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    1.5.2.Epistemic modality
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    Modality is used as a cover term for various meanings that can be expressed by modal verbs and adverbs. Barbiers (1995:ch.5), for instance, has argued that example (276a) can have the four modal interpretations in (276b).

    Example 276
    a. Jan moet schaatsen.
      Jan  must  skate
    (i) Dispositional: Jan definitely wants to skate.
    (ii) Directed deontic: Jan has the obligation to skate.
    (iii) Non-directed deontic: It is required that Jan skate.
    (iv) Epistemic: It must be the case that Jan skates.

    The first three interpretations of (276b) can be seen as subcases of event modality and stand in opposition to interpretation (iv), which can be seen as a subcase of propositional modality. The main difference is that event modality expresses the view of the speaker on the moving forces that favor the potential realization of the event referred to by the proposition expressed by the lexical projection of the embedded verb (obligation, volition, ability, etc). Epistemic modality, on the other hand, expresses the view of the speaker on the truth of this proposition (necessity, probability, likelihood, etc). The examples in (277) show that the two groups can readily be distinguished syntactically given that they exhibit different behavior in perfect-tense constructions that refer to eventualities preceding speech time n; dispositional/deontic modal verbs appear as non-finite forms in such constructions, whereas epistemic modal verbs normally appear as finite forms; note that this distinction this does not hold for perfect-tense constructions that refer to future eventualities, which can be four-fold ambiguous. We refer the reader to Section 5.2.3.2, sub III, for a more detailed discussion of the distinction between event and epistemic modality.

    Example 277
    a. Jan heeft gisteren moeten schaatsen.
    event modality
      Jan has  yesterday  must  skate
      'Jan had to skate yesterday.'
    b. Jan moet gisteren hebben geschaatst.
    epistemic modality
      Jan must  yesterday  have  skated
      'It must be the case that Jan has skated yesterday.'

    This section will focus on epistemic modality, subsection I starts with a brief discussion of the epistemic modal verbs moeten'must' and kunnen'can', subsection II argues that the verb zullen behaves in all relevant respects as an epistemic modal verb and that the future reading normally attributed to this verb is due to pragmatics, subsection III supports this conclusion by showing that we find the same pragmatic effects with other verb types.

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    [+]  I.  The epistemic modal verbs moeten'must' and kunnen'may'

    Epistemic modality is concerned with the mental representation of the world of the language user, who may imagine states of affairs different from what they are in the actual world, states of affairs as they will hold in the future, etc. Consider the examples in (278).

    Example 278
    a. Dat huis stort in.
      that house  collapses prt.
      'It is the case that that house collapses.'
    b. Dat huis moet instorten.
      that house  has.to  prt.-collapse
      'It must be the case that that house will collapse.'
    c. Dat huis kan instorten.
      that house  may  prt.-collapse
      'It may be the case that that house will collapse.'

    By uttering sentences like these the speaker provides his estimation on the basis of the information available to him of the likelihood that eventuality k will actually occur. Under the default (non-future) reading of (278a), the speaker witnesses the collapse of the house. In the case of (278b) and (278c) there is no collapse at speech time n, but the speaker asserts something about the likelihood of a future collapse. By uttering (278b) or (278c), the speaker in a sense quantifies over a set of possible, that is, not (yet) actualized worlds: the modal verb moeten'must' functions as a universal quantifier, which is used by the speaker to assert that the eventuality of that house collapsing will take place in all possible worlds; kunnen'may', on the other hand, functions as an existential quantifier, which is used by the speaker to assert that this eventuality will take place in at least one possible world. Note in passing that the future reading triggered by the epistemic modal verbs need not be attributed to the modal verb itself given that example (278a) can also be used with a future reading; see Section 1.5.4 for more discussion of this.
          We will represent the meaning of examples like (278b&c) by means of temporal diagrams of the type in Figure 20, which are essentially the same as the ones introduced in Section 1.5.1 with the addition of possible worlds. Again, n stands for the speech time, i stands for the present of the speaker/hearer, ia for the actualized and i◊ for the non-actualized part of this present. The index k stands for the event denoted by the lexical projection of the embedded main verb and the continuous line below it for the actual running time of k. Index j, finally, represents the present of k, that is, the temporal domain within which k must be located. The possible worlds in Figure 20 may differ with respect to (i) whether eventuality k does or does not occur, as well as (ii) the precise location of eventuality k on the time axis. Possible world representations like Figure 20 are, of course, simplifications in the sense that they select a number of possible worlds that suit our illustrative purposes from an in principle infinite set of possible worlds.

