1 Introduction
It has long been agreed that some nouns (e.g. mayor, governor, president, capital, time, place, location, price, number…) can have an interrogative reading in some interrogative contexts, as illustrated in (1).

The semantics of such ‘concealed question’ nouns has been extensively studied (see Baker Reference Baker1968; Grimshaw Reference Grimshaw1979; Nathan Reference Nathan2006; Frana Reference Frana2010; Barker Reference Barker2016; Frana Reference Frana2017 inter alia). It is usually agreed that Concealed Questions (CQ) correspond to identity questions (similar to interrogatives introduced by who or what), as illustrated in the paraphrase provided in (1), and that other wh-questions, such as where/when/how much X is, are not possible meanings for a CQ (Nathan Reference Nathan2006; Frana Reference Frana2017). Nathan (Reference Nathan2006: 21) states that ‘insofar as a concealed question denotes a question, that question is an identity question, i.e. one of the form who X is or what X is’.Footnote 2 Our hypothesis is that this assumption should be questioned. First, it has recently been argued (Jugnet & Miller Reference Jugnet, Miller, Gardelle, Mignot and Neveux2024) that a distinct subclass of nouns, which they call polar nouns, can have a different type of interrogative readings, a Polar Concealed Question (PCQ reading), i.e. interrogative readings similar to polar interrogatives, in a subset of interrogative or modal contexts.Footnote 3 Such nouns differ from ‘concealed question’ nouns in that they never denote first order entities (rather, they can denote states or eventualities involving a state).

This article argues that a large set of nouns (e.g. dedication, effectiveness, failure, honesty, involvement, likelihood, loyalty, suitability, usefulness, willingness, …), partially overlapping with those that allow a polar concealed question use, can have a degree reading, and involve a questioning on a gradient, in a subset of interrogative contexts.

The possibility of a degree/level of reading is mentioned by Nathan (Reference Nathan2006: 98–9), who hypothesizes that there may be two classes of relational nouns, one class (including nouns such as price, height, area and age) corresponding to ‘abstract relational nouns’. The distinction between degree nouns and other intensional nouns has also been mentioned in the analysis of Bangla data (Bhadra & Mendia Reference Bhadra and Mendia2019). Focusing on English data, this article will first motivate the distinction between Degree Concealed Question (or DCQ) and Identity Concealed Question (or ICQ) readings, by describing the specificities of nouns that can have a DCQ reading, or DCQ nouns, as opposed to ICQ nouns. More specifically, in an attempt to determine what makes the DCQ reading possible, the subset of (possibly polar) nouns that can have a degree reading, and the subset of contexts that allow this reading, are circumscribed and described. This description is followed by an analysis of key lexical semantic features of DCQ nouns. The DCQ reading is then shown to depend not only on lexical, but also on contextual parameters, in a discussion of the potential ambiguities of DCQ nouns.
2 The class of Degree Concealed Question (DCQ)
Before we discuss some semantic features of nouns that can have Degree Concealed Question readings, we examine the similarities and differences between Degree Question Nouns and other Concealed Question nouns. This leads us to argue that DCQ nouns should be identified as a distinct subclass of nouns.
2.1 Some similarities between ICQs and DCQs
Nouns that can have Degree Concealed Question readingsFootnote 4 and nouns that can have (traditional) Identity Concealed Question readingsFootnote 5 share some properties. All of these nouns have an interrogative interpretation and can be paraphrased by a wh-clause (in some contexts):Footnote 6

The semantics of concealed question nouns thus seems similar to that of a clause, even though their syntax is typically nominal: as shown by (Grimshaw Reference Grimshaw1979) concealed question nouns have the distribution of Noun Phrases rather than that of clausal complements: they can undergo subject–auxiliary inversion and they cannot be extraposed.

