diesing 1992, whereby the syntactic domain of the existential closure operator is the VP. As a result, it is predicted that the ex of quex is possible only inside the VP. When an indefinite outside of the VP is needed, Postma predicts that only nonquexistential iets ‘something’ is possible.

Some of Postma’s data are the following.¹⁰ As (21b) shows, the ex of quex is not possible in subject position (not even of an unaccusative), and instead the nonquexistential iets must be used.

Furthermore, taking the adverb snel ‘quickly’ to be situated at the VP border, Postma notes that the quexistential wat cannot appear to its left, while the nonquexistential indefinite iets can.

In general, Postma argues that the ex of quex is not possible when the quexistential has moved out of the VP by scrambling or extraposition.¹¹

For Postma, then, the lexical status of quexistentials in Dutch and German is that of a variable, and by appealing to the VP location of Diesing’s (1992) existential closure, he predicts a topology for the ex of quex in these languages: it is only possible inside the VP. For this reason, for now we will refer to these two languages as the topological group. We return to Dutch in some detail in section 5.

So far, we have discussed two factors that affect the distribution of the existential reading of quexistentials in some languages but not in others: polarity sensitivity, and sensitivity to syntactic structure, in particular the VP boundary. However, there is also a factor that has been argued to affect the interpretation of quexistentials in a very similar way across all languages: namely, as mentioned in section 1, it has been argued that quexistentials are interpreted as question words if and only if they are focused.¹² We refer to this generalization as the quexistential-focus biconditional (QF biconditional for short).

The central point of investigation in this article is the QF biconditional. In other words, we will not investigate the lexical semantics of quexistentials, nor the syntactic/semantic source of their interrogative/existential duality. We remain neutral here with respect to the various proposals that have been made in this regard (e.g., Cheng 1994, Postma 1994, Lin 1998, Yanovich 2005, Bruening 2007, Tran and Bruening 2013, Chierchia and Liao 2015) and pursue an understanding of the QF biconditional that does not hinge on assumptions made in any of these competing proposals.

Moreover, since the QF biconditional appears to cut across the polarity divide, we will remain neutral here as to what makes quexistentials polarity-sensitive in some languages but not in others, and we will attempt to understand the QF biconditional independently of that opposition.

The QF biconditional, as explicitly stated by, for instance, Haida (2007:47, 51, 169, 182) and adapted to our terminology, is as follows:

Haida (2007) provides the following examples from German, a language from the topological group:

Russian, a representative of the polarity group, exhibits the same pattern.

And finally, in Passamaquoddy, a language in the undique group, the pattern obtains as well (though note that the Passamaquoddy stress system is quite different overall; see LeSourd 1993).

The QF biconditional consists of two conditionals.

Haida (2007:169) provides a long list of languages that support (31), with references to previous work providing more detail on each of these languages. We indeed accept it as a universal property of quexistentials. Obviously, it is of high importance to understand why quexistentials across languages, and across the three different groups we have described, have this particular property in common.

We will show, however, that the universal status of (32) appears to be counterexemplified in Dutch, even if it seems to be supported by the above examples in German, Russian, and Passamaquoddy. The ex of quex can in fact be contrastively focused in Dutch, as shown in (33) (VF=verum focus; we will use ↓ and ↑ to indicate falling and rising pitch accents, respectively).¹³ Korean facts also point in this direction.¹⁴

Moreover, the QF biconditional leads us to expect that a quexistential on its existential reading should be able to receive stress by virtue of default prosody, as long as it does not receive focal stress. This is not the case, however, at least not in Dutch, German, or Russian. In Dutch default prosody, a sentence like (34) has stress on the object.¹⁵

But when the object is a quexistential on its existential use, stress falls on the verb rather than on the object.

Ruling out focus-induced stress on the quexistential will not suffice to rule out stress by virtue of default prosody. Whatever we might say about focus, then, we would need to say something in addition about the fact that the ex of quex cannot receive stress by virtue of default prosody in cases like (36). We will therefore discuss the relation between quexistentials and default stress separately from the relationship between quexistentials and focal stress.

Now that we have given some background on quexistentials and made some basic observations concerning their interaction with stress and focus, we will proceed as follows. First, in section 4 we will further examine how the interrogative use of quexistentials relates to stress and focus. We will propose that quexistentials on their interrogative interpretation—and question words in general—are typically marked as contrastive foci because questions characteristically put forward a set of contrasting propositions (resolutions/answers). The existence of such contrasting propositions results in the use of focal stress. Making this idea more explicit and precise requires a generalization of the common view on contrastive focus, but one that we think is very natural.

Second, in section 5 we will further examine how quexistentials on their existential use interact with stress and focus. In particular, we will consider some possible explanations for the fact that the ex of quex cannot receive stress by virtue of default prosody, and we will show in some detail that the ex of quex can receive focal stress in certain cases in Dutch, though not in other languages that we have considered. We also offer an account of this crosslinguistic difference.

In this section, we will show that the qu of quex behaves just like other interrogative items. That is, once the quexistential has been set to its interrogative guise, it behaves just like nonquexistential interrogative words (as we said in section 2, we do not think that the mechanisms by which the qu of quex or the ex of quex are derived affect the current discussion). This holds for the postmovement position in the left periphery, but, much more interestingly, for in-situ positions as well.

First, a quick word about suitable testing environments: the interrogative use of a quexistential in a wh-movement language like Dutch is best explored by inspecting the second (or third) interrogative word in a multiple wh-question, and not the one that has moved to the left periphery. This is because in the in-situ position the interrogative use of a quexistential can be compared with the existential use. Once wat has moved to the left periphery, it enters a territory where it is very hard for the ex of quex to survive, as we noted in section 2.3. So our simplest initial testing ground is the quexistential in object position of a multiple wh-question, where the quexistential can in principle be interpreted as an interrogative or an existential, and where we have already shown that absence of stress blocks the qu of quex.

Moreover, even though Dutch permits focal stress on the ex of quex when the alternatives are overtly mentioned, as in example (33b), in their absence stress on the quexistential blocks the ex of quex.

The first question that needs to be asked is whether the interrogative quexistential behaves similarly to nonquexistential interrogative words in this respect. The answer to this, at least for Dutch, is yes. Dutch nonquexistential interrogative words like wie ‘who’ also necessarily receive stress in this environment.

The same is also true, however, for referring (noninterrogative) object DPs.

