2.1 Polarity focus and QUD

The term polarity focus (PF, also known as verum focus) traditionally refers to a focus phenomenon that triggers an emphasis on the truth or the falsity of the proposition expressed by the sentence. Consider, for instance, the answer in (2). While the auxiliary did receives the main accent, what is semantically focused is not the verb but the truth of the proposition John read the book.

Goodhue (2018) proposes an analysis of polarity focus within the framework of Alternative Semantics¹ (Rooth 1992). According to Rooth, each sentence has two different semantic values: an ordinary semantic value ⟦ϕ⟧^o and a focus value ⟦ϕ⟧^f, which expresses a set of alternative propositions. Informally speaking, these propositions are the result of replacing the denotation of the focused constituent with contextually relevant objects of the same semantic type. In order to get this contextual restriction, Rooth also posits a presuppositional operator, ~, that adjoins to ϕ along with a variable Γ for sets of semantic objects, or γ for individual objects. This operator introduces the following presuppositions:

As for polarity focus, Goodhue argues that it involves F-marking on a polarity head POL, which c-commands the TP (Laka 1990, Holmberg 2016). Adopting Rooth’s theory, the resulting set of focus alternatives at the POLP node is {p, ¬p}, that is, the set that contains the proposition and its negation. Coming back to (2), according to Goodhue this sentence exhibits the focus structure in (4a) and its focus value is the set of propositions in (4b).

Regarding PF licensing, Goodhue posits the following condition:

Remember that according to (3b), the context should offer some antecedent γ that (i) is a member of the focus semantic value of ϕ and (ii) is distinct from the ordinary semantic value of ϕ. Thus, since the set of focus alternatives of a PF sentence is {p, ¬p} and the ordinary semantic value of ϕ is p, the antecedent γ should be ¬p. In consequence, PF is only licensed when the context provides such an antecedent.

(6)

This proposal accounts for several empirical phenomena related to polarity focus. First, PF utterances cannot be used out of the blue (7). This is totally expected under this approach: like other kinds of focus prominence shifting, PF requires a salient antecedent and in these cases the context does not provide it.

Second, it has been claimed that polarity focus emphasizes the truth of the proposition that it appears with (Höhle 1992, Romero & Han 2004, Gutzmann et al. 2020, among others). Goodhue (2018: 52) argues that this pragmatic effect emerges as a consequence of the general theory of focus semantics. He points out that in an answer like (8a) two things happen: on the one hand, p is asserted, which entails that ¬p is false, and on the other hand, the information structure of polarity focus draws explicit attention to the alternative ¬p, the focus antecedent for PF. As a result, the contrast between the truth of p and the falsity of ¬p is ‘highlighted’ and the emphasis of the truth of p arises. In (8b), however, there is no polarity focus. Therefore, the utterance does not draw explicit attention to the falsity of ¬p and, consequently, it does not emphasize the truth of p.

(8)	A: Are you happy?
	a.	B: I AM happy.
		↝ B emphasizes the truth of the proposition B is happy.
	b.	B: I’m happy.
		B emphasizes the truth of the proposition B is happy.

Third, as can be observed in the last example, polarity focus seems to be optional in response to polar questions. This is surprising since the use of focus in answers to wh-questions is obligatory in order to make the answer congruent.

In a nutshell, Goodhue argues that the optionality of polarity focus in responses to polar questions is due to the fact that these questions can make both p and ¬p salient as antecedents for focus prominence. Thus, polarity focus occurs if the speaker takes ¬p to be the antecedent. If not, they use broad focus.

Now, as shown in the previous examples, focus is closely related to the context of utterance. In order to capture this connection between discourse and focus marking, I also adopt the Focus Principle in (10) from Beaver & Clark (2008):

The Question Under Discussion (QUD) can be understood as an explicit or implicit question that corresponds to the current discourse topic (Roberts 1996). In semantic terms, the QUD denotes a set of alternative propositions, namely, the set of its possible answers (Hamblin 1973). Thus, as Beaver & Clark claim, the Focus Principle establishes the link between ‘what is accented in a declarative sentence, and what question the sentence can be used to answer’ (2008: 37). From this perspective, the main discourse-semantic function of focus is to establish a formal congruence between an utterance and its corresponding QUD. As Onea & Zimmermann (2019) point out, this congruence relation can be formalized within an alternative semantics framework as follows:

Considering its focus value and the Focus Principle in (10), I assume that polarity focus on p signals the presence of the (implicit) QUD ?p,³ that is, the set of its possible answers {p, ¬p} (Samko 2016, Gutzmann & Castroviejo Miró 2011). To illustrate, for instance, the sentence in (12a) evokes the QUD⁴ in (12b), which denotes the set of propositions {John read the book, John did not read the book}.