Furthermore, concealed question nouns can occur in some indirect interrogative contexts. More precisely, they appear in intensional contexts, as shown by the fact that no inference holds in the following examples: the sentences in (c) cannot be inferred from (a) and (b):

Yet Identity Concealed Questions and Degree Concealed questions do differ in several respects, which justifies our claim that Degree Concealed Questions deserve further study. Nouns that can have DCQ readings (in contexts described in section 2.4) will be argued to differ from ICQs in that: (i) their (‘default’) semantic types are different; (ii) the set of ICQs and the set of DCQs only marginally overlap; some nouns can have distinct ICQ and DCQ readings; and (iii) ICQs and DCQs are not selected by the same predicates. These differences are examined in turn.
2.2 Different semantic types
The class of Concealed Question Nouns has been shown to differ semantically from nouns that cannot have interrogative readings, and usually denote objects. The semantic conditions of the concealed question reading have been discussed (by Baker Reference Baker1968; Grimshaw Reference Grimshaw1979; Nathan Reference Nathan2006; Frana Reference Frana2010; Barker Reference Barker2016; Frana Reference Frana2017 inter alia). Nouns that can have Identity Concealed Question readings have been shown to denote objects or measures in non-interrogative contexts, and ‘an identity question, i.e. one of the form who X is or what X is’ (Nathan Reference Nathan2006: 21) in interrogative contexts.

Contrary to classical Identity Concealed Question nouns, DCQs do not denote objects in non-interrogative contexts, but rather second-order or third-order entities such as states or properties (e.g. dedication, willingness, effectiveness, likelihood, suitability, honesty, loyalty, usefulness, …), or eventualities (e.g. failure, success, support, …)
Besides, in interrogative contexts, these nouns may be argued to correspond to Degree questions, which is reflected in the fact that they can be paraphrased by clauses introduced by how (but not by clauses introduced by what or who):

The paraphrase by a clause introduced by how (Adj) can obviously be argued to be equivalent to a clause introduced by what the level/degree of… is.

But even though such paraphrases are possible, the similarity to usual paraphrases of ICQs is only superficial: the paraphrase cannot simply be introduced by what; rather what must be followed by level of or degree of. It is then necessary to explain why the paraphrase introduced by what has to include level of or degree of, in other words why a ‘usual’ individual reading is not possible.
Possible paraphrases (by how vs by what) obviously should not be the only criterion to delineate the class of DCQs. The fact that a paraphrase by how + Adjective is possible can then help to identify DCQs, but is not a necessary and sufficient condition for a noun to be analysed as a DCQ. Indeed, some nouns allow for both paraphrases by clauses introduced by what and by clauses introduced by how (e.g. height, weight, age, strength, depth, length or width allow both paraphrases).

These nouns all correspond to functional nouns, more specifically to functions from indices to numbers or measures, and as such may be argued to correspond to (Identity) Concealed Question Nouns.
Now it seems difficult to argue that DCQs correspond to functions from indices (world/time pairs) to entities or to measures, like ICQs. This is reflected in their different distributions: while nouns that can have ICQ readings, such as temperature, can be found in equative sentences involving extensional identity (e.g. The temperature is 90), nouns such as success cannot be found in such equative sentences. This can be related to the fact that nouns that can have DCQ readings do not correspond to different entities or different values at different indices. For example, a noun such as discomfort denotes a state whose intensity can vary at different indices, which may justify the analysis of such nouns as intensional (Bolinger Reference Bolinger1972), but they cannot be assigned values.
The semantic types of (traditional) Individual Concealed Questions and Degree Concealed Questions thus clearly differ (the semantics of DCQs will be discussed further in section 3). This (semantic) difference is reflected in linguistic differences, examined in section 2.3 (which shows that ICQs and DCQs correspond to distinct sets of nouns) and section 2.4 (which shows that DCQs and ICQs do not have the same distribution).
2.3 Two sets of nouns
DCQs and ICQs clearly differ in that the set of nouns that can have DCQ readings and the set of nouns that can have ICQs are different, and only marginally overlap. Most nouns that can have Identity Concealed Question (ICQ) readings never have Degree Concealed Question (DCQ) readings.

On the other hand, nouns that can have DCQ readings mostly do not have ICQ readings (which motivates our claim that DCQs correspond to a distinct set of CQ nouns).
Yet a small set of nouns (such as ability, commitment, expertise, inclination, interest, motivation, skill, or talent) can have either an ICQ reading or a DCQ reading in (different) interrogative contexts.