    Figure 20: Epistemic modality and present tense

    Figure 20 is a correct semantic representation of the assertion in example (278c) with existential kunnen given that there is at least one possible world in which the eventuality denoted by the lexical projection of the embedded main verb takes place, but it is an incorrect representation of the assertion in (278b) with universal moeten because the eventuality does not take place in possible worlds 3 and 4.
          The examples in (279) show that epistemic modal verbs can readily occur in the past tense. The additions of the particle/adverbial phrase within parentheses will make these examples sound more natural in isolation, but they are also perfectly acceptable without them in a proper discourse.

    Example 279
    a. Dat huis moest (wel) instorten.
      that house  had. to   prt  prt.-collapse
      'It had to be the case that that house would collapse.'
    b. Dat huis kon (elk moment) instorten.
      that house  might   any moment  prt.-collapse
      'It might have been the case that that house would collapse any moment.'

    Now consider the representation in Figure 21, in which n' stands for the virtual speech-time-in-the past that functions as the point of perspective, and i stands for the relevant past-tense interval. Figure 21 is a correct representation of the assertion in (279b) given that there are possible worlds in which eventuality k takes place, but an incorrect representation of the assertion in (279a) given that there are possible worlds in which eventuality k does not take place. Figure 21 is again a simplification; it selects a number of possible worlds that suit our illustrative purposes from an in principle infinite set of possible worlds. From now on our semantic representations will contain only the minimal selection of possible worlds that is needed to illustrate our point.

    Figure 21: Epistemic modality and past tense

    It should further be noted that examples such as (279) are normally used if speech time n is not included in the past-tense interval. Examples such as (279a) are used if eventuality k did take place before n in order to suggest that the occurrence of k was inevitable. Examples such as (279b), on the other hand, are used especially if eventuality k did not take place in the actual world in order to suggest that certain measures have prevented k from taking place, that we are dealing with a lucky escape, etc. We will return to these restrictions on the usage of the examples in (279) in Section 1.5.2, sub IIC, and confine ourselves here to noting that the epistemic modals differ in this respect from their deontic counterparts, which normally do not carry such implications: the past-tense construction with deontic moeten in (280), for example, may refer both to factual and counterfactual situations.

    Example 280
    Jan moest verleden week dat boek lezen, ...
      Jan had. to  last week  that book  read
    'Jan had the obligation to read that book last week, ...'
    a. ... maar hij heeft het niet gedaan.
    counterfactual
      but  he  has  it  not  done
      '... but he didnʼt do it.'
    b. ... en het is hem met veel moeite gelukt.
    factual
      and  it  is him  with much trouble  succeeded
      '... and he has managed to do it with much trouble.'

          In Figure 20 and Figure 21, the splitting point into possible worlds (from now on: split-off point) starts at n or n'. This is, however, by no means necessary. Suppose the following context. There has been a storm last week and on Sunday the speaker inspected his weekend house and saw that it was seriously damaged. Since it will remain stormy this week the speaker has worries about what will happen to the house and on Tuesday he expresses these by means of the utterance in (281).

    Example 281
    Mijn huis moet deze week instorten.
      my house  has.to  this week  prt.-collapse
    'It must be the case that my house will collapse this week.'

    Given that the speaker does not know whether the house is still standing at n, the utterance refers to the situation depicted in Figure 22, in which the split-off point is situated at the moment that the speaker left the house on Sunday; the present j of eventuality k, which is specified by the adverbial phrase deze week'this week', therefore starts on Monday and ends on Sunday next. In this situation it is immaterial whether eventuality k precedes, overlaps with or follows n.