The next question, therefore, is whether the qu of quex (and the nonquexistential interrogative) receives stress in (39) simply because it is in a position that receives stress in default prosody, as Jan does in (41), or whether there is something special about its being an interrogative word. To determine this, we must look at slightly more complex examples.¹⁶

Consider the following question:

Here, nuclear stress falls on the object (as predicted by theories of nuclear stress) and on the rightmost constituent inside the object (also as predicted). But the contour in the multiple wh-question version of (42) is different: the in-situ wh-phrase welk schilderij ‘which painting’ in (43) must receive stress, unlike the indefinite een schilderij ‘a painting’ in (42).

Quexistentials behave similarly in this respect: if we replace welk schilderij by wat and we still want to express a multiple wh-question, wat needs to be stressed (see figure 1).¹⁷

If stress is placed on Rembrandt instead of wat (see figure 2), only the existential reading is possible.

To sum up so far, in-situ quexistentials on the qu of quex reading and nonquexistential interrogative words behave alike: they both need to be stressed, even if they are not in a position that attracts stress due to the rules of nuclear stress placement. The next question is, what could be the difference between indefinites like een schilderij ‘a painting’ and interrogative words such as welk in welk schilderij ‘which painting’ such that the latter, unlike the former, must be stressed when in situ?

According to Haida (2007) and the body of earlier work he surveys, interrogative words in languages like Dutch, German, and English are always stressed when in situ because such words must generally be marked as contrastive foci.¹⁸ Before we address the question of why interrogative words would be marked as contrastive foci, let us first consider whether this hypothesis is compatible with the prosodic patterns we find in Dutch, and then turn to some languages in which focus is not (only) expressed prosodically, but (also) by means of movement or a specific focus particle.

Consider example (42) again, but now in a context in which een schilderij ‘a painting’ is contrasted with something else, namely, een ets ‘an etching’ by Rembrandt.

In this case, een schilderij must be stressed in order to mark contrastive focus.¹⁹ The stress that marks constrastive focus in (46) is perceived to be very similar to the stress on the quexistential in (44). This similarity is also visible in the pitch contours displayed in figures 1 and 3.²⁰ While more systematic empirical work is evidently required here, we take this to provide initial support for the hypothesis that question words (whether quexistential or not) require contrastive focus in Dutch.

Now let us consider two languages where contrastive focus is not (only) marked prosodically. In Hungarian, contrastive foci are placed in a designated focus position. In Gungbe, on the other hand, they are accompanied by a focus particle. We will start with Hungarian, discussed for instance in É. Kiss 1992 and Haida 2007:sec. 7.2.2. First consider the following sentence, without focus (examples below from Dóra Takász, pers. comm.):

Contrastive focus on the object requires deviance from the baseline order in (47). The object must move to a preverbal position, and the verb itself moves in front of its particle (meghívni ‘to invite’ is a particle-verb in Hungarian).

The same two relevant order effects obtain in the corresponding question.

While (49a) and (49b) differ in the position of the subject, they share the necessity for a preverbal object, and verb-particle order.

Turning now to Gungbe, the examples in (50) show that question words and (other) contrastively focused constituents are marked by means of the same focus particle (Aboh and Pfau 2011).

What is important here is that, even though the strategy for marking contrastive focus differs across Dutch, Hungarian, and Gungbe, in each case interrogative words are marked in the same way as contrastive foci. This supports what we will call the contrastive focus requirement on interrogative words.²¹

Above we have shown that languages may use syntactic (Hungarian), morphological (Gungbe), and prosodic (Dutch and Korean) means to mark contrastive foci. And where languages use prosodic means, these may vary across languages again, as shown above for Dutch (see ^{footnote 13}) and Korean (see ^{footnote 14}). The important point is, however, that we predict that, whatever the strategy used to mark contrastive focus, interrogative words will be marked the same. Furthermore, we should note that in wh-movement languages fronted interrogative phrases are not necessarily accented the way contrastive foci are. In fact, in many cases they can be left completely deaccented. Following Truckenbrodt (2013), we assume that in these languages, fronting of a wh-word to a designated position in the left periphery is in itself a way to mark contrast.²² This is in line with the observation that in many languages, contrastive foci can or even must appear in exactly this position in the left periphery (see, e.g., Rizzi 1997, Aboh 2016).

We thus assume that in wh-movement languages like Dutch and English, interrogative phrases generally require marking of contrastive focus, but that there are two ways of doing so, movement and prosody. Independently, there is a requirement in these languages that in wh-questions, exactly one interrogative phrase moves to the left periphery. This interrogative phrase, then, does not require prosodic contrastive focus marking, while in-situ interrogative phrases do.

If there is indeed a general requirement for interrogative phrases to be marked as contrastive foci, we would of course like to understand why this is the case. To this we turn next.²³ In section 4.3, we discuss existing accounts that aim to understand the relation between interrogatives and contrastive focus. We then turn to our proposal in section 4.4.

There are several existing accounts of the contrastive focus requirement (either as a language-particular constraint or as a crosslinguistic pattern). Most of these are synchronic accounts; one is diachronic. The synchronic accounts can be divided into syntactic and semantic ones, and among the semantic ones a further distinction can be made between two major approaches: one that is based on the assumption that questions involve a question operator in the left periphery that operates on focus alternatives generated by the associated wh-elements (and crashes if those wh-elements do not generate focus alternatives), and one based on the assumption that focus “activates” the latent inquisitive content of wh-elements. A schematic overview of the various accounts is given in figure 4. We will discuss each in turn, starting with the syntactic ones.

Eckardt (2007) provides a diachronic account of the focus requirement on question words. Specifically, she proposes that question words are etymologically rooted in focused deictic elements. This proposal is motivated as follows:

Suppose that the deictic this in (52a) refers in a given context to some object a. Then the question in (52a) asks whether or not the addressee wants a. At the same time, however, by virtue of the focus on this, a range of alternative polar questions are evoked as well: whether the addressee wants b, whether she wants c, whether she wants d, and so on. Eckardt suggests that there are two possible reasons for a speaker to evoke this range of alternative polar questions:

Thus, the overall communicative effects of the focused polar questions in (52) are very similar to those of the corresponding wh-questions in (53).

Eckardt proposes that it is plausible to expect that speakers of the restricted language, without wh-questions, will over time reanalyze the pragmatic effects of polar questions with focused deictic elements to be part of the conventional, semantic content of such constructions. The focused deictic element would then form the basis for the corresponding question word.²⁴

If this is how question words come into existence, Eckardt proposes, it is to be expected that they retain, at least to some extent, the formal features that realize focus in the language at hand (prosody, a focus particle, or movement to a dedicated focus position). She refers to this as lexical focus and distinguishes it from bona fide focus. The lexical focus on question words reflects their diachronic roots, but does not contribute anything to their synchronic semantic interpretation. In particular, question words with lexical focus do not generate focus alternatives, unlike items with bona fide focus.