As expected, the focus value of a polarity focus sentence is congruent with its corresponding QUD. Thus, the denotation of the polar question did John read the book? constitutes a subset of the focus value of the sentence John did read the book.

2.2 Factivity: emotive and cognitive predicates

In their seminal paper, Kiparsky & Kiparsky (1971) distinguish a class of predicates that presuppose the truth of their complement clause (e.g., (14b) and (14c)). These predicates are known as factive predicates.

Although at first verbs like know (14b) and regret (14c) were grouped together as factive predicates without further distinctions, several authors have soon recognized some differences between them, specially in what concerns the presuppositional status of their complement. Thus, Karttunen (1971: 64) observes that cognitive factives (e.g., know), unlike emotive factives (e.g., regret), can lose their factivity in certain contexts, for example, when functioning as the antecedent of a conditional sentence. For instance, in (15a) there is a possibility that the speaker has not told the truth. That means that in this case the truth of the complement of realize is not presupposed. In (15b), on the contrary, the truth of the embedded clause is always inferred. For that reason, Karttunen calls cognitive factives ‘semi-factives’.⁵

Moreover, Hooper & Thompson (1973) and Simons (2007) observe that cognitive factives, contrary to emotive factives, may exhibit parenthetical interpretations. In these cases, the embedded clause of the sentence constitutes the ‘main point’ of the utterance, while the matrix predicate functions as a kind of evidential, signaling the source and reliability of the information contained in the embedded clause (Simons 2007: 1036). Consider for instance the contrast between the answers in (16) and in (17): while the clause selected by the cognitive factive discovered can be taken to answer the question what did John read?, the one embedded under the emotive factive regretted cannot. Once again, this pattern shows that cognitive factives, unlike emotive factives, can have non-presuppositional readings.

Finally, another difference between cognitive and emotive factives concerns projection. As is well known, one of the main characteristics of presuppositions is that they project, that is, they survive in embedding contexts in which normal entailments do not, e.g., negation (18b), polar questions (18c), or the antecedent of conditionals (18d). For instance, in all the following sentences, the presupposition ‘Mary used to smoke’ follows.

If cognitive factives can introduce non-presupposed clauses in certain contexts, it predicts that in these cases these clauses do not project. As Karttunen (1971: 63) shows, this prediction is borne out. Consider the following example from Karttunen:

This question is ambiguous between two readings: one, in which the complement is presupposed and the speaker assumes that the addressee has not told the truth, and another one, in which the embedded clause is not presupposed and the speaker also asks about its truth. These interpretations correspond to the presuppositional (non-parenthetical) reading (20a) and to the non-presuppositional (parenthetical) reading (20b), respectively.

In sum, the examples in this section show that there is a relevant difference between cognitive and emotive factives: the former, unlike the latter, may exhibit non-presuppositional readings.

2.3 Impossible Presuppositions

So far, I have laid out the main assumptions regarding polarity focus and factivity. Concretely, I assumed that a polarity focus sentence denotes the focus value {p, ¬p} and evokes the QUD ?p, and I took for granted that cognitive factives, contrary to emotive factives, can have non-presuppositional interpretations. In what follows, I briefly introduce, from a theoretical perspective, the core proposal of this article.

Consider the abstract scenario in (21), in which an emotive factive predicate embeds a polarity focus sentence. According to the previous assumptions, the following configuration arises: on the one hand, the emotive factive presupposes the truth of its complement (call it p), and on the other, the polarity focus occurring in the embedded clause evokes ?p (i.e., the set of alternatives {p, ¬p}).

(21)

The straightforward consequence of this structure is that it triggers an inevitable presupposition failure: the proposition p will never be presupposed since ?p should be (part of) the immediate QUD. In other words, no possible context can take for granted p while ?p is under discussion at the same time.

I argue that this scenario is an instance of a more general phenomenon that I call impossible presupposition. In a nutshell, an impossible presupposition is a configuration that carries a presupposition that cannot be satisfied in any possible context. The reason of this failure resides in the fact that no QUD evoked by the focus value of the sentence presupposes the relevant proposition. Because of this underlying interaction between presupposition and focus, the sentence gives rise to a systematic presupposition failure, which makes the sentence ungrammatical. The impossible presupposition scenario can be defined as follows:

As for the second clause of the definition, I posit the following condition which explicitly states when a QUD presupposes a proposition p.