    Figure 22: Epistemic modality and present tense (revised)

    The fact that k can be located anywhere within time interval j is related to the fact that the speaker has a knowledge gap about his actual world; he simply does not know at n whether the house is still standing, that is, in which possible world he is actually living. In fact, this is made explicit in (282) by the addition of a sentence that explicitly states that the collapse may already have taken place at speech time n.

    Example 282
    Mijn huis moet deze week instorten. Mogelijk is het al gebeurd.
      my house has.to  this week  prt.-collapse  possibly is  it  already  happened
    'It must be the case that my house collapsed or will collapse this week. Possibly it has already happened.'

    The situation is quite different, however, when the knowledge of the speaker is up-to-date. Suppose that the speaker is at the house with someone on Tuesday and that he utters the sentence in (283).

    Example 283
    Dit huis moet deze week instorten.
      this house  has.to  this week  prt.-collapse
    'It must be the case that this house will collapse this week.'

    From this utterance we now will conclude that the house is still standing at speech time n, and infer from this that it is asserted that the collapsing of the house will take place in the non-actualized part of the present-tense interval i◊. This is, however, not a matter of semantics but of pragmatics. The infelicity of utterance (283) in a world in which the speaker already knows that the house has collapsed follows from Grice's (1975) maxim of quantity given that the speaker could describe that situation more accurately by means of the perfect-tense construction in (284), which places the eventuality in the actualized part of the present-tense interval ia; see Section 1.5.4.2.

    Example 284
    Dit huis is deze week ingestort.
      this house  has  this week  prt.-collapsed
    'This house has collapsed this week.'

    The observations concerning (283) and (284) show that the simple present can only be used to refer to an eventuality preceding speech time n if the speaker is underinformed: if he has more specific information about the location of the eventuality, he will use the tense form that most aptly describes that location. As a result, example (282) does not primarily provide temporal information concerning the eventuality of a collapse but information about the necessity of this eventuality.
          We conclude with an observation that is closely related to this. The past-tense counterpart of (281) can also be followed by a sentence that explicitly states that the collapse may already have taken place at speech time n. We assume here the same situation as for (282): the sentence uttered on Tuesday looks back to some virtual speech-time-in-the-past at which it was said that the house would collapse during the time interval referred to by the adverbial phrase deze week'this week', that is, a time interval that includes speech time n. Given that the speaker is underinformed about the actual state of his house, what counts is not the actual eventuality of a collapse but the necessity of this eventuality.

    Example 285
    Mijn huis moest deze week instorten. Mogelijk is het al gebeurd.
      my house had.to  this week  prt.-collapse  possibly  is  it  already  happened
    'It had to be the case that my house will collapse this week. Possibly it has already happened.'

    The observations in (282) and (285) show that the use of an epistemic modal shifts the attention from the actual location of eventuality k within the interval j to epistemic information; the speaker primarily focuses on the necessity, probability, likelihood, etc. of the occurrence of eventuality k within j. Information about the precise location of k is of a secondary nature and dependent on contextual information that determines the split-off point of possible worlds as well as information about the knowledge state of the speaker. Our findings are summarized in (286).

    Example 286
    Temporal interpretation of epistemic modal, simple present/past constructions:
    a. If the split-off point of the possible worlds is located at speech time n, eventuality k cannot be situated in the actualized part ia of the present/past-tense interval because the maxim of quantity would then favor a present/past perfect-tense construction.
    b. If the split-off point of the possible worlds precedes speech time n, the temporal interpretation depends on the knowledge state of the speaker:
    (i) if the speaker is underinformed, that is, not able to immediately observe whether eventuality k has taken place, eventuality k can be situated before speech time n.
    (ii) if the speaker is not underinformed, that is, able to immediately observe whether eventuality k has taken place, eventuality k cannot be situated before speech time n, because the maxim of quantity would then favor a present/past perfect-tense construction.
    [+]  II.  The verb zullen'will': future auxiliary or epistemic modal?

    The binary tense system discussed in Section 1.5.1 takes zullen in examples such as (287a) as a future auxiliary. However, it is also claimed that zullen can be used as an epistemic modal verb in examples such as (287b); cf. Haeseryn et al. (1997:944). On this view there are two verbs zullen, one temporal, and the other modal.