Finally, Eckardt (2007:222–223) proposes that question words, as interpreted in her framework, may receive the interpretation of an existential indefinite through a simple shift in semantic type.²⁵ She discusses the fact that the existential interpretation of question words generally requires the absence of any formal features realizing focus. She notes, however, that this is not predicted on her account: the shift in semantic type from question words to existential indefinites is not connected in any way on the proposed account to a loss of lexical focus.

Let us now comment on the various aspects of Eckardt’s proposal. First, while Eckardt provides interesting motivation for the idea that question words are etymologically rooted in focused deictic elements, if this were the only way for question words to come into existence, one would expect to see a stronger typological affinity between question words and deictic elements. On the other hand, if the route that Eckardt describes is just one way for question words to come into existence, we would expect to see a considerable number of languages in which question words are not necessarily focused. But at present there is no evidence that such languages exist.

Second, if question words are formed on the basis of focused deictic elements, it is plausible that they would initially retain the formal features that realize focus. However, one would expect that these formal features would in many cases erode over time. Certainly, in languages where focus is realized prosodically, it would be natural for the prosodic features that question words would initially inherit from their deictic ancestors to disappear in later stages of grammaticalization. However, if this is indeed a natural possibility, the theory does not lead us to expect question words to be focused across so many languages today. Rather, it would predict that question words would only involve lexical focus in languages that have resisted erosion.

Finally, as noted by Eckardt herself and already mentioned above, the account does not explain why question words with lexical focus would lose their lexical focus property when used as indefinites.

The proposals by Haida (2007) and Truckenbrodt (2013) are syntactic in nature as far as the contrastive focus requirement on interrogative phrases is concerned. Essentially, they assume that interrogative phrases must enter into an Agree relation with a question operator in the left periphery. Moreover, this Agree relation requires the presence of an F-feature on the interrogative phrase, which has the same prosodic reflexes as the F-feature on contrastive foci. We should say at the outset that neither account explains why the F-feature should be necessary to mediate this Agree relationship (other than the fact that we know that focus is present on wh-words).

While both Haida and Truckenbrodt assume that interrogative phrases and contrastive foci must carry an F-feature with the same prosodic reflexes, there are also differences between the two accounts. In particular, for Haida the F-feature on an interrogative phrase must be accompanied by a wh-feature; otherwise, an Agree relationship with the question operator is not possible. This prevents non-wh contrastive foci from being interpreted as standing in an Agree relationship with a question operator. In other words, in Haida’s account the F-feature, while necessary, is not sufficient to establish an Agree relationship between the question operator and the wh-word; a wh-feature must be present as well.

Truckenbrodt does not assume wh-features in addition to F-features. However, on his account the F-feature on interrogative phrases has a completely different syntactic and semantic status from the F-feature on contrastive foci. What they share is just their prosody.

These proposals, while capturing the empirical generalization, do not explain why interrogative words would have to be marked as contrastive foci.

Moreover, an empirical issue for Haida’s account is that it predicts focus on wh-words to be both necessary and sufficient to yield an interrogative interpretation. As already briefly mentioned in section 3 and discussed in much more detail in section 5, this prediction is at first sight not always borne out. For instance, in example (33), repeated here, focus on Dutch wat, which might be a wh-item on Haida’s assumptions, is not always sufficient to force an interrogative interpretation.

We now turn to a possible semantic account of the focus requirement on question words, based on the work of Beck (2006).²⁶ We should note at the outset that Beck herself did not present her proposal as an account of the focus requirement on question words; rather, she viewed it as an account of so-called focus intervention effects in questions. However, when viewed from a slightly different angle, the proposal may be seen as providing an account of the focus requirement on question words as well—and this interpretation of the proposal is of course the one that is most relevant here.

We will first briefly present the original motivation for Beck’s proposal, and the core assumptions of the account. Then we will clarify how it could be viewed as providing an account of the focus requirement on question words. Finally, we will critically discuss the proposal, both as an account of intervention effects and as an account of the focus requirement on question words (with the caveat, again, that Beck herself never claimed to provide an account of the latter).

Let us first illustrate what focus intervention effects in questions are. Consider the examples in (54) and (55) (we use German examples here because demonstrating focus intervention effects in English requires more complex constructions; see Pesetsky 2000, Beck 2006, and Kotek 2019 for discussion).

While (54) is interpreted as a multiple wh-question, inserting the focus-sensitive operator nur ‘only’ in (55) makes this interpretation unavailable. Such intervention effects have been observed to arise in many typologically unrelated languages (e.g., Kim 2002, Beck 2006). According to Beck (2006), this is because a wh-word generates focus alternatives, and these alternatives must be visible to the interrogative complementizer (more specifically, the complementizer turns these focus alternatives into alternatives in the ordinary semantic value of the question, representing its inquisitive content). Focus-sensitive operators like nur ‘only’ “consume” any focus alternatives that are generated within its scope, and make these focus alternatives invisible for operators outside of its scope. Thus, in a configuration like (55) nur ‘only’ makes the focus alternatives generated by wo ‘where’ invisible for the interrogative complementizer. Beck proposes that this gives rise to uninterpretability.²⁷

On Beck’s account of intervention effects, then, for a lexical item to function as a question word, it must generate focus alternatives. After all, if an interrogative complementizer receives no focus alternatives as input, it will never output a set of alternatives in the ordinary semantic value of the sentence representing the inquisitive content of a wh-question. Thus, the proposal explains why question words need to be focused.

We will discuss two issues for Beck’s proposal (see Eckardt 2007, Mayr 2014, and Li and Law 2016 for further critical discussion of the approach). The first issue concerns the original motivation for the proposal based on intervention effects. For the approach to deliver an account of focus intervention effects in questions, it is crucial that focus-sensitive operators like only are assumed to be unselective—that is, that they operate on all focus alternatives that are generated within their scope. However, as Beck (2006: sec. 5.2) herself discusses, the validity of this assumption is controversial. Consider example (56).

In (56b), only associates with the focus alternatives generated by SUE, while also associates with the focus alternatives generated by FATHER. Krifka (1991) and Wold (1996), among others, have concluded from such observations that focus-sensitive operators can be selective; that is, they do not necessarily associate with all focus alternatives generated within their scope. If this conclusion is valid, Beck’s account of focus intervention effects in questions cannot be right.

