2.1 English had-to

According to many authors, English epistemic modals scope over tense (Groenendijk & Stokhof 1975:68—69; Iatridou 1990; Stowell 2004; Hacquard 2006; 2010; 2011; Hacquard & Cournane 2016, a.o.). Stowell (2004) originally discussed the example in (3):²

Stowell (2004) claims that sentences like (3) express a present epistemic claim: ‘given the evidence available now, it is likely that (in the past) there were at least a hundred people there’. Stowell contrasts this interpretation with root uses of modals—as we saw in (2), with a root interpretation, had-to is uncontroversially interpreted under tense.

Example (3) in isolation does not prove that the tense>epi interpretation is not available. Indeed, the sentence is both acceptable whether the modal scopes over or under tense, since a past epistemic claim (‘given the evidence available in the past, it was likely that there were a hundred people there’) could still hold in the present. To tease apart the two readings, we need to consider some more elaborate scenarios, like (4) (introduced by Hacquard & Cournane 2016). In (4), the speaker—a detective investigating a crime—used to believe some fact P (e.g., P: “Al was in Montreal at the time of the crime”), but then receives some new evidence that P was false and that an alternative fact, Q (incompatible with P), is in fact true (e.g., Q: “Al was in DC”). Crucially, in such scenarios, past and present epistemic claims (paraphrasable by, respectively, “I used to believe P” vs “I now know P”), cannot both be true at the same time. Hacquard & Cournane claim that in such contexts, “it had to Q” is acceptable. They contrast had-to with seemed, which (uncontroversially) scopes below tense and shows the opposite pattern: acceptable in (4), but not in (4), where one has to use present tense (“Al seems to have been in DC last night”).³

As put forward in the introduction, the view according to which epistemic modals scope over tense is disputed. Rather, a number of authors argue that epistemic modals can (von Fintel & Gillies 2007), or must (Rullmann & Matthewson 2018) scope under tense. Their claim is based on several arguments.

The first point, made by Rullmann & Matthewson (2018), is that the examples used as evidence that had-to expresses present epistemic claims, like (3)/(4a), sound “(at best) marginal” to native speakers (Rullmann & Matthewson 2018: 326). To support this, they ran an informal questionnaire asking native English speakers to evaluate had-to sentences in contexts that force the epi>tense interpretations, like (5). They report that 3/8 speakers judge (5) marginal and only 3/8 accept Stowell’s example (3) presented in a context that supports a present epistemic claim (6).⁴

Second, Rullmann & Matthewson (2018) provide naturalistic corpus examples (from the COCA Corpus, Davies 2008–2015), which, they argue, can only be taken to convey past epistemic claims and not present ones. As support, they ran another informal questionnaire (n = 11), showing most speakers accept had-to sentences in contexts like (7).

Many authors (Boogaart 2007; Hacquard 2006; 2011; Laca 2012 for French) propose to treat such cases as instances of Free Indirect Discourse (FID), a mode of narration where we “listen to a protagonist’s thought” (Eckardt 2014). As we will see in Section 2.3 and 2.4, very similar examples (i.e., cases where, within narrative context, past epistemic modals seem to be interpreted as past epistemic claims and cannot be interpreted as present ones) have been discussed for Dutch and French.

2.2 Free Indirect Discourse and epistemic modals

FID is a mode of narration where the perspective is shifted to one of the agents in a story, without it being overtly marked (Banfield 1982; Schlenker 2004; Eckardt 2015; Maier 2015; Charnavel 2025; see review in Reboul et al. 2016). There are two main types of approaches to FID, one in which it more closely resembles direct discourse (Banfield 1982; Schlenker 2004; Eckardt 2015; Maier 2015), and one in which it more closely resembles indirect discourse (Doron 1991, Sharvit 2008; Charnavel 2025).⁵ Of course, here we by no means intend to do an exhaustive overview of the literature on FID. We focus on the parts that are crucial for the puzzle at hand: Do examples like (7) show that epistemic modals scope under tense?

First, there is no real disagreement regarding the naturalness proper of examples like (7). They are generally judged acceptable, by linguists, their informants, as well as naïve native speakers (at least when presented in narrative/story-telling contexts, as Rullmann & Matthewson’s (2018) informal study shows). Furthermore, they are attested in corpus data, as evidenced by Rullmann & Matthewson (2018) and Reisinger et al. (2022). In particular, Reisinger et al. (2022), in a larger corpus-based study on English, provide multiple examples of FID involving might have, may have, and must have—which they categorize as having “past TP”.⁶

The first point of disagreement is however how to describe such cases. In FID contexts, there are two temporal reference points to distinguish: the speaker’s (uttering the sentence now), and the protagonist’s (the character in the story). Depending on whether one defines the TP as relative to the speaker’s, or to the protagonist’s reference point, there are two ways to characterize TP: if we define the TP as relative to the speaker, we should say that the TP of had-to is past—as the epistemic claim is made before speech time (e.g. Rullmann & Matthewson 2018; Reisinger et al. 2022). Others (e.g. Hacquard 2011; Falaus & Laca 2020), say that in those examples, the TP is present—because it is simultaneous to the time of the protagonist’s context.

The second, but deeper, point of disagreement, is whether examples like (7) can be taken to falsify the claim that epistemic modals only scope above tense. For Hacquard (2006; 2011), it doesn’t, because the past tense morpheme does not have a semantic backshifting effect. Crucially, the epistemic claim is made simultaneous to the time of the context, which is set in the past. Hacquard proposes a similar mechanism as when epistemic modals appear embedded under past attitude verbs, as in (8): since the modal is under the attitude verb, its local time of evaluation is shifted to the past, and we obtain an epistemic claim at the time of the thinking. For her, in both (7) and (8), the past tense morpheme does not carry semantic tense as the epistemic claim is not further backshifted from the tense in the main clause; it is instead the result of the sequence of tense effect (Abusch 1997; Ogihara 2011).

A challenge for Hacquard’s proposal is that, as shown by Banfield (1982), it might not be possible to reduce FID to sentence embedding for independent reasons.⁷ But this is an ongoing debate. For instance, Charnavel (2025) presents an analysis of FID where, instead of a verb, there is a logophoric operator that semantically embeds FID (Charnavel 2019; 2020), binding the indexicals. Charnavel claims that past tense in FID in a language should be analyzed as a zero tense if sequence of tense effects exists in that language, making explicit the parallel between FID and indirect discourse. Falaus & Laca (2020), similarly, argue for a semantically zero tense in cases of epistemic modals in FID and embedded contexts. Unlike Hacquard however, they argue that past epistemic modals in FID falsify the claim that epistemic modals cannot scope under tense: A zero tense, similar to a regular tense, should be hosted in a TP phrase.