In the following section, I offer empirical evidence supporting this idea and discuss in more detail the theoretical notion of impossible presupposition.

3.1 Predicate doubling in Spanish

Predicate doubling is a cross-linguistically attested construction in which two instances of the same lexical verb occur. The first one consists of an infinitive which appears dislocated in the left periphery of the sentence, while the second one is an inflected form that occupies a clause-internal position. As can be observed in the following examples, the dislocated predicate can be either a bare infinitive, e.g., (25) and (26), or an infinitival phrase, e.g., (27) and (28).

Like many other languages, Spanish also exhibits predicate doubling, both with bare infinitives (29a) and with infinitive phrases (29b):

As Vicente (2007) points out, predicate doubling in Spanish gives rise to polarity focus interpretation. Consider for instance the dialogue in (30). In this case, the doubling sentence in (30) emphasizes the truth of the proposition Juan read the book in contrast to the previous same proposition with the opposite polarity (i.e., Juan did not read the book). Importantly, in these constructions the contrastive accent falls on the finite verb.

Polarity focus is not the only possible interpretation for predicate doubling. Muñoz Pérez (2017) notices that it can also display narrow focus marking on other elements, such as objects (31a), subjects (31b), or adjuncts (31c).

Besides the obligatory focus marking, predicate doubling also triggers a ‘continuation effect’. Consider, for instance, the following dialogue: while the polarity focus sentence lo leyó ‘he did read it’ constitutes a complete answer for the polar question in (32), the dislocated predicate leer ‘to read’ suggests a possible continuation in which Juan did not do something else with the book (e.g., he did not understand it).

The same effect arises in predicate doubling constructions with narrow focus interpretation. As in the previous case, the sentence in (33) fully addresses the question what did Juan read?. However, the dislocated predicate evokes a continuation in which Juan did something else with the magazine (e.g., he had a look at it).

Following Muñoz Pérez & Verdecchia (2020), I assume that the dislocated predicate functions as a contrastive topic⁷ (Büring 2003). According to Buring, contrastive topics signal the presence of a complex discourse strategy: they mark the existence of a higher superquestion, and, at least, an alternative sister-question to the immediate QUD. Thus, while focus introduces a set of alternative propositions, contrastive topic introduces a set of alternative questions.

To illustrate, consider the doubling sentence in (34), which exhibits a polarity focus interpretation:

While in these cases the finite verb receives the contrastive accent, in semantic terms it is the polarity head POL which is F-marked (Goodhue 2018). In addition, as mentioned above, the dislocated predicate functions as a contrastive topic (i.e., it is CT-marked).

According to what has been assumed in Section 2.1, polarity focus on p (implicitly) evokes the immediate QUD ?p, that is, the set of alternatives {p, ¬p}. Therefore, the sentence in (34) signals the presence of the polar QUD did Juan read the book?. Following Büring (2003), this can be represented in a discourse tree as follows:

(36)

Moreover, since the sentence contains a contrastive topic, it indicates the presence of a more complex discourse structure which involves the immediate QUD, a set of alternative questions to that QUD, and a higher super-question. Informally speaking, this set of alternative questions is obtained by replacing the CT-marked constituent in the QUD with contextually salient alternatives of the same semantic type. In predicate doubling constructions, the contrastive topic will always be a predicate (a bare infinitive or an infinitive phrase). Thus, the sentence in (34) evokes a set of alternative polar questions of the form did Juan X the book?, where X is a transitive verb (e.g., to read, to understand, to buy, etc.). The introduction of this set of questions derives the ‘continuation effect’ observed in the previous cases: the sentence not only addresses the immediate QUD, but also points to implicit alternative questions. This analysis can be summarized in the following discourse tree:

(37)

At this point, it is worth mentioning an advantage of this analysis. Vicente (2007: 64) distinguishes two types of polarity focus: the contradictory and the non-contradictory. While the former emphasises the truth of a proposition in contrast to the same proposition with the opposite polarity (i.e. p and ¬p), the latter contrasts the truth of a proposition with a different proposition (i.e., p and q). Vicente claims that predicate doubling in Spanish receives a non-contradictory polarity focus interpretation. For instance, according to his proposal, in (30) polarity focus establishes a contrast between the proposition Juan read the book and Juan did not understand the book.