Such nouns can be analysed as polysemous, the identity and degree meanings being clearly distinct (if the Identity Concealed Question reading is selected in a context, the Degree Concealed Question is not available, and vice versa). The fact that very few nouns can have either the ICQ or the DCQ reading, but both readings cannot be simultaneously available (the polysemy will be further discussed in section 4.1), justifies the distinction between two (marginally overlapping) sets of nouns.
Besides, in contexts allowing concealed question readings, many DCQ nouns can have both a DCQ and/or a PCQ reading (i.e. similar to a clause introduced by whether), but not a (classic) ICQ reading (these nouns, and the possible ambiguity between degree and polar readings, will be further discussed in section 4.2):

As already mentioned, DCQ readings are available in some interrogative contexts. But not all interrogative contexts allow this reading, and the contexts that allow DCQ readings differ from those that allow ICQ readings. We will now examine the contexts that allow the DCQ interpretation.
2.4 Selectional restrictions: predicates selecting DCQ readings
Degree Concealed Question readings are possible with a subset of interrogative predicates which differ from the predicates selecting Identity Concealed Question readings.Footnote 7 While ICQ nouns have a concealed question reading when selected by some epistemic verbs, i.e. verbs of mental attitude such as know, reveal, forget, ask (Nathan Reference Nathan2006; Frana Reference Frana2010; Heim Reference Heim, Bäuerle, Egli and von Stechow1979), DCQ nouns have a degree reading when selected by another set of (epistemic or unconditional) predicates – similar to predicates that can select PCQs.
The hypothesis that the set of predicates selecting CQ nouns should be explained by semantic parameters has been supported by Dor (Reference Dor1992), who assumes that CQs can be selected by predicates implying negative epistemic commitment, i.e. implying that the subject does not know the answer to the question complement (or has not assigned the true value to the variable represented by a wh-phrase). According to Nathan (Reference Nathan2006: 45–8), this hypothesis is not completely convincing, as some predicates implying negative epistemic commitment (such as wonder) do not take ICQs. Nathan’s hypothesis is that the predicates that usually take ICQs are those which can have (direct) NP complements, and select a clausal question or a clausal proposition (e.g. know, forget, tell, guess, predict but not wonder). This supposedly explains which verbs can select concealed questions, among verbs that can have question arguments listed in the semantic typology by Karttunen (Reference Karttunen1977): predicates of retaining knowledge (John {knew/recalled/remembered/forgot} the price of milk), predicates of acquiring knowledge (John {learned/noticed/found out/discovered} the price of milk), predicates of communicating (John {told/showed} me the price of milk, John {indicated/disclosed/revealed} the price of milk), predicates of decision (John {decided/determined/specified} the price of milk), predicates of conjecture (John {guessed/predicted/estimated} the price of milk). This hypothesis supposedly explains why DPs with CQ meanings are excluded by some predicates which usually take prepositional complements, i.e. some predicates of opinion (*John {was certain / was convinced} the price of milk), some predicates of relevance (*John cared the price of milk), as well as some predicates of inquisition (John asked (me) the price of milk. / *John {wondered/inquired} the price of milk).
Now, predicates selecting or rejecting DCQ readings are not the same as those selecting ICQ readings. To compare these sets more easily, we also used Karttunen’s typology of predicates (Karttunen Reference Karttunen1977). What emerges is that three subsets of predicates can be distinguished. A first subset selects DCQs as well as ICQs: this is the case for predicates of conjecture (such as predict or estimate), predicates of decision (such as agree on, control, determine …) in negative or modal contexts as well as some inquisitive predicates (ask about,Footnote 8 investigate, be interested in, …). With such predicates, the answer to the question complement is not known, hence the compatibility with both types of concealed questions (ICQs and DCQs). A second subset of predicates can select DCQs, but not ICQs according to (Nathan Reference Nathan2006) – this