Given the lack of consensus on how to generally analyze FID, it is not easy to decide what to conclude from examples like (7). Do they constitute evidence that epistemic modals scope under tense? For the remainder of this data section, we will put aside such examples involving overt narrative contexts, and focus on the question whether, beyond those cases, we can find convincing examples of past epistemic modals with past TP.⁸

2.3 Dutch moest

In Dutch, it has also both been argued that epistemic modals scope over (Ter Beek 2008) and under tense (Boogaart 2007; Aelbrecht 2010; Rullmann & Matthewson 2018). But the data exhibit interesting differences.

According to Boogaart (2007), the possible interpretations of Dutch epistemic modals constitute the “mirror image of English” (Boogaart 2007:51). For him, sentences where moeten ‘must’ bears past tense, like (9), can express past epistemic claims, but not current ones. Rullmann & Matthewson (2018) also provide examples where moest has to be interpreted under tense, like (10) which asserts that at some time (yesterday) preceding the utterance time (now), it was epistemically necessary for the speaker that the key was in the drawer.

Both cases could be instances of FID, similar to (7). Yet, Aelbrecht (2010) provides another example, (11), that suggests that even outside past narrative discourse contexts, moest can be interpreted under tense. In (11), the question under discussion is whether a man, on his birthday, was in Portugal. The second part of the sentence (“but the new evidence…”) establishes that we now know he was not: therefore, the claim ‘he was in Portugal’ can’t be made at the present. Still, moest is acceptable. Crucially, contrary to (10), there is no context that shifts (11) to the past. Aelbrecht argues that this shows that moest can scope under tense (it is interpreted in the scope of yesterday).¹¹

Other authors, notably Ter Beek (2008:108), claim that Dutch epistemic modals can embed tensed complements, i.e., they can scope over tense (she doesn’t argue that they can’t scope below). To show that epistemic modals can scope over tense, Ter Beek uses evidence from sentences in which the auxiliary hebben ‘have’ appears in the modal’s complement, and from the interaction between modals and the future tense. Both arguments being more complex than the past modal sentences we focus on this paper, we do not review them here (but see van Dooren 2020b for discussion).

2.4 French devait

In French as well, it has both been argued that epistemic modals scope over tense (Hacquard 2006; 2011; Laca 2012) or under tense (Martin 2011; Homer 2013; Falaus & Laca 2020). Again, there is no clear consensus on the data.

In French, there are two main ways modals like devoir ‘must’ combine with past tense, illustrated in (12): the imparfait (devait in (12)), used for past imperfective, and the passé composé (a dû in (12)), which consists of an auxiliary and past participle, and is used either for past perfective or present perfect.¹²

Laca (2012) claims that both (12) are interpreted as present epistemic claims (i): here again, though appearing on the modal, past tense only scopes over the prejacent. By contrast, Homer (2013) argues that both interpretations are possible (see also Martin 2011, who rejects the view that epistemics scope over tense with the possibility modal pouvoir). As support, Homer provides example (13), which cannot be interpreted as a present epistemic claim, since the speaker cannot still be believing that the addressee had a heart attack.¹³ Homer further argues that (13) cannot be treated as FID because the sentence is used in the context of a conversation and directly targets the addressee with the indexical you. This argument seems flawed, however, because it is not true that FID is restricted to narrative past text (see Fludernik 1993, who argues that FID has spread into oral communication and is not restricted to narrative text); precisely in conversational contexts, indexical adverbials behave differently (Charnavel 2025).

3.1 Three theories of modal temporal interactions

What are the consequences for the syntactic analysis for modals? In this section, we focus on three (competing) syntactic analyses of modals which have used data from Section 2 as supporting evidence for their theories.¹⁴

As mentioned in the introduction, the literature on modals draws a major distinction between epistemic and ‘root’ (non-epistemic) flavors. The cross-linguistic generalization is that modals with epistemic interpretations tend to scope higher than root ones. This is notably captured in Cinque’s (1999) hierarchy in which epistemic modals appear in a higher functional projection than Tense, Aspect, and root modals (14).

There is a tension here: on the one hand, given the cross-linguistically robust fact that in many languages, modals can be used for both flavors (Kratzer 1977), one may want to keep one single lexical entry for epistemics and root modals. But on the other hand, we need to capture the differences between epistemic and roots in how they interact with other scope bearing elements in the sentence, and the fact that not all scope interpretations are available. Our question, how modals interact with tense, is one piece of this general puzzle.

Kratzer (1981; 1991) originally proposed that root and epistemic modals share the same lexical entry, and that modal flavor is determined via two contextually determined conversational backgrounds, which provide the set of worlds the modal quantifies over. Yet, this doesn’t predict differences between roots and epistemics’ scope behaviors. Building on Kratzer, Hacquard (2006; 2010) offers a way to explain those differences while keeping one single entry for modals. For her, modal sentences are structurally ambiguous, with two possible underlying syntactic structures: one where the modal is high (above TP, (15)), the other where the modal is low (above VP, (15)). The main departure from Kratzer is in how the modal base is determined: modals have an event variable, which gets bound by the higher event of evaluation. Modals located above tense get an epistemic interpretation because the modal’s event variable is bound by the higher speech event, whereas modals located below tense get a root interpretation because the event variable is bound by the aspect quantifying over the VP event.

Rullmann & Matthewson (2018) offer a potentially simpler analysis, aimed at capturing data from a wider range of languages (English, Dutch, Gitksan (Tsimshianic), and St’át’imcets (Salish)). They propose that both root and epistemic modals are in the same projection, below tense and above aspect (see also Homer 2013). They argue that all modals scope under tense and therefore receive past TP if the tense provides a past reference time. As we saw in 2.1, one of their empirical arguments is that epistemic had-to-sentences where tense is interpreted below the modal, like (3), are “marginal at best” in English, whereas speakers accept sentences where tense is interpreted above the modal, like (7) (FID contexts).

Van Dooren (2020b) proposes (contra Rullmann & Matthewson, following Hacquard) that epistemics scope above tense cross-linguistically, but that Hacquard’s account needs to be recast in terms of complement size (see also Ramchand 2014; Ramchand & Svenonius 2014). Her generalization is spelled out in (16) (from van Dooren 2020b):

Van Dooren proposes that the crucial difference between English and Dutch comes from the lexical status of the modal: while English modals are (semi-)auxiliaries (Jespersen 1909–1949), Dutch modals are verbs (as independently argued by Den Dikken & Hoekstra 1997; Barbiers 2006; Aelbrecht 2010; Broekhuis & Corver 2015; see Haeseryn et al. 1997; IJbema 2001; Van Riemsdijk 2002 for a contrasting view).¹⁵

Modal (semi-)auxiliaries are functional elements inside a functional projection (FP, (17a)): they form a monoclausal structure with the main verb in the sentence. Modal verbs, on the other hand, head a verbal projection and project their own functional projections, including tense (17b).