    Example 287
    a. Marie zal dat boek morgen versturen.
    temporal: future
      Marie will  that book  tomorrow  send
      'Marie will send that book tomorrow.'
    b. Marie zal dat boek wel versturen.
    modal: probability
      Marie will  that book  prt  send
      'It is very likely that Marie will send that book.'

    That zullen need not function as a future auxiliary is also clear from the fact that examples with zullen of the type in (288b) behave similar as examples with epistemic moeten/kunnen'must/may' in (288a) in that they refer to an eventuality k that overlaps with speech time n as is clear from the use of the adverb nu'now'.

    Example 288
    a. Het is vier uur. Marie moet/kan nu wel thuis zijn.
      it  is 4.00 p.m.  Marie must/may  now  prt  at.home  be
      'It is 4.00 p.m. Marie must/may be at home now.'
    b. Het is vier uur. Marie zal nu wel thuis zijn.
      it  is 4.00 p.m.  Marie will  now  prt  at.home  now
      'It is 4.00 p.m. Marie will be at home now.'

    The examples in (287) and (288) do not necessarily lead to the conclusion that zullen is homonymous. The fact discussed in Subsection I that epistemic verbs like moeten/kunnen can also be used in examples with a future interpretation in fact suggests that zullen functions as an epistemic modal throughout; see Janssen (1983/1989), and also Erb (2001), who concludes the same thing for German werden'will'. The following subsections will more extensively motivate this conclusion.

    [+]  A.  The verb zullen is not homonymous

    The claim that zullen is homonymous is often motivated by the meaning attributed to sentences such as (287). Example (287a) strongly suggests that the eventuality of Marie sending that book will take place tomorrow, thus giving room to the idea that the information is primarily about the location of the eventuality with respect to speech time n and therefore essentially temporal. The idea is then that (287b) is about whether or not Marie will send that book and the speaker finds it probable that she will; we are dealing with epistemic modality—temporality is not a factor.
          A contrast between a temporal and a probability reading should come out by adding the conjunct ... maar je weet het natuurlijk nooit echt zeker'... but one never knows for sure, of course' as this should lead to an acceptable result with sentences expressing probability only; in sentences expressing future the result should be semantically incoherent given that the added, second clause contradicts the presumed core meaning of the first clause. That this does not come true is shown by the fact that both examples in (289) are fully acceptable.

    Example 289
    a. Marie zal dat boek morgen versturen ... (maar je weet het natuurlijk nooit echt zeker bij haar).
      Marie will  that book  tomorrow  send  but  you  know  it  of.course  never  really  certain  with her
      'Marie will send that book tomorrow (although one never knows for sure with her, of course).'
    b. Marie zal dat boek wel versturen .... (maar je weet het natuurlijk nooit echt zeker bij haar).
      Marie will  that book  prt  send  but  you  know  it  of.course  never  really  certain  with her
      'It is very likely that Marie will send that book (although one never knows for sure with her, of course).'

    Haeseryn et al. (1997:994) note that examples with a probability reading normally include the modal particle wel, which opens the possibility that the probability reading is not part of the meaning of the verb zullen but should be ascribed to the particle. This suggestion is supported by the fact that examples such as (290) receive a probability reading without the help of the verb zullen, and it is also consistent with the fact that Van Dale's dictionary simply classifies wel as a modal adverb that may express a conjecture or doubt.

    Example 290
    Marie stuurt dat boek wel.
      Marie sends  that book  prt
    'It is very likely that Marie will send that book.'

    If wel is indeed responsible for the probability meaning of examples such as (287b), it is no longer clear that the two occurrences of zullen in (287) differ in meaning. That these occurrences may have identical meanings might be further supported by the fact that the two examples in (287) receive similar quantificational force when we add modal adverbs like zeker'certainly' or misschien'maybe', as in (291).

    Example 291
    a. Marie zal dat boek morgen zeker/misschien sturen.
      Marie will  that book  today  certainly/maybe  send
      'It will certainly/maybe be the case that Marie will send that book tomorrow.'
    b. Marie zal dat boek zeker/misschien wel sturen.
      Marie will  that book  certainly/maybe  prt  send
      'It will certainly/maybe be the case that Marie will send that book.'