includes predicates of dependency,Footnote 9 such as depend on, be related to, have an influence on, be a function of, make a difference to, … and predicates of relevance (matter, be relevant, be important, care, be significant, …) in negative or modal contexts.Footnote 10 These differ from the other sets in that their arguments can be questions but not propositions (Nathan Reference Nathan2006: 138–9). The fact that DCQ readings are available may be due to their semantics, as these predicates can be used to state that variables in one dimension correlate with values in another dimension.Footnote 11 Another subset of predicates that can take DCQs is unconditionals (such as regardless of or no matter). As argued by Frana & Rawlins (Reference Frana and Rawlins2011: 502), such predicates ‘take interrogative clauses of all types, as well as just those DPs that have a CQ interpretation’. A third subset of epistemic predicates cannot, or can only marginally, select DCQs (while they can easily select ICQs): this subset corresponds to predicates of acquiring knowledge (he discovered its importance), predicates of retaining knowledge (John knows her intelligence,Footnote 12 John remembered her involvement), and predicates of communicating (John {indicated/disclosed/revealed} their availability / the likelihood of population collapse / ??He told me their importance). Many DCQ nouns are thus not (or very rarely) selected by predicates which usually take propositional arguments. This may be related to the fact that DCQs (contrary to ICQs) cannot easily be paraphrased by propositions identifying the value of a variable: levels of involvement, autonomy, or loyalty are not easy to quantify, and hence are not specific pieces of information that can be communicated, learned or remembered (unlike prices, lists of capitals or governors or presidents of countries).
The contexts allowing DCQ nouns therefore correspond to a subset of (non-presupposing) predicates that differs from the set of predicates selecting ICQ nouns. Predicates selecting DCQ nouns seem rather similar to the set of predicates selecting PCQs (Jugnet & Miller Reference Jugnet, Miller, Gardelle, Mignot and Neveux2024). While ICQ nouns are selected by verbs that can have proposition as well as question arguments, DCQ nouns (as well as PCQs) can be selected by predicates that can take question arguments, or can be found in contexts of presupposition cancellation.
More precisely, in the COCA corpus DCQ are frequently selected by the following predicates: depend, regardless of,Footnote 13 ask/inquire about, investigate, predict, unclear, uncertain, determine, decide, or agree on (most of which do not select nouns with Individual Concealed Question readings, according to Nathan (Reference Nathan2006)).
The differences in selectional restrictions discussed in this section confirm that DCQs are a subclass of CQs which differ from ICQs in various respects (while they share some similarities with PCQs). Our assumption is that nouns that can have DCQ readings share specific semantic properties. These are discussed in the following section.
3 Semantic features of DCQs
As stated in section 2.4, the concealed degree reading is only possible in a restricted set of contexts. But not all nouns can have a concealed degree reading in such contexts (some can have an ICQ reading only). This section examines which lexical semantic features allow some ‘central’ DCQ nouns to have a DCQ reading. The possible influence of dependents will be examined in section 4.
3.1 States
Our hypothesis is that one of the prerequisites for the DCQ reading is that the noun involves the description of a state. Two subcases will be examined in turn: nouns denoting stative eventualities, and nouns denoting non-stative eventualities but describing a related state.
3.1.1 Tropes
In non-intensional, non-interrogative contexts, most of the nouns that can have DCQ readings denote states, properties, or eventualities implying a (scalar) property (they do not denote first-order entities). Most of the nouns that denote eventualities and can have a DCQ reading can be characterized as non-dynamic, atelic and homogeneous situations, i.e. stative eventualities (Rothstein Reference Rothstein2004 inter alia) – about seventy nouns corresponding to this description were found to occur with DCQ readings in the COCA.Footnote 14 As such, they cannot be the arguments of take place, happen or occur, nor can they be the complements of undertake or make.