The difference in lexical status, in combination with the generalization in (16), makes the following predictions. Modal (semi-)auxiliaries (like English have-to) allow only one scope interpretation, where the modal is interpreted above tense for epistemic flavors (18a), and where the modal is interpreted below tense for roots (18b). By contrast, modal verbs (like Dutch moest) head their own functional projections, including tense and aspect. Sentences with root modal verbs only have one tense phrase (because they select for at most a vP complement (16)), where the modal scopes below tense (19c). Epistemic modal verbs, however, combine with a TP-complement (19b); as a consequence, the sentence has two tense projections. Van Dooren therefore predicts two possible interpretations for Dutch epistemic modal sentences (contra English): (19a), with the modal scoping over tense, or (19b), with tense scoping above the modal.

Table 1 schematically summarizes these three proposals.

3.2 Cleaning the table

There is no general consensus on the judgments, and how they might vary across languages and speakers. The majority of the data comes from researchers’ own intuitions, fieldwork involving a limited number of informants, or informal questionnaires, such as those employed by Rullmann & Matthewson (2018). Corpus data are not so informative: epistemic modals in the past are quite rare, with root modals being far more prevalent (see e.g., for English: van Dooren et al 2022; for Dutch: Nuyts 2001; van Dooren et al 2019; for French: Dieuleveut 2023), and amongst these rare cases, contexts that allow to tease apart the two readings in (1) (with new contradicting evidence) almost never occur (for discussion of how hard it is to determine subtle semantic distinctions such as TP/TO or protagonist vs narrator’s perspective from corpus data, see Reisinger et al. 2022).

There has been only one controlled experimental study on the topic. Van Dooren (2020a) used an online Truth-Value Judgment Task to assess judgments on past epistemic modal sentences in scenarios similar to Cournane & Hacquard’s (2016) example (4), comparing English (had-to/seemed) and Dutch (moeten/leek). In the experiment, participants were asked to indicate whether different sentences were true or false in a given context. The four conditions are spelled out in (20)a/b/c/d. In order to control for FID and favor epistemic (vs. root) interpretations, the sentences were presented as uttered by a detective, in direct discourse. Since seem/leek, as lexical verbs, (only) scope under tense, (20a) should be judged false, and (20c) true. For test cases, the rationale is that if had-to/moest can scope over tense, participants should accept (20b) (contra seem/leek). If had-to/moest can scope below tense, they should accept (20d) (like seem/leek).

Van Dooren finds that in English, participants judge had-to-sentences as true in 89% in (b) vs 6% in (d), the contrast we expect if had-to only scopes over tense. In Dutch, participants judge moest-sentences as true in 74% in (b) vs 46% in (d). She takes this to show that, both Dutch moeten and English have-to can scope over tense. Note that while she doesn’t discuss it, the difference seems lower for Dutch than for English—which could reflect that the interpretation tense>epi is (more) available in Dutch. However, a problem is that she finds unexpected results for the baselines seem/leek—namely, 84% of acceptance for English seemed in (a) (expected false), and only 47% in (c) (expected true); for Dutch, she obtains 46% vs. 74%. Van Dooren speculates that this relates to focus, and comes from some participants “ignoring” past tense morphology to focus on evaluating the truth of the information provided by the embedded clause. Alternatively, her results may come from participants being free to assess seemed to any time point in the past. To resolve this issue, in our experiment, we added “to me” to ensure that seemed and thought were attributed to the same speaker.

3.3 Testing the predictions

The three theories we described in Section 3.1., combined with the less than clear results from van Dooren (2020a) in Section 3.2. give rise to several questions. Do epistemic modals always scope over tense or below tense? Are there languages where both options are available? How much variation is there between languages and what explains it? Do they come from differences in modals’ syntax?

The subtle nature of these judgments, added to the potential competition with root interpretations (especially in the case of English have-to), makes the question hard to reliably elicit through fieldwork, or to settle based on corpus observations: we need scenarios with explicit contrasts between the two readings, and clear baselines ensuring that potential unacceptability does not arise from the intrinsic peculiarity of these scenarios. The experiments we present in the next sections build on van Dooren’s (2020a) paradigm, crucially adding French as a test case.

While van Dooren does not discuss French, we take that her prediction would be for French devoir to pattern like English have-to. Indeed, French modals are usually taken to be (semi)-auxiliaries (Borgonovo & Cummins 2007; Hacquard 2010).¹⁶

We ran the same experiments in Dutch (D), English (E) and French (F), asking participants to judge the acceptability of sentences like “It had to be raining”, presented in contexts that made either the epi>tense or the tense>epi interpretation warranted. We compare the judgments on had-to/moest/devait to seemed/leek/semblait, which we assume scopes under tense. We ran two versions of the experiment: in the first version (Experiment 1: offline ‘reflective’ judgments), participants had unlimited time to answer; in the second version (Experiment 2: online ‘speeded’ judgments), they were asked to answer as quickly as possible.

4.1 Participants

60 native speakers per language were recruited (Dutch, English, French) (30 participants per Lemma condition (had-to/seemed), counterbalanced across four lists).¹⁸ English participants were recruited via Amazon Mechanical Turk (www.mturk.com), Dutch and French participants via Prolific (www.prolific.com) (mean age: D: 26.5; E: 37.6; F: 28.2; D: 20 females; E: 19 females; F; 23 females). Two participants were excluded based on a native speaker check presented at the beginning of the experiment (1 Dutch, 1 French). An additional 25 participants were excluded because of low accuracy on fillers in the AJT and the BetT, as detailed below (D: 8, E: 7, F: 10). We therefore report results for 153 participants (D: 51, E: 53, F: 49).

4.2 Materials and design

Critical sentences were of the form “It had to/seemed to me to P,” with two possible continuations: “…but I thought that Q” or “…but now I know that Q.” P and Q were chosen to be mutually exclusive (for instance, P: “be raining yesterday” vs Q: “be snowing yesterday”). We call the two continuation contexts Cont-Past and Cont-Pres, respectively. The four sentence types are spelled out in (21). (22) provides English’s (21) equivalents in Dutch and French.