In the present account, however, this distinction between contradictory and non-contradictory polarity focus is not necessary. Following Goodhue (2018), I assume that polarity focus always involves a contradictory interpretation, that is, it signals a contrast with a proposition with the opposite polarity. This can be observed, for instance, in the dialogue in (30): the proposition Juan read the book is contrasted with Juan did not read the book. As for the non-contradictory reading noticed by Vicente, it arises out of the presence of one of the alternative questions introduced by the contrastive topic, i.e., it constitutes the ‘continuation effect’ introduced by the dislocated predicate leer ‘to read’ (Muñoz Pérez & Verdecchia 2020).

Summarizing, predicate doubling in Spanish exhibits the information structure schematized in (38): on the one hand, some constituent within the clause (including polarity) receives narrow focus; on the other, the dislocated predicate functions as a contrastive topic. It should be noted, however, that only focus marking plays a crucial role in what follows.

Having seen the information structure of predicate doubling, let us return to the asymmetry previously presented in (24) and see in more detail the data. As Vicente (2007) observes, predicate doubling is also acceptable if the inflected verb appears in a complement clause:

However, as seen, there is a contrast between cognitive and emotive factives: while predicate doubling is possible with complement clauses embedded under cognitive factives (40a), it is unacceptable with clauses selected by emotive factives (40b).

Nevertheless, this is not the complete picture. As can be observed, the doubling sentences in (40) involve polarity focus marking of the embedded clause. That is, in both cases the (intended) interpretation of the embedded clause is that Juan did read the book. In these cases, predicate doubling with emotive factives is banned. Now, consider the following sentences:

Contrary to what happens in (40b), the doubling sentence in (41b) is grammatical, even though the inflected predicate haya leído ‘has read’ occurs within a clause embedded under an emotive factive verb. Crucially, this case does not involve polarity focus, but narrow focus. Therefore, there is a double asymmetry regarding predicate doubling and factivity: on the one hand, there is contrast between clauses selected by cognitive and emotive factives with respect to polarity focus marking (i.e., (40a) and (40b)); on the other, there is also a contrast between polarity and narrow focus assignment in clauses embedded under emotive factives (i.e., (40b) and (41b)). These interactions between factivity and focus in predicate doubling constructions are summarized in Table 1.

In the next sections, I consider each case and propose a presuppositional account for the twofold asymmetry.

3.2 Predicate doubling with emotive factives

As seen above, predicate doubling with polarity focus interpretation is blocked in clauses embedded under emotive factives. Consider again (40b), repeated below in (42). Following Goodhue (2018), I assume that this sentence involves F-marking on the polarity head POL in the embedded clause:

In consequence, the focus value of (42) is the set of alternatives {I regret p, I regret ¬p}, where p represents the proposition she/he read the book:

Since polarity focus on p signals that ?p is under discussion, the focus structure of the sentence in (42) should evoke a QUD⁸ whose denotation is the set of alternatives {you regret p, you regret ¬p}. Such a QUD is congruent with (43): this set of alternatives constitutes a subset of the focus value of (42).

Importantly, note that this set of alternatives does not presuppose the proposition p, i.e., she/he read the book. This follows from the QUD-Presupposition Condition presented in (23), repeated below for convenience. As can be observed, it is not the case that all the propositions in (44) presuppose that she/he read the book.

Now, as shown in Section 2.2, emotive factives typically select presupposed clauses⁹ (among other things, they do not exhibit parenthetical readings). Thus, the sentence in (42) presupposes the content of the embedded clause, that is, the proposition she/he read the book.

These facts lead to the following scenario: on the one hand, the emotive factive triggers the presupposition ‘she/he read the book’ (47b); on the other, the QUD congruent with the focus value of (47a) evokes a set of alternatives which does not presuppose the proposition ‘she/he read the book’ (47c):

The straightforward consequence is that predicate doubling involving emotive factive predicates with polarity focus interpretation will always lead to a presupposition failure: the embedded proposition p should be presupposed, however, the polarity focus evokes the QUD you regret ?p, which does not take for granted p. The interaction between the emotive factive and the polarity focus in the embedded clause causes that the presupposition cannot be satisfied in any possible context. Schematically, this construction involves the following presuppositional skeleton:

(48)

However, this is not an isolated case: this ban in predicate doubling is not a problem of predicate doubling itself, but it is an instance of the more general phenomenon introduced in Section 2.3: the impossible presupposition scenario.