However, there is no full consensus yet as to whether the conclusion is indeed valid. Beck (2006:sec. 5.2) surveys further literature on this topic and also presents a small empirical study. The results of this study are mixed. Whether unselective association is possible seems to depend both on the specific focus-sensitive operators involved and on the language/dialect under consideration (Beck tested in English and German, and found variation between the two languages as well as within each language among different speakers/dialects). Of course, it may be that focus intervention effects in questions arise exactly with those focus-sensitive operators and for those speakers that do not allow for selective association with focus alternatives. This, however, remains to be investigated. For now, it is an open issue whether focus intervention effects in questions correlate with the impossibility of selective association.²⁸

The second issue for Beck’s proposal that we will discuss pertains both to the underlying motivation based on intervention effects and to the explanation of the focus requirement on question words. The crucial observation is that focused non-wh-words cannot be interpreted as question words. For instance, (57a) can only be interpreted as a polar question, not as a wh-question, and (57b) can only be interpreted as a single wh-question, not as a multiple wh-question.

This means that generating focus alternatives is not sufficient for an item to be interpreted as a question word. As a consequence, it must be assumed under Beck’s approach that the interrogative operator, let’s call it Q, is a selective focus-sensitive operator: it can only associate with focus alternatives generated by wh-words, not with focus alternatives generated by non-wh-words. This weakens the motivation for the proposal based on intervention effects. After all, the account needs to assume that Q is selective, while other focus-sensitive operators such as only are not. Apart from the fact that the empirical validity of the latter assumption is controversial (as discussed above), the presumed difference between Q and other focus-sensitive operators would have to be explained.

At the same time, the fact that Q can only associate with alternatives generated by wh-words also undermines the explanation of the focus requirement on question words. On the proposed account, Q is looking for focus alternatives, so question words need to provide such alternatives. This entails their focus requirement. However, since “wh-related focus alternatives” must be separated from other focus alternatives (so as to avoid the possibility that all focused items could be interpreted as question words), there is nothing really substantial about the fact that “wh-related focus alternatives” are treated as a kind of focus alternatives. The account may just as well assume, for instance, that wh-words are variables (unrelated to focus) and that Q generates alternatives in the ordinary semantic value of the question corresponding to the possible values of the associated wh-variables. This account would derive the same semantic values for questions as Beck’s original account, except it would not entail a focus requirement on question words. This means that the original account does not really provide an explanation for the focus requirement either.

The proposals of AnderBois (2012) and Möller Kalpak (2018) are also semantic in nature, but differ substantially from Beck’s (2006). For concreteness, we focus here on AnderBois’s proposal, though our main concerns also apply to Möller Kalpak’s.

AnderBois argues that in Yucatec Maya, wh-questions are formed using quexistentials marked as contrastive foci.²⁹ If these quexistentials are not marked as contrastive foci, they are interpreted as existentials. AnderBois proposes that quexistentials have both informative content, conveying that there is some individual with a certain property, and inquisitive content—namely, the issue of which individual it is that has the given property (see Groenendijk and Roelofsen 2009). He proposes, however, that the inquisitive content is in some sense latent: the issue is only raised if the informative content of the sentence is trivial in the context of utterance. For instance:

Against this background, AnderBois proposes that when contrastive focus is placed on the quexistential, it contributes an existential presupposition (i.e., the presupposition that some individual has the given property), which renders the informative content of the sentence contextually trivial. This, in turn, “activates” the latent inquisitive content of the sentence, which results in an interrogative interpretation.

So on AnderBois’s proposal, a semantic reflex of contrastive focus that has been independently argued for in other work (see, e.g., Geurts and van der Sandt 2004)—namely, an existential presupposition—makes it possible, and is in fact necessary, for a quexistential to get an interrogative interpretation in Yucatec Mayan.

However, when applied to other languages this type of account encounters a number of challenges. One question that the account leaves unanswered is why nonquexistential interrogative phrases generally require contrastive focus marking just as much as quexistential interrogative phrases. Since nonquexistential interrogative phrases are always interrogative (i.e., do not allow for a plain existential interpretation), it would be natural to assume that their inquisitive content is not “latent” but surfaces automatically. Why, then, do such phrases still need contrastive focus marking?

Let us make this point in somewhat more general terms. One of the fundamental ideas behind AnderBois’s account is that contrastive focus is necessary in order for quexistentials to receive an interrogative interpretation. So the assumed causal connection between contrastive focus and interrogative interpretation is as follows:

Our point is that, if this is indeed the causal connection, it is unclear why purely interrogative (nonquexistential) phrases require contrastive focus marking as well.³⁰

We propose that the causal connection between contrastive focus and interrogative interpretation is as in (60) (i.e., the opposite direction from (59), repeated here).

In other words, contrastive focus does not automatically and necessarily yield an interrogative interpretation. Rather, it is the other way around: phrases that receive an interrogative interpretation must generally be marked as contrastive foci. This in fact naturally follows, we propose, from only a slight generalization of existing theories of contrastive focus.

To develop this idea, we must first briefly review what we take to be a common view on contrastive focus. To do so, we consider a simple case that involves contrastive focus but has nothing to do with interrogativity.

B’s response, Tom married Sam, contrasts with A’s initial statement, Tom married Kim, and this contrast is signaled by the focal stress on Sam. Many theories of contrastive focus (from Rooth 1992 to Büring 2016 and Kratzer and Selkirk 2018) essentially hold that in order to mark some constituent E as contrasting with another constituent E′, a speaker places focus on subconstituents of E in such a way that the focus semantic value of E (F) has the ordinary semantic value of E′ (O) as one of its elements. This is exactly what happens in (61), because the focus semantic value of B’s response is as shown in (62), and this set contains the ordinary semantic value of A’s initial statement.

Let us make this a bit more general and precise. The basic effect of marking a constituent E with contrastive focus is to evoke a set of alternatives to the ordinary semantic value of E. These alternatives, together with the ordinary semantic value itself, make up the focus semantic value of E. Marking a constituent with contrastive focus and thereby evoking alternatives may be done for a number of reasons. For instance, the alternatives may serve as input for focus-sensitive operators like only. But another reason to evoke focus alternatives, most relevant here, is to signal the presence of contrasting alternatives in the discourse. It is assumed that speakers should signal the presence of contrasting alternatives in the discourse by means of focus whenever they can, while on the other hand they should never “overfocus”—that is, they should not focus constituents without any purpose (e.g., Schwarzschild 1999).

In (63), we summarize the three main tenets of the common view on the use of focus to signal the presence of contrasting alternatives.