Most of these nouns correspond to tropes, i.e. ‘instantiations of a static property’ (Moltmann Reference Moltmann2007), rather than to abstract states (or Kimian states). A trope can be defined as a concrete entity that instantiates a property, or ‘concrete manifestations’ of a property (Moltmann Reference Moltmann2007: 371), while a state (‘abstract state’, or ‘Kimian state’) corresponds to a property holding of an entity (to a relevant positive degree). Trope-referring terms can refer to objects that have changing concrete manifestations (John’s talent may change, increase or decrease, while John’s being talented does not). This is reflected in several linguistic differences between tropes and (abstract) states, such as (i) the possibility for tropes (but not abstract states) to be measured, (ii) the compatibility of nouns denoting tropes with some predicates or modifiers, or (iii) the compatibility of nouns denoting tropes with some determiners. DCQ nouns seem to have all these properties. (i) Nouns denoting tropes are typically gradable, as the degree to which tropes instantiate a property (the property expressed by the base predicate) can be measured (while abstract states cannot be measured) (Moltmann Reference Moltmann2007: 370):

Gradability is a key feature of DCQ nouns, which will be further discussed in section 3.2.
Besides, as argued by Moltmann (Reference Moltmann2007), (ii) nouns referring to tropes can be the arguments of predicates implying that the internal structure or complexity of an argument is taken into account (e.g. describe, investigate, examine or admire) (while nouns denoting abstract states cannot). DCQ nouns can be the arguments of at least one of these predicates.

Tropes allow manner predicates or manner adverbials, which describe the ways the property is manifested, while states do not. Some nouns that can have DCQ readings also allow manner modifiers:

(iii) Tropes allow a variety of determiners, and in particular ‘allow for demonstrative reference … and mass quantification’ (Moltmann Reference Moltmann2007: 370) (while abstract states ‘act like definite descriptions only’). DCQ nouns also allow various determiners in non-interrogative contexts – but note that when they have a DCQ reading, they can only be introduced by a definite determiner or by a possessive.

Based on these criteria, most nouns that allow a DCQ can be identified as tropes (rather than abstract states) in non-interrogative contexts. But not all nouns allowing DCQ readings are stative – as we will show in the following section, some dynamic nouns can be DCQs.
3.1.2 Stative feature: dynamic eventualities with a correlative state
Among nouns allowing DCQ readings, some are not simple states but rather correspond to dynamic eventualities, e.g. assimilation, involvement, success. Such nouns can be the arguments of happen, take place or make, like usual dynamic nouns.

These nouns can then be characterized as dynamic, yet they differ from other dynamic nouns (e.g. arrival or creation or walk) in that they do not describe actions or correspond to a prototypical type of dynamic eventuality (e.g. many different eventualities can be characterized as successes, many different (agentive) dynamic eventualities can require involvement). Such nouns rather describe states correlated with (implicit) actions.Footnote 15 The (gradable) stative dimension is thus the most important or salient semantic feature of these nouns, which may explain why they can have a DCQ reading (as illustrated in (33)–(35)), while most dynamic nouns (e.g. running, return, recognition) cannot.

As already hinted at, the states associated with DCQs have to be gradable. This property is examined in the following section.
3.2 Gradability
Definitions of gradability differ (Bolinger Reference Bolinger1972; Schnedecker Reference Schnedecker2010; Matushansky Reference Matushansky2002; Morzycki Reference Morzycki2009 inter alia),Footnote 16 and the idea that nouns can be gradable has been questioned (Wierzbicka Reference Wierzbicka1986; Constantinescu Reference Constantinescu2011; Croft Reference Croft1991 inter alia). The idea that gradability in the nominal domain is similar to gradability in the adjectival domain has been questioned, as nouns are multidimensional (Sassoon Reference Sassoon2017; Wierzbicka Reference Wierzbicka1986): the semantics of nouns is often more complex (involves more semantic features) than that of adjectives (which can be reduced to a gradable property). Constantinescu (Reference Constantinescu2011: 229–30) concludes ‘in the nominal domain there are no grammatical phenomena that are exclusively sensitive to gradability and no expressions that perform the type of operations that are involved in degree modification as we know it from the adjectival domain, i.e. involving comparison of degrees or operations on ordered sets (depending on the approach)’. This contradicts Kennedy & McNally (Reference Kennedy and McNally2005), according to whom ‘gradability is a feature of grammatical categories other than adjectives’, and ‘gradability is characteristic not only of adjectives but also of verbs and nouns’. We adopt Kennedy & McNally’s view that some nouns can be analysed as gradable; more specifically nouns whose semantics is very close to that of gradable adjectives in that they denote a gradable property.
3.2.1 ‘Intensively gradable’ nouns
Most of the nouns that have traditionally been analysed as ‘intensively gradable’ (in Bolinger’s (Reference Bolinger1972) sense)Footnote 17 can have DCQ readings. More specifically, the DCQ reading is possible with ‘intensive’ degree nouns (nouns of states or properties).Footnote 18 These nouns pass all the traditional tests of gradability, i.e. the compatibility with wh- exclamatives (36), with the ‘degree’ or ‘intensifying’ interpretation of such or quite (37), or the compatibility with some modifiers with a degree reading (e.g. great, terrible, real, sheer, pure, complete, total (38)). Besides, such nouns can be the complements of degree(s) of as well as level(s) of (39) – as noted by Nicolas (Reference Nicolas2010: 183) inter alia. Even though the validity of some of these tests can be questioned (Constantinescu Reference Constantinescu2011),Footnote 19 the fact that the nouns pass all the above-mentioned tests can be argued to support the hypothesis that DCQ are gradable:

Nouns that have a DCQ reading can then be assumed to correspond to gradable states, while nouns that correspond to non-gradable states (e.g. absence, authenticity, death, knowledge, life, presence, recovery, state, survival, truth …) cannot have DCQ readings (as discussed by Jugnet & Miller (Reference Jugnet, Miller, Gardelle, Mignot and Neveux2024), some can have polar readings).
Yet, as already hinted at, not all gradable nouns allow for a DCQ reading. This case is examined in the following section.
3.2.2 Evaluative nouns: gradable nouns without DCQ readings
Among nouns that have traditionally been analysed as ‘intensively gradable’ (in Bolinger’s (Reference Bolinger1972) sense),Footnote 20 only some subcategories can have DCQ readings. More specifically, most evaluative nouns (analysed as gradable by Bolinger (Reference Bolinger1972) and Matushansky (Reference Matushansky2002) inter alia) seem to exclude that reading. Two subcases will be examined: evaluative nouns denoting events, and evaluative nouns denoting individuals.
Most dynamic ‘evaluative’ nouns which involve a gradable feature, such as blunder, disaster, or mistake, do not have concealed question readings, even though they are compatible with the above-mentioned structures testing gradability,Footnote 21 and are traditionally analysed as gradable (Bolinger Reference Bolinger1972 inter alia). The only exception we found is success, when a reference is made to some future possibility, whose characterization as a success cannot be established, or still has to be determined (reflected by the use of the modal will in the following paraphrases):

Now success could be analysed as a noun denoting an eventuality which indirectly describes an individual: the agent at the origin of the (underspecified) successful event can be characterized as (potentially) successful – the implied state of the agent being stage-level. The noun success thereby differs from evaluative terms which cannot have DCQ readings, such as failure, blunder or disaster. The latter are typically used to characterize present or past events, and cannot be indirect ways of characterizing an agent. This may be related to the fact that the (subjective) gradable feature does not correspond to a (gradable) property of an individual involved in the event. While the modernization of a building can be defined as the process of making the building more modern, or the integration of individuals as the process of making these individuals more integrated, the characterization of the action of an individual as a blunder does not imply that this individual is a blunderer, just as the characterization of an action as a mistake does not imply that its agent is generally mistaken. Our hypothesis is that the degree reading is excluded because these gradable terms are ways of characterizing actions, but not characterizing the individuals involved in this action: they are not indirect characterizations of participants. It could then be argued that a key feature of DCQs is that they can both denote eventualities and describe properties of individuals.
Another set of evaluative nouns does not allow the DCQ readings: evaluative nouns which can denote individuals (e.g. idiot, fool, fan, blunderer). These are not compatible with degree of or level of:

The unavailability of the Concealed Degree Question reading with these nouns may be explained by the fact that they denote individuals. As already mentioned (in section 2.2) nouns that can have concealed degree readings usually cannot have identity concealed question readings.
3.3 DCQs: shared properties
Based on the preceding remarks, our conclusion is that DCQ readings are possible with nouns that may denote eventualities and have a stative, gradable feature (which can be understood as a property of an individual involved in the eventuality). These properties set DCQs apart from other nouns allowing CQ interpretations. These specificities allow us to delineate a subclass sharing particular semantic features, but this does not imply that the semantic analysis of DCQs should be completely different from that of (traditional) (I)CQs.
According to Nathan (Reference Nathan2006: 19), ‘a DP can be a concealed question [ICQ in our terms] if: (a) its head noun is relational: it describes a relationship between two individuals (e.g. a state and its governor, a commodity and its price), or (b) its head noun is nonrelational, but is modified in certain ways (e.g. with a relative clause)’. More precisely, concealed question meanings are possible when the head of a DP is a relational noun, or when the context (such as dependents of the noun) can force a relational interpretation (Nathan Reference Nathan2006: 116). For example, nouns modified by relative clauses (such as the semanticist who teaches at USNDH), which can be the arguments of intensional predicates, can also have CQ meanings. Our hypothesis is that DCQ nouns describe the relation between a property and a grade – or a position on a gradient associated with a (gradable) state described by a noun denoting an eventuality. Just as ‘traditional’ concealed question meanings can be fostered by contextual elements, we will now see the DCQ reading can also be favoured by dependents. So far we have focused on the DCQ readings of gradable nouns, and examined what makes a DCQ reading available, without discussing possible ambiguities between different types of concealed question readings. We will now examine various cases of polysemy or ambiguity.
4 Polysemy and potential ambiguities
Very few nouns that can have DCQ readings in interrogative contexts get the degree reading only. Most DCQ nouns can have more than one concealed question reading: some can have either a degree or an identity question reading, or both a degree and a polar reading. These two cases will be examined in turn.
4.1 The ICQ/DCQ ambiguity
The sets of ICQs and DCQs have been argued to differ and to overlap only marginally in section 2.3, as most DCQs do not have ICQ readings (and vice versa). Yet, as already mentioned, a rather limited set of nouns (ability, expertise, fear, inclination, interest, motivation, skill or talent) can have either a DCQ or an ICQ reading.

Potential ambiguities can be resolved in context, as some contextual elements clearly favour the DCQ reading, while others favour the ICQ reading. Some dependents provide an answer to the (potential) identity question, and consequently ‘coerce’ the DCQ reading.

In example (44), the ICQ reading is not available as the adjective modifier academic provides an answer to the ICQ (as it specifies a type of motivation – motivation for one’s studies), so the ICQ reading becomes unavailable.
Disambiguation of DCQ/ICQ nouns by dependents is quite frequent; e.g. in most of its occurrences (in CQ contexts) in the COCA corpus, the noun ability is followed by a complement introduced by to which corresponds to the answer to the individual question, so the only reading that remains possible is then the polar, or the concealed degree question reading.

Besides, predicates implying measurement such as test seem to favour the DCQ reading (rather than the ICQ reading):

In some cases, both the selecting predicate and a dependent favour the DCQ reading:

Another contextual element favouring the ICQ (rather than the DCQ) reading is the plural form. Most nouns that can have DCQ readings can be analysed as mass nouns (Tovena Reference Tovena, Megerdoomian and Bar-el2001). As shown by Barque, Fabregas & Marin (Reference Barque, Fabregas and Marin2012), some (psychological) state nouns can have both mass and count uses. When used as mass nouns they typically denote a psychological state, while when used as count nouns, they can have object readings and denote the cause of the corresponding state. The fact that these nouns can have object readings explains that in interrogative (non-presupposing) contexts, they can have Individual Concealed Question readings (when used as count nouns).