As seen, an impossible presupposition involves a configuration that carries a presupposition that can never be satisfied. This is so because no possible QUD evoked by the focus value of the sentence satisfies this presupposition. Thus, the sentence will be systematically infelicitous in any context and, consequently, ungrammatical. Note that this notion differs from contingent presupposition failures. Consider, for instance, the following dialogue:

The answer in (50) is pragmatically infelicitous: the embedded clause should be presupposed, but it is not common ground that Juan read Ficciones. Thus, employing this sentence in such a context leads to a presupposition failure. However, this case is not the same as (42): while the doubling sentence is ungrammatical, the example in (50) is grammatical, but pragmatically deviant. This is because the presupposition failure in the former case is contingent or occasional: there is at least one context in which it can be satisfied. This can be observed in the following dialogue:

The impossible presupposition scenario involves a stronger instance of presupposition failure, since the anomaly of the sentence does not depend on the particular context in which it is uttered, but on the deeper structural interaction between presupposition and focus, which leads to a systematic presupposition failure.

Consider now predicate doubling with narrow focus interpretation. As shown in the previous section, this doubling pattern is possible with predicates appearing within clauses embedded under emotive factives. For instance, the doubling sentence in (52B) with narrow focus on the object el libro ‘the book’ constitutes a proper answer to a question like (52A):

Notice that in this case the QUD associated with (52) denotes the set of propositions in (53b).

The crucial question now is whether the set of alternatives in (53b) presupposes the proposition embedded under the factive predicate in the answer in (52), i.e., ‘Juan read the book’. At first sight, it seems that this is not the case. As seen, according to (23) a QUD Q presupposes p iff all the propositions denoted by Q presuppose p. However, in this case, the proposition ‘you regret that Juan read the magazine’ clearly does not presuppose that Juan read the book. Nevertheless, I assume that the QUD in (52) can be understood as a super-question which dominates two polar sub-questions: do you regret that Juan read the book? and do you regret that Juan read the magazine?, as represented in (54) (Roberts 2012: 16). Thus, each subquestion presupposes that Juan read the book and that Juan read the magazine, respectively. In consequence, the ‘bigger’ QUD in (52) also carries these presuppositions.¹⁰

(54)

Now, consider again the doubling sentence with narrow focus interpretation in (52B). Contrary to what happens in polarity focus cases, in this kind of doubling sentences the presupposition triggered by the emotive factive (i.e., ‘Juan read the book’) is met. The complete scenario can be summarized as follows:

As a result, no presupposition conflict arises: there is, at least, one QUD which can properly satisfy the presupposition triggered by the emotive factive. Therefore, predicate doubling is possible.

3.3 Predicate doubling with cognitive factives

As shown before, predicate doubling with cognitive factives is acceptable both with polarity and narrow focus interpretation. A natural question that immediately arises is why cognitive factives, unlike emotive factives, do not trigger an impossible presupposition. I argue that this difference is due to the fact that, as explained in Section 2.2, cognitive factives can exhibit parenthetical readings (Hooper & Thompson 1973, Simons 2007). To begin with, consider the following dialogue:

As can be observed, the doubling sentence with polarity focus interpretation in (56) can be taken to answer the polar question did Juan read the book?. Crucially, notice that in this case the cognitive factive predicate has a parenthetical behavior: the embedded clause constitutes the main point of the utterance, while the matrix verb functions as a kind of evidential (Simons 2007). Thus, (56) presents the following focus structure:

Now, since the main predicate receives a parenthetical reading, it is not part of the QUD.¹¹ In other words, the sentence in (56) does not address the QUD what do you know?, but the polar question did Juan read the book? (58a), which denotes the set of alternative propositions in (58b). Importantly, the QUD does not presuppose the proposition ‘Juan read the book’; in fact, it constitutes the main assertion in the answer.

Therefore, because of the non-presuppositional interpretation of the cognitive factive, no conflict with polarity focus arises. In other words, there is no systematic presupposition failure as in (42) because there is no presupposition at all. As a result, predicate doubling with polarity focus interpretation is possible in these cases.

As for predicate doubling with narrow focus interpretation, the explanation follows the same line of reasoning. Consider the following dialogue:

Once again, in this case the cognitive factive exhibits a parenthetical reading: the embedded clause is what addresses the question. Therefore, the sentence evokes the QUD in (60a), which denotes the set of alternatives propositions in (60b). As in the previous case, this set does not presuppose the proposition ‘Juan read the book’.