The continuation context Cont-Past (“but I thought Q”) allows us to test the availability of the epi>tense interpretation. “But I thought Q” describes a past (mistaken) belief that Q, which is compatible with a present epistemic claim that P, but not with a past epistemic claim that P. Therefore, if participants get the epi>tense interpretation for the modal verb, they should judge the full sentence ‘sensible.’ If they get tense>epi, they should judge the full sentence ‘nonsensical’ since it leads to a contradiction (P and Q cannot be true at the same time). In other words, Cont-Past forces the epi>Tense interpretation. Here, we expect seemed ((21a)) to be unacceptable, since seem scopes below tense.

The continuation context Cont-Pres (“but now I know Q”) allows us to test the availability of the tense>epi interpretation. “But now I know Q” describes a present certainty about Q, which is compatible with a past epistemic claim that P, but not with a present one. Therefore, if participants get the epi>tense interpretation, they should judge the full sentence ‘nonsensical’. If they get tense>epi, they should judge the full sentence ‘sensible’ (it does not lead to a contradiction). In other words, Cont-Pres forces the tense>epi interpretation. Here, we expect seemed ((21c)) to be acceptable (there is no contradiction).

We created 8 different critical sentences, listed in Table 2. Particular care was taken to ensure that the sentences make deontic interpretations unlikely. As discussed in the introduction, this is particularly important, since under a deontic interpretation, the modal is uncontroversially interpreted under tense.¹⁹ Note that for seemed, we add “to me” (respectively, “leek me” in Dutch, and “me semblait” in French) to make sure that seemed and thought are evaluated by the same individual (if they are evaluated by different individuals, “seemed P… but I thought Q.” is non-contradictory).²⁰

For fillers, we used sentences either sounding contradictory for no-controls (e.g. “Aron is American, and indeed, he is Italian”, expected to be judged ‘nonsensical’) or not contradictory for yes-controls (e.g. “Aron is American, and indeed, he was born in New York,” expected to be judged ‘sensible’).²¹ We had 8 fillers with yes/no variants. All sentences (critical cases and fillers) in Dutch, English and French are available in Appendix A.

Continuation context (Cont-Past vs Cont-Pres) was tested within subjects, Lemma (had-to/seemed) and Language (Dutch/English/French) between subjects.

4.3 Procedure

The experiment was run online using the IBEX platform (Drummond, n.d.).²² The experimental material and procedure were identical in Dutch, English and French. After instructions (Appendix B), participants had a short training (3 examples with feedback). In the test phase, they were asked to judge the acceptability of 16 sentences (8 fillers, 8 critical cases), presented in randomized order. They first had to indicate, whether the detective uttering the sentence was speaking in a ‘nonsensical’ vs. ‘sensible’ way (Acceptability Judgment Task, AJT), and second how they would distribute a $100 bet on what really happened, P or Q (Betting Task, BetT). Examples of the display are given in Figure 1 (critical case with had-to) and Figure 2A/B (yes- and no-fillers). For the bet, participants could distribute their bet going from $100 on P and $0 on Q, to $75 on P and $25 on Q, $50 on P and $50 on Q, $25 on P and $75 on Q, and $0 on P and $100 on Q. The Betting Task further allowed us to increase the contrast between P and Q, indicating that they could not both be true at the same time. The placement of the P/Q options (right/left part of the screen) was counterbalanced across participants.

Figure 1

Example of a critical trial, Experiment 1 (English, Cont-Pres).

Expected answer: AJT: ‘nonsensical way’; BetT: 50/50.

Figure 2

Examples of Yes-/No-fillers, Experiment 1 (English).

4.4 Rationale and expectations

For had-to /moest/devait), we test the hypotheses that: (H1) in all languages, epistemic can scope above tense (Hacquard 2006; van Dooren 2020b; contra Rullmann & Matthewson 2018); (H2) epistemic modals like Dutch moeten are modal verbs, therefore can both scope above tense (the tense of their complement), and below tense (the tense of their own clause). By contrast, English have-to and French devoir are (semi-)auxiliaries and only scope above tense (van Dooren 2020b). We compare judgments on had-to to judgments with the verb seemed (to me), which we assume is interpreted below tense in the three languages (*epi>tense, tense>epi). Table 3 summarizes our expectations.

Acceptability Judgment Task (AJT). In the Cont-Past condition (i.e., +thought continuations), we expect participants to reject seemed-sentences, Table 3, row (a)), as seemed is interpreted below tense in the three languages ((a) should sound contradictory, since P and Q are incompatible). For test cases (had-to/moest/devait), if (H1) is true, participants in all languages should accept sentences (Table 3, row (b)). In Cont-Pres (i.e., +know continuations), we expect participants to accept seemed-sentences, Table 3, row (c)) (no contradiction). For test cases, if (H2) is true, only Dutch participants should accept these sentences, whereas English and French participants should reject them (Table 3, row (d)).

Betting Task (BetT). We use the Betting Task both as a control and exclusion criteria (for fillers, we excluded participants who made more than 2 mistakes out of the 4 ‘sensible’ fillers), and as an indicator of the actual interpretation of test sentences (as it shows whether participants think that P or Q is true). Note that we didn’t give specific instructions for nonsensical utterances on the Betting Task: participants could either use the 50/50 option or pick at random.

4.5 Results

4.5.3 Results

Figure 3 displays the mean proportion of ‘sensible’ answers by conditions for Dutch, English and French on the AJT (see Appendix C, Table C1). We see that in the Cont-Past condition, participants in all languages tend to reject baseline seemed/leek/semblait sentences, though at slightly higher rates than expected ((a): D: 23%; E: 24%; F: 24%). By contrast, they tend to accept had-to/moest/devait sentences—at least, more often than seemed sentences ((b): D: 55%; E: 40%; F: 57%). In Cont-Pres, participants in all languages tend to accept seemed/leek/semblait sentences, as expected ((c): D: 85%; E: 80%; F: 91%). For had-to/moest/devait, participants in English and French tend to reject the sentences—at least, more often than the same sentences with seemed, whereas in Dutch, the difference between moest and leek is smaller ((d): D: 79%; E: 52%; F: 70%) Results from the model comparison testing for the Lemma*Context Interaction are reported in Table 4, with associated β-estimate, z-values and p-values of the full model. Simple effects of Lemma based on EMMs are summarized in Table 5.

Figure 3

Proportion of ‘sensible’ responses by condition for Dutch (orange), English (blue) and French (green) for seemed (light) and had-to (dark), AJT, Experiment 1 (n = 153).

Table 4

Result of the model comparison testing Interaction Context*Lemma with associated Estimate (β), Std. Error, z-value, p-value for m1 by language, Experiment 1 (full model m1: Answer==1~Lemma*Context+(1+Context|Subject)+(1+Context+Lemma|Item)).