Note that this view as such does not account for the contrastive focus requirement on interrogative words. Suppose A walks up to her colleague B and says the following:

Clearly, there is no sentence in the discourse that the question in (64b) could possibly be taken to contrast with. So at first blush, there seems to be no reason for the (optional) contrastive accent on who and the (obligatory) contrastive accent on what.³¹

However, we will propose a generalization of the common view that provides an explanation for these facts. The crucial observation underlying this generalization is that it is implicitly assumed in (63b) that the type of contrast that speakers signal by means of focus is always a contrast between two different expressions. In our example above, these two expressions are Tom married Kim and Tom married Sam. The ordinary semantic value of each of these expressions is usually taken to be a proposition. So the contrast is taken to involve two propositions. Focus is placed on a subconstituent of the second sentence, Sam, such that the focus semantic value of this sentence contains both of the contrasting propositions.

Now consider the question in (65).

This question can be resolved in a number of ways: by providing the information that Tom married Sam, that he married Kim, that he married Lyn, and so on. We propose that it is natural to think of these possible resolutions as contrasting with each other in much the same way as Tom married Kim and Tom married Sam contrast with each other in the dialogue in (61).

To make this more precise, let us assume—in line with theories of questions based on Hamblin 1973, Karttunen 1977, or Groenendijk and Stokhof 1984, as well as more recent theories based on inquisitive semantics (Ciardelli, Groenendijk, and Roelofsen 2018)—that the ordinary semantic value of a question is (or at least determines) a set of propositions, each corresponding to a minimal piece of information resolving the question. For (65), this set of propositions is given in (66). Note that it contains exactly the same propositions as the focus semantic value of Tom married SAM, which was given in (62).

The idea is that these propositions (i.e., these alternative resolutions of the question) contrast with each other, and that this contrast must be signaled by contrastively focusing a subconstituent of the question in such a way that the focus semantic value of the question contains the contrasting propositions. This means contrastively focusing who (under the assumption that the focus alternatives of who are Sam, Kim, Lyn, etc.)—for, if who is focused, the focus semantic value of the question becomes the following:³²

Note that, indeed, as a result of focusing who, the contrasting propositions in the ordinary semantic value of the question, given in (66), are all elements of the focus semantic value of the question in (67). So focusing who successfully signals the presence of contrasting propositions.

As discussed above, we assume that in languages like English and Dutch, contrastive focus on wh-words manifests itself either as movement to a designated position in the left periphery, or prosodically, or both. So in (65), prosodic marking of focus is not necessary because the wh-word has moved to the left periphery, but in the case of in-situ wh-words prosodic marking of contrastive focus is necessary.

What does it mean, then, for a speaker uttering an expression E in a context C to signal contrast by means of focus? As reviewed above, Rooth (1992) and others have proposed that this means for the speaker to place focus on a subexpression of E in such a way that the focus semantic value of E includes the ordinary semantic value of some other expression E′ that has been used in context C.

We propose something slightly more general: namely, that in order to signal a contrast, a speaker places focus on a subconstituent of E in such a way that the focus semantic value of E includes at least two (nonidentical) alternatives α and β such that α is an element of the ordinary semantic value of E, and β is an element of the ordinary semantic value of some expression used in C, which may be either E itself or some other expression E′.³³ Given this general notion of what it means to signal a contrast by means of focus, we can identify two special cases:

External contrast is exactly the same as the standard Roothian notion of contrast. On the other hand, internal contrast is the one that is relevant for questions. The fact that both are subcases of a single more general notion makes it natural for languages to mark them in the same way, although it is also imaginable that certain languages mark them differently.³⁴

Let us return now to the common view on contrastive focus, whose three main tenets we summarized in (63). What we propose is to leave the first and third tenets untouched, but to slightly adapt the second one in view of our more general notion of contrast. That is, we propose to replace (63b) by (70).

Together with the pragmatics of focus placement in (63c), this generalized notion of contrast accounts for the fact that interrogative words (whether quexistential or not) generally must be focused. On this account, the focus on interrogative words signals an internal contrast. Depending on the way(s) in which focus is generally expressed in a given language, the focus on interrogative words may manifest itself through movement, prosody, a focus particle, or a combination of these.

Let us sum up what we have established so far on how the qu of quex interacts with stress and focus. First, we have shown that an in-situ qu of quex in a language like Dutch always requires focal stress. Second, following Haida (2007) and others, we have suggested that this fact is a particular instance of a much more general pattern—namely, that interrogative words (whether quexistential or not) always require contrastive focus marking. We have argued that existing accounts of this generalization are not fully satisfactory, and we have offered an alternative account.

We should (re)emphasize that while our proposal predicts a tight connection between contrastive focus and wh-questions, we do not run the risk of being confronted with questions like “Why isn’t it the case that focus on any pronoun/noun yields a question?” The reason is that we do not take contrastive focus to be an ingredient in the construction of inquisitiveness. In this article, we say nothing about the source of the latter. What we do say is that once inquisitiveness enters the picture, contrastive focus follows it (in the case of wh-questions; polar questions are a different matter and remain to be explored from this perspective, possibly in relation to the expression of verum focus).

We now turn from the qu of quex to the ex of quex.

We have shown that a quexistential in the qu of quex interpretation behaves just like any nonquexistential interrogative word when it comes to stress and focus. In this section, we will ask a related question for the ex of quex: to what extent does the ex of quex behave like nonquexistential indefinites when it comes to stress and focus?

We already argued in section 3 that an account of how the ex of quex relates to focus will not be sufficient on its own to capture the relation between the ex of quex and stress in general. This is because we would expect that in an out-of-the-blue context, without focus on any particular constituent, the ex of quex should receive stress when it is in a position that normally receives stress in default prosody. But this is not the case, as we already illustrated with Dutch examples (36) and (37), repeated in (71) and (72).

This means that we are faced with two tasks: to understand the relation between the ex of quex and stress in default prosody, and separately from that, to understand the relation between the ex of quex and focus. Starting with the first question, we will show that the ex of quex behaves like nonquexistential indefinites.

In this section, we discuss the ex of quex as it relates to stress in default prosody. In the following sections, we will look at focus. We propose that (72) is ruled out by general prosodic constraints, which prohibit stress in default prosody falling on existential quantifiers across the board. Indeed, the Dutch nonquexexistential existential iets ‘something’ shows the same behavior. It does not receive a pitch accent in default prosody even when it is in the position where that accent is usually placed; instead, the accent shifts to the verb.³⁵

The fact that existential quantifiers resist a pitch accent in default prosody is known. It also manifests itself in English. The examples in (75) show that the existential quantifier does not receive stress in default prosody even when it appears in a position where such stress is usually placed, as seen in (75c).