Given that the sentence does not trigger any presupposition, no impossible presupposition scenario arises and the doubling, again, becomes acceptable.

Now, as one reviewer points out, the current analysis predicts that predicate doubling with a cognitive factive should be blocked when a parenthetical reading is not possible, i.e., when the factive predicate embeds a presupposed clause. Such a configuration should lead to an impossible presupposition: the sentence would presuppose p while ?p is under discussion. This prediction is borne out. Consider the following example:

As can be observed, polarity focus marking becomes unacceptable when the embedded clause is presupposed, even if the matrix predicate is a cognitive factive. This pattern provides further evidence for the claim that the anomaly of sentences like (42) is due to the underlying interplay between presupposition and focus.

4.1 Polarity focus outside the scope of the emotive factive

In the previous section, I showed that predicate doubling with polarity focus interpretation involving emotive factives is ungrammatical. Nevertheless, there are some contexts in which it seems to be acceptable. Consider, for instance, the following dialogue:¹²

It should be noted, however, that this case is not identical to the previous one in (40b). As can be observed, in the answer in (62) the matrix predicate lamento ‘regret’ receives the main accent. This is so because in this context it is the matrix clause and not the embedded one which is polarity focus marked. Therefore, the sentence has the following focus structure:

In consequence, the QUD evoked by (63) is ‘do you regret having read the book?’ (64a), which denotes the set of alternatives in (64b):

Crucially, this QUD presupposes the proposition ‘you read the book’, since it is presupposed by all the propositions denoted by the question (i.e., the QUD-Presupposition Condition (23) is met). Therefore, the grammaticality of (62) is expected under the present approach: since the polarity focus marking is outside the scope of the factive verb, there is no presupposition failure. In other words, while the focus structure evokes ?p (i.e., ‘do you regret having read the book?), the emotive factive presupposes the proposition q (i.e., you read the book). Thus, no impossible presupposition scenario arises and predicate doubling is acceptable.

4.2 Non-presupposed clauses

Since the problem with predicate doubling involving emotive factives with polarity focus reading resides in the fact that this construction leads to an impossible presupposition, it predicts that it should be possible if the emotive factive, for some reason, exhibits a non-presuppositional use. This prediction is borne out. Consider the following example from Karttunen (1974: 191):

As Abbott (2000) points out, an announcement embedded under a verb of regretting is taken as new information, i.e., it is not presupposed, despite the matrix factive predicate, as in (65). Thus, as can be observed in (66), predicate doubling with emotive factive predicates is possible if the matrix predicate embeds an announcement (in this example, the verb informar ‘to inform’ makes the announcement explicit):

In these cases, the factive predicate does not trigger any presupposition. Therefore, no impossible presupposition arises and, consequently, predicate doubling with polarity focus involving emotive factives is acceptable.

4.3 Other polarity focus constructions

If the analysis developed here is on the right track, one direct consequence is that other polarity focus constructions should be banned in clauses embedded under emotive factive predicates, even if they do not involve predicate doubling. As I show below, once again this prediction borne out for, at least, two other polarity focus structures in Spanish.

First, Spanish, like other Romance languages, exhibits a construction in which a non-interrogative indefinite NP is fronted, as (67) shows. According to Leonetti & Escandell-Vidal (2009), this structure is not an instance of clitic left-dislocation nor of contrastive focalization, but another kind of dislocation that marks polarity focus. That means that the fronted indefinite triggers an emphasis on the positive polarity of the sentence. For that reason, Leonetti & Escandell-Vidal call this construction verum focus fronting (for the sake of simplicity, I will call it polarity focus fronting).

It should be noted that polarity focus fronting is not restricted only to main clauses, but it can occur in an embedded clause (68):

However, there is, again, a contrast between cognitive and emotive factives: while polarity focus fronting is possible in clauses embedded under cognitive factive predicates (69a), it is excluded in clauses selected by emotive factives (69b). This is the same pattern observed previously regarding predicate doubling with polarity focus interpretation.

The second phenomenon is related to the positive polarity particle sí ‘yes’ (Batllori & Hernanz 2013). This particle manifests an emphasis on the positive polarity of a proposition, in contrast to the same proposition with the opposite polarity. This can be observed in following dialogue:

As in the previous case, this particle can also appear in an embedded clause:

Nevertheless, once again, there is an asymmetry between clauses embedded under cognitive and emotive factives: while the former admit the particle sí (72a), the latter do not¹³¹⁴ (72b).