	Result of the LRT (model comparison)	Estimate (β), Std. Error, z-value, p-value
Dutch	χ²(1) = 8.36, p = .0038**	β = –1.50, SE = 0.47, z = –3.19, p = .001
English	χ²(1) = 15.21, p < .001***	β = –1.45, SE = 0.34, z = –4.31, p < .001
French	χ²(1) = 22.03, p < .001***	β = –2.06, SE = 0.40, z = –5.12, p < .001

Table 5

Simple effects of Lemma (seemed vs. had-to) within each Context by Language, based on estimated marginal means (EMMs) from the full model (m1), Experiment 1.

	Cont-Past				Cont-Pres
	β	SE	z	p-value	β	SE	z	p-value
Dutch	–2.07	0.54	–3.83	0.0001**	0.94	0.87	1.09	0.27 (NS)
English	–0.91	0.47	–1.91	0.056 (NS)	1.99	0.61	3.26	0.0011**
French	–2.44	0.68	–3.60	0.0003**	1.68	0.59	2.84	0.0045**

Comparison between Languages. For seemed/leek/semblait, model comparison reveals no significant interaction between Language*Context (χ²(2) = 2.82, p = 0.244), indicating that participants across the three languages treat seemed-sentences similarly. Looking at simple effects, only the main effect of Context is significant (β = 3.35, SE = 0.36, z = 9.42, p < .001) (reflecting that participants overall accept more sentences in Cont-Pres than Cont-Past). For had-to/moest/devait, likewise, there is no significant Language*Context interaction (χ²(2) = 2.04, p= .36). Looking at simple effects, the model shows a significant effect of Language (β = 1.32, SE = 0.53, z = 2.51, p = .012*; β = 1.06, SE = 0.45, z = 2.34, p = .019*), indicating lower acceptance rates for English had-to than French and Dutch. Results of the models’ output are available in Appendix G.

Figure 4 shows results by subject. Each dot corresponds to a participant (a jitter was added in order to make the results readable). We see that seemed participants (grey dots) are distributed across the bottom part of the graph (right to the diagonal). Had-to participants (black dots) are spread, and do not show a clear pattern. This is interesting, since one possibility was that the tense>epi interpretation is accepted only by some speakers. This doesn’t seem to be the case. Details of the results by context and sentence are available in Appendix C.

Figure 4

Answers by subject for seemed (grey) and had-to (black) (seemed: 77 participants across the 3 languages; had-to: 76 participants). Each dot corresponds to one participant. The y-axis corresponds to the proportion of ‘sensible’ answers given for Cont-Past (out of 4 trials), the x-axis, the proportion for Cont-Pres. Participants who always reject sentences with had-to would appear in the left bottom corner (0;0); participants who always accept it, in the right up corner (100:100).

Figure 5 shows the distribution of bets on ‘sensible’ answers.²³ We merged answers 0/25 together, and 75/100. We see that regardless of the lemma (seemed/had-to), when participants answer ‘sensible’ in Cont-Pres, they always pick the Q option (white bar).

Figure 5

Distribution of bets based on condition (raw counts, only out of ‘sensible’ answers), Experiment 1.

4.6 Interim discussion

In the Cont-Past condition, we find higher acceptance rates for had-to/moest/devait in all languages, when compared to seemed/leek/semblait. This is what we expect if these sentences can be interpreted as a present epistemic claim about a past eventuality (epi>tense) (contra seemed/leek/semblait). This is in line with predictions from Hacquard 2006; Hacquard & Cournane 2016; van Dooren 2020b; contra e.g. Rullmann & Matthewson 2018). In Cont-Pres, conversely, we find both in English and in French lower acceptance rates for had-to/devait than for seemed/semblait. This is what we expect if the epistemic modal cannot be interpreted as a past epistemic claim (*tense>epi). In Dutch however, the difference is not significant in this condition (moest: 78% vs leek: 87%), which is what van Dooren’s (2020b) theory predicts: according to her, for Dutch, the two interpretations are available. It is worth highlighting there does not seem to be interspeaker variation: we don’t find two groups of participants, some always accepting had-to and some always rejecting it in the Cont-Pres condition. A third important result, allowed by the direct comparison between languages, is that English had-to is judged significantly less natural than its Dutch and French counterparts (app. –15/20%). This result aligns well with Rullmann & Matthewson’s (2018) point that had-to in sentences like (5)/(6) are disliked by native speakers (Section 2.1). We think specificities of English have-to can help clarify part of the debate. We will come back to this in the general discussion, where we discuss the idea that the lower acceptability of had-to comes from specific licensing conditions on have-to (Williams et al. in prog.).

While we do find differences between had-to and seemed, our results are not as clear cut as one might expect. In particular, the acceptance rates we find for had-to sentences in Cont-Pres, both in English and French, are quite high: around 52% in English, and 70% for French, in situations where we expect participants to simply reject the sentence. Second, we also find quite high acceptance rates for seemed in Cont-Past (sentences like “It seemed to P but I thought that Q”), with average acceptability ratings around 25% in all language, while we expected participants to reject it. Why is that so?

Starting with the latter, it may be that participants interpret the two epistemic claims, seemed P and thought Q, at different past times. If so, the claims are not incompatible anymore. However, we still find a consistent pattern across the three languages—showing that the design of our controls is an improvement on van Dooren (2020a).

Then, why do participants accept had-to in Cont-Pres? Several factors could play a role. It could be that our contexts and design did not make the incompatibility between P and Q salient enough: for instance, one could construct worlds where snow and rain might happen at the same time. However, in 3 cases, there was an explicit contrast between ‘P’ and ‘not P’ (sentences 1, 5 and 8 in Table 2); we would then expect differences between these and the other contexts, which we don’t seem to find (see Appendix C). Moreover, the betting task helped partitioning worlds, by forcing to bet on P- against Q-worlds. A second possible explanation is that some participants (re)interpret had-to/devait sentences as expressing deontic modality (e.g. “had-to P” as ‘based on past rules, it was necessary that P’, which does not contradict now knowing Q). Again, we don’t think this is the explanation: we built the material to avoid this option (footnote 19), making sure that the deontic was extremely unnatural if not impossible (e.g. “The AC had to be broken” or “The driver had-to be at fault”). Finally, despite our design avoiding any overt narrative context (sentences were presented as direct speech, and set in the present tense), participants might read the utterances as FID, read this as a detective novel set in the past tense: “It had to be snowing, he thought.”

The original goal of Experiment 2 was to try to get to the “primary” interpretations and prevent potential reinterpretation strategies by asking participants to answer under time pressure. While we now believe that our design was not well suited to test for this, the study still serves as a (partial) replication of Experiment 1, testing the robustness of the findings.