If the sense of a (D/I)CQ noun is not disambiguated by some linguistic dependent in the noun phrase, elements in the preceding context can help to determine which reading is more likely (which is often not the case with the DCQ/PCQ ambiguity). In the following occurrence of the noun expertise, the relevant area of expertise is specified in the preceding sentence (biking), hence the ICQ reading is not plausible, and the DCQ reading seems more relevant:

The analysis of occurrences of potentially ambiguous nouns in the COCA has led us to conclude that the DCQ/ICQ ambiguity is quite rare.Footnote 22 This is not surprising, as this ambiguity is only possible with (very) few nouns, in a very limited number of contexts (as dependents or other contextual elements can disambiguate these nouns). This may confirm our claim that ICQ and DCQ correspond to clearly distinct senses of nouns, corresponding to semantic types of objects so different that the interpretation cannot remain undetermined.
The ICQ/DCQ ambiguity is clearly much less frequent than the DCQ/PCQ polysemy, discussed in the following section.
4.2 The Degree/Polar Concealed Question polysemy
As previously mentioned, many nouns can have both a degree and a polar reading in certain contexts, so can be paraphrased either by a degree how or by whether.

Contrary to the ICQ/DCQ ambiguity, the DCQ/PCQ equivocacy seems quite frequent, as many nouns allow it,Footnote 23 in various contexts. The predicates selecting DCQs and PCQs are similar, hence predicates typically do not coerce or exclude one reading. In many cases, no dependents give any cues as to which reading is more likely. It could even be argued that the distinction is in many cases not crucial, the polar/degree ambiguity causing no difficulties of interpretation. In contexts of presupposition cancellation, either only two poles of a gradient, or all the possible degrees (from one end of the gradient to the other, including all intermediary degrees), can be considered.

Our analysis of nouns that can have DCQ and/or PCQ readings in the COCA has revealed that most occurrences are ambiguous (can be understood as having a DCQ and/or a PCQ reading, without obvious consequences on the interpretation of the following context).Footnote 24
Obviously, unambiguous (or less ambiguous) examples can be found. Some dependents can favour one reading, such as the modifiers continued, long-term or full, which make the PCQ reading more likely, as the concealed questioned is whether the property denoted by the adjectival modifier (continued, long-term or full) can be assigned to the eventuality denoted by the noun (or not):

Other dependents can make one reading more salient – for example, the coordination with a contradictory antonym clearly favours the polar reading:

Linguistic cues can also be found in the complement: in (58), the modifier key in the complement of importance as well as the modifier successful both exclude the possibility that the variables are not important, hence exclude the polar reading.

In other cases, no linguistic clues are given, but one interpretation is favoured based on one’s world knowledge. For example, readers who are not familiar with astronomy may accept both readings of accessibility in (59), while those who are more familiar with the field may favour one reading. Similarly, in (60) the degree reading may be more likely for specialists of pragmatics. General shared knowledge may also explain why most speakers would agree on the degree reading of (61).

It might also be argued that with some nouns such as abundance, closeness, severity or sophistication, which imply that the top of a scale is considered, degree readings seem more readily available:

In some cases, the DCQ reading may then seem more likely. But these contexts – and the disambiguating parameters illustrated in (54) to (58) – are clearly less frequent than the cases where both the degree and the polar readings are plausible. This confirms that the DCQ and the PCQ readings are clearly similar to one another, while the DCQ and the ICQ readings more clearly differ.
5 Conclusion
The main claim of this article is that, contrary to what is generally assumed, the class of concealed questions is not limited to (the subclass of) Identity Concealed Questions (contra Nathan Reference Nathan2006 inter alia), but includes the distinct subclass of Degree Concealed Questions. This class differs from (traditional) Identity Concealed Questions in that Degree Concealed Questions cannot denote individuals (contrary to ICQ) but can denote eventualities involving a gradable intensive property: only nouns that are intensively gradable allow the Degree Concealed Question reading – such nouns (indirectly) describing the state of an individual. Given the limited number of nouns and the limited set of contexts allowing the DCQ reading, occurrences of nouns with a DCQ reading are not very frequent. This may explain why this subclass has been overlooked so far, just as nouns that allow a polar (PCQ) reading have been overlooked. The differences between two subclasses of nouns clearly deserve further investigation. Our main aim was to show that the set of Concealed Questions is not uniform, and that even if a uniform semantic analysis may be advocated, the analysis of concealed questions nouns should include a discussion of the specificities of Degree Concealed Questions, and of Polar Concealed Questions (with which they share many properties), as opposed to Identity Concealed Questions.