The proposal developed here can account for these cases without further assumptions: the ungrammaticality of (69b) and (72b) can be explained as instances of impossible presuppositions. In both sentences, the polarity focus is assigned within the clause selected by an emotive factive predicate, leading to the following underlying structure:

(73)

Consequently, the QUD evoked in each case should denote the set of alternatives in (74). Crucially, this set does not presuppose the proposition ‘Juan read the book’, since the QUD-Presupposition Condition in (23) is not met (i.e., it is not the case that all the propositions of the set presuppose ‘Juan read the book’).

As happened in doubling sentences seen in Section 3.2, in these cases there is no QUD congruent with ⟦(69b)⟧^f or with ⟦(72b)⟧^f which satisfies the presupposition triggered by the emotive factive (i.e., ‘Juan read the book’). Therefore, these sentences give rise to a systematic presupposition failure.

5.1 Predicate doubling asymmetries in other languages

As seen at the beginning of Section 3, predicate doubling is a cross-linguistically widespread construction which is commonly assumed to exhibit polarity focus marking. If the analysis developed here is on the right track, one would expect to find in other languages the asymmetry with factive verbs observed in Spanish. In what follows, I show that this prediction is borne out.

Consider again the cases of Hebrew (75), Hungarian (76), Yiddish (77), and Brazilian Portuguese (78). As it happens in Spanish, predicate doubling in these languages triggers a polarity focus interpretation of the clause.

Notice that all these languages allow predicate doubling even if the inflected predicate appears in a complement clause:¹⁵

Crucially, these languages show the same pattern regarding factive clauses attested in Spanish: emotive factives, unlike cognitive factives, block predicate doubling with polarity focus interpretation.

This asymmetry is expected under the impossible presupposition account: just like in Spanish, the interplay between the factive presupposition and polarity focus marking leads to a systematic presupposition failure. It is important to underline that the fact that this contrast holds across languages constitutes further evidence in favour of a general restriction. In other words, this pattern is not due to a particular constraint in predicate doubling in Spanish.

5.2 Polarity focus, factivity and denial contexts in German

As is well-known, polarity focus in German is realized through a pitch accent on the finite verb in V2-position (Höhle 1992). Consider, for instance, the sentence in (87). While it is the verb which receives the main stress, what is focused is the truth of the proposition expressed by the sentence.

As for embedded clauses, German exhibits two strategies for polarity focus marking. The first one is that the complementizer receives a pitch accent:

The second one consists in focusing the verb-final position. This option, however, is only possible with semantically light verbs, such as auxiliaries (89) or copulars (90). Focusing a lexical verb can only be interpreted as standard narrow focus (91), as can be observed in the following examples from Driemel (2016: 207):

Now, Stommel (2012: 23) observes an interesting interaction between polarity focus and factivity: it is not possible to mark the complementizer with polarity focus when the clause is embedded under an emotive factive predicate.

Moreover, Driemel (2016) observes that polarity focus marking in V-final position is not possible either if the embedding predicate is factive¹⁷ (93). Importantly, Driemel points out that in the following dialogue A’s utterance imposes an ‘uncertainty context’, that is, a context in which the truth of the proposition ‘today is Peter’s birthday’ is undecided (i.e., it is not part of the Common Ground).

Nevertheless, the claim that emotive factive predicates cannot embed polarity focus sentences in German is not entirely correct. In fact, as Driemel (2016: 212) argues, it is possible in denial contexts. Consider the dialogue in (94). Roughly speaking, B’answer seems to correct a wrong belief that speaker A takes for granted.

This phenomenon is not restricted to polarity focus marking in V-final position. As the dialogue in (95) shows, it is also possible in cases in which it is the complementizer what is focused.¹⁸

Summarizing, the complete picture can be described as follows: polarity focus marking in clauses embedded under factive predicates is not possible in uncertainty contexts, i.e., when ?p is under discussion (96a); however, it is acceptable in denial contexts, i.e., when the QUD is, roughly speaking, factive ?p (96b). Let us consider each case.

As for the first scenario, it can be straightforwardly explained under the account developed here. In other words, it constitutes another instance of an impossible presupposition. Once again, the following configuration arises: on the one hand, the emotive factive predicate presupposes the truth of its complement p, on the other, polarity focus evokes the QUD ?p. As previously discussed, this pattern leads to a systematic presupposition failure, since no context can take for granted p while ?p is under discussion at the same time.¹⁹ It is important to underline that these cases in German show that this constraint does not depend on any particular feature of predicate doubling, but it arises as a general consequence of the interaction between presupposition and focus.