5.1 Goal

In Experiment 1, participants were encouraged to take their time to make the judgments, which we hypothesized may have pushed them to reinterpret the sentences—either with a deontic interpretation or imagining a past narrative context (FID). The (initial) goal of Experiment 2 was to prevent such reinterpretation strategies by asking participants to answer quickly. the paradigm also allowed us to record participants’ response time, which we couldn’t analyze in Experiment 1 since the AJT and the BetT appeared on the same screen.²⁴

Manipulating time pressure has been used as one way to study the online processing of various phenomena, notably potentially “ambiguous” sentences. It has been used to show, for instance, that there is a “cost” associated to scalar implicature generation (see e.g. Bott & Noveck 2004; Noveck & Posada 2003).²⁵ Here—if we assume that FID is not the “default” reading, in absence of past narrative discourse context, it should come with a “cost”: we therefore expect, if the high rates found for had-to in Cont-Pres in Experiment 1 reflect FID, to obtain lower acceptance rates in had-to in Cont-Pres when time pressure is added.

5.2 Participants

180 participants were recruited using Prolific (www.prolific.com) (D: 61; E: 58; F: 61; 8 groups for counterbalancing) (mean age: D: 31.3; E: 41.3; F: 32.4; D: 25 females, 35 males, 1 non-binary; E: 29 females, 26 males, 1 non-binary, 2 unknown; F; 25 females, 34 males, 1 non-binary, 1 unknown). We excluded 1 (Dutch) participant who participated twice in the experiment, 29 participants because of low accuracy (<75%) on fillers on the AJT (D: 4, E: 20, F: 5) and 4 participants for low accuracy (<75%) on comprehension questions (D: 1, E: 2, F: 1). We therefore report results for 148 participants (D: 55, E: 38, F: 55).²⁶

5.3 Procedure

All experiments were coded using PennController for Ibex (Zehr & Schwarz, 2018) (https://www.pcibex.net/). We used the same material as in Experiment 1. The main change was that participants were now asked in the instructions to answer as quickly as possible: instead of “Please take your time in completing this task, you may want to read them a second time or take a break in between”, they saw: “IMPORTANT // Time is limited, so answer as quickly as possible! // Just make sure you’ve read the whole sentence before answering”. Like in Experiment 1, after instructions and a short training, they had 16 sentences to judge (8 test, 8 fillers), presented in randomized order. On a first screen, they had to indicate whether the sentence was ‘nonsensical’ vs. ‘sensible’ (AJT, i in Figure 6); then on a second screen, after clicking a fixation cross, they had to indicate what they thought really happened, ‘P’ or ‘Q’ (BetT, ii in Figure 6). This allowed us to record their response time.

We also modified the way the sentence appeared: while in Experiment 1, the whole sentence was presented at once, in Experiment 2, it unfolded incrementally from left to right, the first part of the sentence over the other, at a rate of 40ms/letter (i.e., on average 3500ms for the full sentence to appear). We counterbalanced for the placement of the answers: half of the participants saw ‘sensible’ on the right and ‘nonsensical’ on the left, the other half saw ‘sensible’ on the left and ‘nonsensical’ on the right. Because we wanted to simplify the display, we removed the fictional detective speaker,²⁷ and changed the Betting Task for a binary choice: rather than having to pick between 5 options to make a bet, participants simply had to click on the true statement, with the two options P or Q displayed in two boxes. At the end, participants were asked for comments about the task. Examples of the experiment are available at https://farm.pcibex.net/r/TLMTmo/ (English), https://farm.pcibex.net/r/vCyMpc/ (Dutch) and https://farm.pcibex.net/r/ffkCsV/ (French). As in Experiment 1, Continuation (+know/+thought) was tested within subjects, Lemma (had-to/seemed) and Language (Dutch/English/French) between subjects.

Figure 6

Display for Experiment 2. (i): AJT; (ii): BetT.

Assuming that reducing the amount of time available to make the judgment prevents participants from reinterpreting the sentence (e.g. deontic or FID), we expect to reduce the amount of answers ‘sensible’ in Cont-Pres for had-to for French and English, but not Dutch. We also expect to reduce acceptance rates for seemed in Cont-Past. Looking at response times, we expect participants to take longer to answer ‘sensible’ than ‘nonsensical’ in Cont-Pres for had-to sentences for French and English.

5.4 Results

5.4.2 Results

Figure 7 displays the mean proportion of ‘sensible’ answers by conditions for Dutch (D), English (E) and French (F) in Experiment 2 (Appendix C, Table C2). As in Experiment 1, we see that participants tend to reject seemed in Cont-Past (i: D: 23%; E: 18%; F: 28%), and accept it in Cont-Pres (ii: D: 94%; E:78%; F: 91%). For had-to, we find higher acceptance rates for had-to than seemed in Cont-Past (iii: D: 62%; E: 44%; F: 60%), and lower than seemed in Cont-Pres (iv: D: 76%; E: 69%; F: 83%).

Figure 7

Proportion of ‘sensible’ responses by condition for Dutch (orange), English (blue) and French (green) for seemed (light) and had-to (dark), AJT, Experiment 2 (n = 148).

5.4.3 Analysis

Analysis per language. Results from the model comparison testing for the Lemma*Context Interaction are reported in Table 6, with associated β-estimate, z-values and p-values of the full model. As in Experiment 1, we find significant Lemma*Context interactions in all languages (Dutch: χ²(1) = 18.2, p < .001***, English: χ²(1) = 11.9, p = 0.00056***; French: χ²(1) = 15.2, p < .001***). Further analysis using EMMs reveal significant simple effects of Lemma in Cont-Past for all three languages, with significantly lower acceptance rates for seemed compared to had-to (in Experiment 1, the difference in English is only marginally significant) (Dutch: β = –2.43, SE = 0.57, p < .0001; English: β = –2.24, SE = 0.89, p = .012; French: β = –2.43, SE = 0.68, p = .0003). In Cont-Pres, Dutch and English showed significant higher acceptance rates for seemed relative to had-to (Dutch: β = 1.86, SE = 0.84, p = .026; English: β = 2.15, SE = 1.06, p = .043), while French showed no significant difference (p = .174) (in Experiment 1, the difference was significant in French but not in Dutch).

Table 6

Result of the model comparison testing Interaction Context*Lemma with associated Estimate (β), Std. Error, z-value, p-value for m1 by language, Experiment 2 (full model m1: Answer==1~Lemma*Context+(Context|Subject)+(Context+Lemma|Item)).