Why would this be? One proposed line of reasoning is that the existential is a functional item and thereby incapable of receiving stress in default prosody, which is reserved for lexical items (see Büring 2016 for discussion and references). One difficulty for this hypothesis is that one would have to assume that just existential quantifiers are functional items, because other quantifiers (e.g., English everything or Dutch alles) have no problem receiving stress in default prosody (see also Wagner 2006 for a critique of accounts based on the existential’s not being able to receive stress because it is a functional item).

At least two alternative proposals exist. Wagner (2006) argues that existential quantifiers are always deaccented because they trivially meet the requirements for givenness, and given items are generally deaccented. Ahn (2015), on the other hand, provides an account that relies on the assumption that the syntax of existentials like something differs from that of DPs like dumplings in a way that is relevant for the mechanism that assigns stress in default prosody.

Whatever the right account of this general phenomenon is, it is clear that the pattern involving quexistentials on their existential use should be seen as a particular instance of it. There is no reason to believe that there is something special about the inability of quexistentials on their existential use to receive stress in default prosody. The contrast in (71)–(72) is due to something that is not specific to quexistentials, but rather is common to all existential quantifiers (their inherent givenness status if Wagner (2006) is right, or their syntactic status if Ahn (2015) is right).

The next question is whether it is possible for the ex of quex to receive stress due to contrastive focus rather than default prosody. We address this question in the next two sections.

The QF biconditional as stated by Haida (2007) and others appears to stand on firm empirical ground. Haida shows that the part of the biconditional that precludes focus on the ex of quex holds for German, and we have found that it also holds for Russian.

When it comes to the ex of quex not being able to receive nuclear stress in default prosody, the facts in German and Russian are the same as in Dutch: like other existential indefinites, the ex of quex resists it.

As for contrastive focus, the ex of quex in German and Russian also abides by the QF biconditional: namely, it never receives stress due to contrastive focus.³⁶

In German, it is possible to use stress to signal the contrast in (76), but only if it is placed either on the auxiliary hat ‘has’ or on a nonquexistential existential quantifier, etwas ‘something’.

Russian behaves the same way as German: while the ex of quex cannot be contrastively focused, the language has a series of other indefinites that can.

So far, then, the relation between quexistentials and focus does appear to be a biconditional. We have proposed an explanation for why the qu of quex requires focus (and in this we showed that the qu of quex behaves like other interrogative words). We have shown that on the ex of quex interpretation, the quexistential resists stress associated with default prosody (and in this we showed that the ex of quex behaves like other existentials). Finally, in this section we showed that in German and Russian, the ex of quex cannot receive contrastive focus either (in this, the German and Russian quexistentials differ from other indefinites in those languages). It would seem, then, that this is the last part of the QF biconditional that needs an explanation.

However, it may be that the conclusion that the ex of quex cannot be contrastively focused is too hasty, and that the “QF biconditional” is not a biconditional at all, but a one-way entailment. In other words, before we try to explain a phenomenon as universal, or at least as being of significant crosslinguistic stability, we need to make sure it is indeed that. In the next section, we show that Dutch provides a potential counterexample to this part of the QF biconditional. We will thus find ourselves faced with two logical possibilities: either we decide that the relation between the ex of quex and contrastive focus is not captured by the QF biconditional (in which case we will need to investigate the difference between German and Russian on the one hand and Dutch on the other), or we try to find grounds for removing Dutch as a counterexample. We attempt this in section 5.4.

In this section, we will give several examples involving focal stress on the ex of quex in Dutch. Since all these examples will involve verum focus, we should start with a general point about verum focus in Dutch. In corrective statements such as (79B), verum focus is expressed using the particle wel with a strong falling pitch accent.³⁷

Note that this is different from English, which expresses verum focus by means of an accented auxiliary verb, as in She DID leave, She HAS left, She IS studying. This is impossible in Dutch.

The same pattern occurs in response to a question that is biased toward a negative answer.

When the question is neutral, stressed wel is not felicitous. Unstressed wel is possible but only as part of a more elaborate answer that itself involves a contrast.

With this background in mind, let us turn to contrastive focus on the ex of quex.

In response to a negative assertion or a negatively biased question, stressed wel appears again. The stress on wel here is the falling pitch accent of contrastive focus. Moreover, the quexistential again behaves the same as a nonquexistential existential in that neither can be focused.

However, both the quexistential and the nonquexistential indefinite can be contrastively focused if they contrast with a subsequent denial of a stronger or more specific alternative. In this case, wel and niet are marked as contrastive topics by means of rising pitch accents, while the contrastively focused quexistential or nonquexistential indefinite receives the falling pitch accent characteristic of contrastive focus.³⁸

In addition, both the quexistential and the nonquexistential indefinite can be marked as contrastive topics, with a falling focus accent on ingeleverd ‘submitted’.

Again, in (84b) and (84c) the nonquexistential iets can appear with the same prosody as the quexistential wat.

In a response to a neutral question, unstressed wel can optionally be used, but it cannot be marked as contrastive focus. As for the quexistential and the nonquexistential indefinite, if they are not contrasted with any stronger or more specific alternative in the response, they must be left unstressed.

However, just as in responses to negative assertions and questions, they both can be contrastively focused if they contrast with a subsequent stronger or more specific alternative. In this case, wel and niet are marked as contrastive topics by means of rising pitch accents, while the quexistential or nonquexistential indefinite is marked as a contrastive focus by means of a falling pitch accent.

Alternatively, both the quexistential and the nonquexistential indefinite can be marked as contrastive topics, with a falling focus accent on ingeleverd ‘submitted’.

So the ex of quex in Dutch can receive either a falling or a rising contrastive pitch accent, depending on whether it is marked as a contrastive focus or a contrastive topic. It behaves just like the nonquexistential indefinite in this respect. In other words, Dutch appears not to conform to both parts of the QF biconditional: it is possible to manipulate the environment in such a way that focus and the ex of quex are compatible.

Contrastive focus on the ex of quex in Dutch seems possible in two further environments as well. First, in the context of sluicing it again behaves exactly as a nonquexistential indefinite does.

Second, it can be stressed, presumably due to contrastive focus, when it appears as the associate of the scalar NPI ook maar (literally ‘also but’, roughly equaling even in English), which compares its argument with amount alternatives and requires that its argument be the endpoint on some amount scale, similar to English even. Of course, focused wat can only appear with ook maar in environments where the latter is licensed. As an NPI, it is not licensed in plain positive environments.