With regards to the second scenario, at first glance these cases seem to be problematic for the impossible presupposition approach: the (emotive) factive predicate embeds a polarity focus clause but the sentence is not ungrammatical. However, notice that in B’s answers the embedded proposition is not part of the Common Ground: crucially, speaker B is correcting A’s wrong belief. In other words, when speaker B answers, this proposition is not commonly accepted by both participants, since it constitutes new information for the addressee. Consider, for instance, the response in the dialogue (95). In this case, the relevant QUD is {he regrets that Paul read the book, he regrets that Paul did not read the book}, that is, he regrets ?p. Nevertheless, the emotive factive predicate does not presuppose that Paul read the book (i.e., this proposition is not part of the Common Ground), since whether Paul read the book or not is part of the question under discussion. What is presupposed is just that Paul’s supervisor regrets something. Schematically, the discourse structure in this case can be summarized as follows:

In short, denial contexts constitute instances of Common Ground revision that allow emotive factives to introduce informative clauses through corrective (polarity) focus. It should be noted that this does not mean that in these contexts emotive factives receives a parenthetical interpretation, since they are part of the QUD.

If this analysis is correct, the fact that polarity focus clauses can be embedded under emotive factive predicates in denial contexts is expected under the approach developed here. Given that in these cases the factive verb introduces new information, no clash between factivity and polarity focus arises. In other words, these sentences do not lead to a systematic presupposition failure. Once again, what is crucial here is not emotive factive predicates themselves, but their presuppositional behavior, as previously discussed in Section 4.2.

5.3 Emphatic do and factivity in English

Wilder (2013) observes that polarity focus in English can occur within a presupposed clause. He offers the following example, in which the do-clause is embedded under the emotive factive predicate was surprised.

Once again, at first this pattern seems to be problematic for the main proposal of this paper: as argued, polarity focus marking appearing within a factive clause should be banned since it gives rise to an impossible presupposition.

Let us examine the example in more detail. One natural question that arises is what is the semantic contribution of polarity focus in this case. Wilder describes it as follows: “the do-clause suggests a contrast with a different possibility, namely that Sue did not (or would not) leave her husband. This could be a previous expectation held by speaker B -so B’s utterance implies that the clash between expectation and fact was what caused B’s surprise” (2013: 153). As can be observed, polarity focus in this sentence is interpreted contrastively, but, unlike typical cases, here the alternative seems to be a counter-factual expectation.

As Callum Hackett (p.c.) points out, this intuition becomes more transparent by appending the phrase “after all” (99), which exposes the implicit expectation.

Crucially, attaching “after all” is unacceptable when there is no focus (100). The only possible interpretation for the following sentences is that “after all” gives rise to a counterfactual expectation regarding the matrix clause, not the embedded one.

The fact that counter-expectation can be grammatically encoded has been largely attested in the literature. For instance, Tawilapakul (2013) argues that the particle lɛɛw45 in Thai expresses counter-expectation, that is, a contrast between the previous expectation and the asserted proposition (101).

Importantly, Tawilapakul makes a further distinction between “denial of expectation”, marked by lɛɛw45, and “denial of belief”, marked by taaŋ22haak22. The contrast is shown in the answer in (102): only taaŋ22haak22 is obligatory in order to deny the false belief about the duration of the flight. In this context, lɛɛw45 is unacceptable.²⁰

Taking this into account, I propose that emphatic do in (98) can be analyzed, roughly, as a counter-expectation marker. In other words, it can be treat as an instance of mirative focus, that is, a category that expresses speaker surprise or exceeded expectation (DeLancey 1997). Recently, mirativity has been analyzed as a non-at-issue content which, in general terms, signals that the proposition is less likely than another one with respect to a contextually relevant modal base (Bianchi et al. 2016), or which reflects the speaker’s attitude towards her utterance (Rett & Sturman 2020). However, whatever the particular implementation one adopts, what is important is that emphatic do in (98) does not seem to evoke (part of) the QUD ?p, since the truth of p is not under discussion. On the contrary, it expresses that the proposition is in some sense unexpected for the speaker.

If this is correct, the sentence in (98) does not constitute a counterexample for the account developed in this paper. Even though superficially polarity focus marking occurs within a factive clause, as argued, ?p is not (part of) the QUD. Therefore, there is no incompatibility between the emphatic do and the factive presupposition (i.e., no impossible presupposition emerges).