	Result of the model comparison	Estimate (β), Std. Error, z-value, p-value
Dutch	χ²(1) = 18.17, p < .001***	β = –2.15, SE = 0.47, z = –4.60, p < .001
English	χ²(1) = 11.90, p = 0.00056***	β = –2.19, SE = 0.59, z = –3.74, p < .001
French	χ²(1) = 15.23, p < .001***	β = –1.68, SE = 0.40, z = –4.24, p < .001

Results by subjects, by context and by sentence are available in Appendix C.

Comparison between Languages. For seemed, as in Experiment 1, model comparison reveals no significant interaction between Language*Context (χ²(2) = 0.0031, p = .99): participants do not treat seemed-sentences differently across the three languages. Again, the main effect of Context is significant (β = 3.27, SE = 0.47, z = 6.97, p = 3.3e–12) (participants overall accepting more sentences in Cont-Pres than Cont-Past). For had-to, there was likewise no significant Language*Context interaction (χ²(2) = 1.82, p = 0.40). The model shows a main effect of Context (β = 1.22, SE = 0.31, z = 3.97, p < .001), and a significant effect of language (β = 1.23, SE = 0.45, z = 2.77, p = .006**). Details of the models’ outputs are available in Appendix G.

Comparison between Experiments. We find no difference between experiments, be it overall (χ²(2) = 0.91, p = 0.34) or looking at each subcondition. Results from likelihood ratio tests by subconditions are given in Table F, Appendix F.

Figure 8 shows the distribution of answers (on ‘sensible’ answers). Results for ‘nonsensical’ answers (where participants were supposed to pick at random) are available in Appendix D. As in Experiment 1, when participants answer ‘sensible’ in Cont-Pres condition, they systematically pick the Q option.

Figure 8

Distribution of answers (Q vs P) based on condition (raw counts, only out of ‘sensible’ answers), Experiment 2.

5.5 Discussion

In Experiment 1, we found quite high acceptance of had-to in Cont-Pres, which we hypothesized could be due to a “reinterpretation” of these sentences as FID. To explore this hypothesis, we implemented a “speeded” version of the Experiment, aimed at testing whether participants change their response when asked to answer quickly, and allowing us to record their Response Times.²⁸ The manipulation did not affect participants behaviors in the way we expected. As in Experiment 1, we find that English, Dutch, and French participants accept had-to/moest/devait in Cont-Past in higher rates than seemed/leek/semblait. Unlike Experiment 1, we find no significant difference between seemed and had-to in the critical Cont-Pres condition for French (Table 7), and a now significant difference for Dutch. This warrants discussion.

The effect in Dutch seems mostly due to the baseline, with higher acceptance of leek sentences in Experiment 2 (94%) than in Experiment 1 (87%) (compared to moest: Experiment 1 78%; Experiment 2: 76%). For French, if this pattern reflects a real trend, it may actually go against the idea that the tense>epi interpretation is “harder to access”. The results may suggest that when asked to answer quickly, participants in fact tend to accept devait slightly more often in Cont-Pres. The difference is not significant, but we expected the opposite pattern. Moreover, when we consider response times on this specific condition (see Appendix E), we see that participants are overall 700ms slower to reject than to accept the sentence (mean RT for ‘sensible’ answers: 4168ms; for ‘nonsensical’ answers: 4816ms), whereas we find the opposite tendency for devait in Cont-Past (participants who accept the sentence, as we expected them to, are 500ms slower than participants who reject it). So, if anything, it seems that the change in our design facilitates the tense>epi interpretation.

If we keep our initial assumption that FID comes with a cost, this means that the high acceptance rates in Experiment 1 are not due to FID. Alternatively, it could be that FID does not come at a cost, even in the absence of an overt past narrative context when participants have to enrich the context themselves.

Finally, another difference we introduced might partly explain the difference with Experiment 1. Indeed, in order to simplify the task, we removed the fictional detective and quotation marks. This change might have left participants more free when judging sentences like “It had to P, but now I know Q”, to introduce a different epistemic source for the first part of the statements, allowing them to anchor “It had to P” for instance to a report in the newspaper, while anchoring “but now I know Q” to themselves. As a result, there is no incompatibility between the two conjuncts. Similarly, acceptance of the “It had to P, but I thought Q” would not show that epistemics can scope under tense, as no potential incompatibility could arise if two separate epistemic sources are chosen for the first and the second part of the statement. This could also explain that participants tend to choose Q in this condition in the betting task (Figure 8).

6.1 Interpreting the findings

The goal of our experiments was to assess three different theories of modal-temporal interactions. These theories make different predictions regarding the interpretation of past tense modals in sentences like “Al had to be in the bathroom” or “It had to be raining.” According to Hacquard (2006), universally, epistemic modals scope over tense. In sentences with a past tense modal, even though the past tense morpheme appears on the modal, it is interpreted in its scope, resulting in a present epistemic claim about a past event. Following her theory, in our experiment, participants in all languages should accept had-to/moest/devait in Cont-Past (“It had to be raining, but I thought that it was snowing”) more than seemed/leek/semblait, as the latter only allow past>epi. They should also reject it in Cont-Pres (“It had to be raining, but now I know that it was snowing”), where they should accept seemed/leek/semblait. Rullmann & Matthewson (2018), contrastingly, state that epistemic modals universally scope below tense. If this is right, in our experiment, participants should reject had-to/moest/devait in Cont-Past, while accepting them in Cont-Pres. Van Dooren (2020b), finally, hypothesizes that the lexical status of the modal (verb or (semi-)auxiliary) determines its scopal interaction: Epistemic modal auxiliaries can only scope over tense, while epistemic modal verbs can scope over and below tense. This theory predicts cross-linguistic differences: assuming that English and French modals are (semi-)auxiliaries, English and French participants should accept had-to/devait in Cont-Past and reject them in Cont-Pres, whereas, assuming that Dutch modals are verbs, Dutch participants should accept them in both Cont-Past and Cont-Pres.

What have we learned by comparing English, Dutch and French? We identify three key results. First, in both experiments, in Cont-Past, we find that participants in all languages accept sentences with had-to/moest/devait (significantly more often than seemed/leek/semblait). This suggests that that epi>tense is available in all three languages, in line with predictions from both Hacquard (2006) and van Dooren (2020b). Recall that this contrasts with judgments for root modal sentences, such as “Al had to do the dishes”—which uncontroversially express past obligations (past>modal) and not present ones (*modal>past). Second, in Cont-Pres, we find in Experiment 1 that both English and French participants accept had-to/devait less often than seemed/semblait. This suggests that past>epi is not (or at least, less) available. In Dutch however, no such contrast is found, which is what we expect under van Dooren’s theory. The other two theories don’t predict differences between languages.