But when ook maar is licensed, the ex of quex reading of wat is compatible with focus.

In short, we have shown again that the ex of quex can be made compatible with focus in Dutch, and as such again behaves just like the nonquexistential indefinite.

The above discussion leads one to expect that it should be possible to set up a case where the qu of quex and the ex of quex have similar prosody. Specifically, when the ex of quex is contrastively focused, it should exhibit the same intonational contour as an in-situ qu of quex, which is always contrastively focused. This expectation is indeed borne out, as can be seen by comparing (91) and (92). The pitch contours for these sentences are displayed in figures 5 and 6, respectively. Note that these contours are very similar.

In Dutch, then, the behavior of the qu of quex with respect to stress and focus is just like that of other question words (always contrastively focused), and the behavior of the ex of quex is just like that of other existentials (never stressed due to default prosody, but possibly stressed due to contrastive focus or topic marking).

So the Dutch reality is not captured by the QF biconditional “qu if focused, ex if not focused.” We are confronted with a choice, then: either we treat the relation between quexistentials and contrastive focus as not being as universal as the QF biconditional would have us believe (and therefore start to explore its parameterization), or we look deeper into Dutch for grounds to explain it away as a counterexample and thereby maintain a stronger belief in the potential universality of the QF biconditional. We attempt the latter in the next section.³⁹

In this section, we will attempt to find a difference between Dutch on the one hand and Russian—and in particular the closely related German—on the other, so that we can explain Dutch away as a counterexample to the QF biconditional. If an orthogonal (to the QF biconditional) difference can be found that is responsible for the Dutch pattern discussed earlier, then we do not have to give up faith in the crosslinguistic stability of the biconditional and try to explain it. We will be explicit with the details, so that future research might find any gaps in our argumentation.

So what difference(s) are there between Dutch and German/Russian⁴⁰ that may cause the different behavioral patterns when the ex of quex is contrastively focused?⁴¹

One difference between Dutch and German is that Dutch wat, unlike German was, can function as a determiner, as in (93) with a plural count noun and in (94) with a mass noun. It cannot function as a determiner on a single count noun; see (95).⁴²

The German quexistential was cannot function as a determiner, as seen in (96) and (97).

Could this be part of the reason why the Dutch ex of quex permits focal stress while the German one does not (e.g., contrast with other determiners would be more straightforward (‘some but not much’))? If the question is put in these terms, the answer cannot be affirmative because this distinction does not cut along the correct crosslinguistic lines: the Russian quexistential kakoj can be used as determiner, but still cannot receive focal stress on its existential reading.

However, maybe it is possible to press this point further: what if Dutch wat as a determiner is not a quexistential at all, while when Russian kakoj is a determiner, it is still a quexistential? Then we would be looking at the following situation: when wat accepts contrastive focus, it is always and only a nonquexistential determiner and, as such, its relationship to focus is irrelevant to the QF biconditional, whose domain is only quexistentials.

The first reason to suspect that wat as a determiner is not a quexistential is that sentences like (98) and (99) are ungrammatical. In other words, determiner wat cannot function as an interrogative word, as one would expect of a quexistential.

If the determiner wat were a quexistential, one would expect (98) and (99) to be grammatical as questions.

Similarly, consider the following examples:

These sentences lack a multiple question interpretation, unlike their counterparts with independent wat.

This is further evidence that when wat is a determiner, it is not a quexistential.

Moreover, determiner wat with an overt restrictor can appear unproblematically in the contrastive environments that we have already illustrated: with a mass noun, as in (104)–(105), and with a plural count noun, as in (106)–(107).

The above are cases in which wat is stressed and clearly functions as a determiner. What then if wat, when it carries focal stress but has no overt nominal restrictor, is still a determiner but with a null noun as restrictor (or null NP; we will not distinguish these here)? (For arguments in favor of the existence of null nouns, see Postal 1969, Panagiotidis 2003, and Corver and Van Koppen 2011, among others. For a possible account of why such nouns are null, see Kayne 2005.)⁴³

If this hypothesis is correct—that is, if every occurrence of focused wat is indeed an occurrence of it as a nonquexistential determiner—then Dutch would not constitute a counterexample to the crosslinguistic generalization that the ex of quex is incompatible with focal stress: any stressed occurrence of wat would be an instance of the nonquexistential determiner. But how safe is this conclusion?

One could counter the claim that wat as a determiner is not a quexistential by arguing that there are in fact cases in which wat receives an interrogative interpretation in determiner position, specifically in the somewhat famous wat voor construction, as illustrated in (108) and (109).

The rationale would be as follows: According to Heck (2009) and Huhmarniemi (2012), among others, when an interrogative XP moves to the left periphery of a clause (e.g., the specifier of CP), there is also XP-internal wh-movement to the left periphery of that XP.

Moreover, following Bennis (1995), voor in the wat voor construction is an interrogative complementizer. Putting everything together, one could conclude that wat voor bloemen ‘what kind of flowers’ and wat voor water ‘what kind of water’ in (108) and (109) are the qu of quex equivalent of the ex of quex in (93) and (94), with the element voor appearing for orthogonal reasons.

One piece of evidence for this is that wat voor bloemen and wat voor water cannot be used as existential expressions.

The voor item appears only in questions, arguably for orthogonal reasons, as we said.

If this rationale is correct, then we are not forced to conclude that when it is a determiner, wat is a pure existential rather than a quexistential: the determiner wat is indeed a quexistential, since it permits both ex of quex and qu of quex readings (albeit the latter with an added interrogative voor that must appear for language-specific purposes). This would mean that Dutch is indeed a counterexample to the QF biconditional, since under this scenario, it does have a quexistential that can be contrastively focused without becoming an interrogative.

To pronounce a verdict on the debate at this point, we must ask whether the above rebuttal (which aims to establish that determiner wat is a quexistential after all) is unassailable.

The answer is no. There are in fact a few weak points: there is an important semantic difference between the ex of quex and the wat voor construction that does not reduce to the difference between the ex of quex and the qu of quex readings. Namely, the only available readings of (108) and (109) are about kinds of flowers and kinds of water.

These questions do not ask the addressee to identify specific entities, unlike the following:

However, the ex of quex in general is not restricted to kind readings. So it would be difficult to maintain that wat voor bloemen and wat voor water are the qu of quex equivalents of the ex of quex phrases wat bloemen and wat water. Moreover, the qu of quex reading of the Russian quexistential kakoj when used as a determiner is not restricted to kind readings. That is, the kind reading is not a necessary consequence of interpreting a quexistential determiner interrogatively. Finally, the German was für construction behaves the same way as the Dutch wat voor construction with respect to the points just mentioned. So the wat voor/was für construction does not rely on the possibility of wat/was being a determiner, which it is in Dutch, but not in German.