However, these first two findings are not so clear cut, and judgments are less crisp than expected. Though we do find the critical difference with seem, English and French participants in Cont-Pres still accept had-to/devait at quite high rates (55%/70%), which is hard to understand if tense>epi is simply unavailable. (i) Why do participants accept those sentences? Conversely, in Cont-Past, they accept had-to/devait at 40%/55% only. (ii) Why don’t they accept them more? What explains that in almost half of the cases, they judge them nonsensical?

Let’s begin with (ii). Why do so many participants reject “had-to P… but I thought Q”? We think this may be explained by independent pragmatic factors. Without any context, “but I thought” continuations sound weird: talking about past mistaken belief is less often a topic of conversation—i.e., less conversationally relevant—than describing the true state of the world. Thus, Cont-Past continuations may be likely to lead to ‘nonsensical’ answers, because they involve stating first a true fact then followed by a mistaken belief about it, which is conversationally odd.²⁹ One interesting follow-up would be to see whether reversing the order of the two clauses affects the judgments (e.g., “I thought that it was snowing, but (in fact) it had to be raining” vs “Now I know that it was snowing, but it had to be raining”), or, since the weirdness of these examples seems to come from the lack of preceding context, to manipulate the Question Under Discussion so that talking about mistaken beliefs becomes relevant.

Let’s turn to (i), which we see as more puzzling, and is a challenge to both van Dooren’s and Hacquard’s approaches. Why don’t French and English participants just reject “had to P… but now I know”)? First, it may be that the contrast between P and Q was not clear enough in some of our sentences (e.g., it can be raining and snowing at the same time). This might have been an issue especially in Experiment 2, where participants saw the sentence in isolation—whereas in Experiment 1, the Betting Task forced them to partition the world into P/Q-worlds. However, that cannot be the whole story, since some items contrasted P and not(P). A second possibility is that (some) participants created scenarios or stories akin to FID-discourse (as discussed in Section 2, examples (7)/(10)/(13)). Namely, they would imagine that the detective is going back in time and talks about an earlier epistemic event (of him falsely believing that P was true). Indeed, though we try in our design to minimize the odds of participants shifting to FID by presenting sentences in direct discourse (cf “The detective says:”), this might leave too many parameters open. Moreover, as noted e.g. by Kaiser (2015) (for theoretical work, see also Fludernik 1993, a.o.), linguistic expressions whose interpretation depends on reference to some kind of judge/evaluator (some kind of ‘epistemic anchor’) like epistemic modals, epithets, predicates of personal taste or appositives, are particularly prone to elicit FID. Her experiment 3 shows that readers indeed tend to switch to FID when sentences involve epistemic modals. Note that if participants’ answers come from FID, we might expect to get patterns looking at variation between participants and/or items.³⁰ And indeed, amongst our 8 sentences, further inspection shows that some might lead to story-telling contexts more easily (for instance “The barking dogs LEMMA be afraid of something last night” vs “It LEMMA be snowing this morning”).

Before getting further, we would like to make a small clarification note. While one could describe had-to/devait/moest sentences as “ambiguous,” it is crucial to specify at what level of analysis. Here, at least two interpretations seem available: the ‘direct discourse’ one, and the ‘FID’ one. The difference between this “ambiguity” and Dutch would be that the ‘epi>tense’ reading that French/English participants access is (contra Dutch) not at the syntactic level proper, it is at the pragmatic one, whereas following van Dooren, the “ambiguity” of sentences is at the syntactic level. (Of course, FID is also available for Dutch speakers.).

Coming back to our main results, our third key finding is the overall lower acceptability for English had-to, as compared to Dutch moest and French devait.³¹ We believe this connects to the fact that in English, have-to is rarely used to convey epistemic modality—as evidenced by corpus studies, must has increasingly specialized for epistemic necessity in English (cf. Leech 2003 for British English and Kranich 2021 for American English).

More precisely, we think that our result is due to the specific licensing conditions of English have-to: Have-to needs strong evidence available in order to be acceptable. This idea is developed by Goodhue & Hacquard (2021) (see also Williams et al. in prog.), who state that have-to is stronger than must. They support this claim by contrasts as in (23), where have-to is infelicitous, whereas must is natural.

Williams et al. furthermore discuss the context in (24), originally introduced by Rullmann & Matthewson (2018). Rullmann & Matthewson argue, based on the contrast between (24a)/(24b), that a present TP is impossible for had-to. Williams et al. point out that (24c) (where have-to uncontroversially has a present TP), is infelicitous in this context as well. This can be explained if epistemic have-to is in general too strong for the context in (24).

In our experiment, we did not specify the strength of the evidence that the detective bases their claim on; for some participants, the sentences might have therefore been judged as infelicitous based on the evidence being too weak to support the use of have-to. This may also be the reason why, when we compare our study to van Dooren’s (2020a), she finds much higher rate of acceptance for had-to in contexts forcing present TP. In her experiment, the contexts specify that there is evidence, and that it is strong.

6.2 Open questions and future directions

To our knowledge, our study is the first that experimentally assesses the acceptability of past epistemic modal sentences, a topic debated since the seventies, using parallel methods in three languages. Our design allows us to study the interaction between tense, epistemic modality, and narrative discourse, comparing the predictions of different syntactic approaches. Where do we go from here?

A first path is to investigate other modals. In this experiment, we focused on necessity modals that can inflect for tense, leaving aside overt aspectual marking. But many of the key examples discussed in the literature on modal temporal interactions involve possibility modals like might:

Sophie seems to be making a claim about a past epistemic state she was in, which von Fintel & Gillies (2007), a.o., have used to argue in favor of the claim that epistemic modals can be interpreted in the scope of tense. Others have provided analyses in which there is an implicit because-clause (Hacquard 2011) or attitude (Falaus & Laca 2020) that embeds the modal. Similar to the debate surrounding FID and embedded modals in Section 2.1., under these alternative analyses, the temporal perspective is not past (relative to utterance time), but present (relative to the tense in the embedding clause). We believe studying such sentences experimentally is a promising avenue for reaserch, especially given the cross-linguistic complexities that arise when aspect is added to the picture.

Finally, a prediction that can be tested by expanding the number of languages, is whether the lexical status of modals matters for their scopal interaction with tense. In this paper, we included two languages in which modals are (semi-)auxiliaries, and one in which modals are verbs. By including languages like German and Norwegian, for which it has been argued that at least some modals are verbs (Abraham 1999 for German; Eide 2005 for Norwegian), van Dooren’s (2020b) theory can be tested in full.