So the previous hypothesis still stands: it is quite possible that Dutch wat, qua determiner, is not a quexistential. And, as we said, this conclusion brings out the possibility that when wat receives focal stress, it always does so as a nonquexistential determiner. This would mean that Dutch is not a counterexample to the crosslinguistic generalization that the ex of quex is incompatible with focal stress. The QF biconditional would still stand.

Under this scenario, Russian would show the regular pattern, as the determiner use of its quexistential does not force a kind reading and has the expected qu of quex reading. The nonfocusability of its quexistential determiners would then be par for the course. So are we ready to declare that Dutch is not a counterexample to the QF biconditional, since focused wat is a focused nonquexistential determiner and the biconditional holds sway only over quexistentials?

We would indeed like to adopt this hypothesis as the one that has the most support: Dutch is not a counterexample to the QF biconditional since focus on determiner wat is not focus on a quexistential.

Of course, challenges remain. We have shown that the conclusion that focused wat is not a quexistential but a nonquexistential determiner is fully compatible with the data. But we have not shown that focused wat is never a quexistential DP. Such a negative existential statement is very hard to prove, possibly like most negative existential statements.

Another remaining question pertains to the interaction of the nonquexistential determiner wat with Postma’s (1994) observation that an ex of quex reading is possible in Dutch only in certain syntactic environments—specifically, only inside the VP. We have shown that focused wat is fine outside the VP, contra Postma’s generalization (see ^{footnote 39}). However, if we are right that determiner wat is not a quexistential, one might expect that this determiner can appear outside the VP even without focus.

But this is not what we find. Unfocused determiner wat is not possible in subject position.

For example:

But inside the VP, it is fine, as we have already shown.

One could thus ask whether the inability of unfocused determiner wat to appear outside the VP might not be an argument in favor of the quexistential status of determiner wat, contra our earlier conclusion. The answer is no—especially if Postma is correct that the restriction to the VP is an indication that wat needs to be bound by existential closure, as in the work of Heim (1982) and Diesing (1992). Heim and Diesing argue that certain determiners lack quantificational force of their own, obtaining it by an existential quantifier that is inserted as a last resort operation on a syntactically defined domain, which, according to Diesing, is the VP.⁴⁴ In other words, being subject to existential closure is a characteristic not of quexistentials but of certain determiners that lack quantificational force of their own and are introduced into a sentence as variables. After all, the original proposals, like Heim’s and Diesing’s, were about nonquexistential determiners. In other words, if indeed determiner wat is introduced into the sentence as a variable and requires default existential closure, this does not mean that it is therefore a quexistential. Under the relevant assumptions, it would only mean that it lacks its own quantificational force.

Having said this, we are not asserting that Dutch wat, whether as a quexistential or a nonquexistential determiner, is in fact subject to existential closure. We remain at best agnostic about that in the current context. In Hengeveld, Iatridou, and Roelofsen 2019, we argue that even for the ex of quex, Postma’s (1994) proposal for existential closure meets with difficulties, because wat cannot be caught by other quantificational elements in the sentence, the way indefinites can in Heim’s and Diesing’s work.

On the other hand, Dutch wat, with or without a nominal restriction, cannot be bound by adverbs of quantification.

These sentences are fine on the intended meaning with bare plural dingen ‘things’.

In this article, then, we do not take a position on the relationship of existential closure to Dutch wat. What we wanted to point out is that the fact that determiner wat is not acceptable in subject position does not mean that it should be considered a quexistential.

Note that when wat is preceded by certain degree modifiers, it is acceptable in subject position.

It is possible that these form complex determiners. We leave them for future research.

In this article, we explored the conditions under which quexistentials can or must be focused, depending on their interrogative or existential interpretation. We did not address the issue of how these two readings come about, nor what the nature of a quexistential must be so that it can yield these two interpretations in different environments.

Previous literature has suggested that quexistentials are always focused on their interrogative use, and never on their existential use. We argued that the first part of this generalization is correct and proposed that the obligatory focus of the qu of quex is a particular instance of a more general fact—namely, that interrogative words (quexistential or not) are always contrastively focused. We proposed an account of this more general fact, based on the idea that focus is used to signal not only external but also internal contrasts.

The second part of the generalization, which holds that the ex of quex is incompatible with focus, took us to Dutch, which appeared to violate it. We identified a number of environments where Dutch wat can receive focal stress without turning into an interrogative item. This could have meant that the second part of the QF generalization does not hold (i.e., it would not be a biconditional), but we proposed an analysis under which Dutch is not a counterexample after all. In short, while we explained only one part of the QF biconditional and did not explain the part that relates to the incompatibility of the ex of quex with focus, we removed one possible counterexample to it, leaving the biconditional open for explanatory accounts.

A natural next step in this investigation would be to look for and examine other languages where the ex of quex is compatible with prosodic prominence. We already noted that Korean appears to permit focus on the ex of quex (see ^{footnotes 14} and ²¹) and therefore should be closely examined soon to determine whether it is indeed a counterexample, unlike Dutch. Further crosslinguistic investigation of the relation among quexistentials, prosodic prominence, and focus will doubtless play an important role in investigating the phenomenon of quexistentials at large.

For their generous help with ideas and/or judgments, we thank Byron Ahn, Paul Boersma, Tanya Bondarenko, Ben Bruening, Seth Cable, Ömer Demirok, Donka Farkas, Edward Flemming, Hana Kalpak, Jo-Wang Lin, Flavia Naehrlich, Hella Olbertz, Roger Paul, Gertjan Postma, Omer Preminger, Norvin Richards, Sergei Tatevosov, Igor Yanovich, Hedde Zeijlstra, and audiences at an NYI seminar in St. Petersburg, an InqBnB workshop at the University of Amsterdam, and colloquia at the University of British Columbia, Princeton University, and Seoul National University. We are also grateful to the development and support team of Praat (Boersma and Weenink 2020), which proved a very useful tool for this project. Finally, we gratefully acknowledge financial support from the Netherlands Organization for Scientific Research (NWO), the European Research Council (ERC, grant 680220), the Royal Dutch Academy of Science (KNAW, grant UPS/RB/3991), and the MIT MISTI fund (grant 1491731). The authors are listed in alphabetical order.