    The acceptability of (291b) would be surprising if the meaning aspect "probably" of (287b) is due to the meaning of zullen. First, this presumed meaning of zullen is inconsistent with the meaning "certainly" expressed by the adverb zeker, and we would therefore wrongly predict example (291b) to be semantically incoherent with this adverb. Second, this presumed meaning aspect of zullen is very similar to the meaning expressed by the adverb misschien'maybe' and example (291b) would therefore be expected to have the feel of a tautology with this adverb. The fact that this is not borne out again suggests that the probability meaning aspect of (287b) is due to the modal particle wel, which can also be supported by the fact illustrated in (292) that the combinations zeker wel and misschien wel can also be used to express epistemic modality in constructions without zullen. We therefore conclude that the two occurrences of zullen in (287) are semantically more similar than is often assumed, if not identical.

    Example 292
    a. Marie stuurt dat boek zeker wel.
      Marie sends  that book  certainly  prt
      'It is virtually certain that Marie will send the book.'
    a'. Stuurt Marie dat boek? ja, zeker wel.
      sends  Marie  that book  yes  certainly  prt
      'Will Marie send the book? Yes, definitely.'
    b. Marie stuurt dat boek misschien wel.
      Marie sends  that book  maybe  prt
      'It isnʼt excluded that Marie will send the book.'
    b'. Stuurt Marie dat boek? ja, misschien wel.
      sends  Marie  that book  yes  maybe  prt
      'Will Marie send the book? Yes, maybe.'

          That the two occurrences of zullen in (287) are similar is less easy to establish on the basis of their morphosyntactic behavior. At first sight, the primeless sentences in (293) seem to show that, like the epistemic modals moeten and kunnen, both occurrences of zullen appear as the finite verb in the corresponding perfect-tense constructions that refer to eventualities preceding speech time n, whereas the primed examples seem to show that they do not allow the syntactic format normally found with deontic modals; see the discussion of the examples in (277) in the introduction to Section 1.5.2. The problem with this argument, however, is that some readers will reject the idea that the (a)-examples with gisteren'yesterday' involve temporal zullen simply because we are dealing with an eventuality preceding n in that case. We nevertheless include this argument given that it should be valid for readers that follow, e.g., Hornstein's (1990) implementation of Reichenbach's tense system, which in fact predicts that the future perfect can refer to eventualities preceding speech time n.

    Example 293
    a. Marie zal dat boek gisteren hebben verstuurd.
      Marie  will  that book  yesterday  have  sent
      'Marie will have sent that book yesterday.'
    a'. * Marie heeft dat boek gisteren zullen versturen.
      Marie has  that book  yesterday  will  sent
    b. Marie zal het boek gisteren wel verstuurd hebben.
      Marie  will  the book  yesterday  probably  sent  have
      'Marie will probably have sent the book yesterday.'
    b'. * Marie heeft het boek gisteren wel zullen versturen.
      Marie has  the book  yesterday  probably  will  send

    We will not, however, press this argument any further and conclude this subsection by observing that the past-tense counterpart of example (293a') seems fully acceptable. However, examples such as (294) are irrealis constructions of a special type, in which hebben does not seem to function as a perfect auxiliary.

    Example 294
    Marie had dat boek gisteren zullen versturen (maar ze had geen tijd).
      Marie had that book  yesterday  will  sent   but  she had no time
    'Marie would have sent that book yesterday (but she couldnʼt find the time).'
    [+]  B.  The verb zullen is not a future auxiliary

    If the two occurrences of zullen in (287) are not homonymous but representatives of a single category, we will have to establish whether we are dealing with a future auxiliary or with an epistemic modal. If zullen is a future auxiliary, we would expect the use of its present-tense forms to have the effect of locating eventuality k in non-actualized part i◊ of the present-tense interval, as indicated in Figure 23, where we assume n to be the split-off point for the possible worlds; note that we have seen earlier that zullen does not imply that eventuality k takes place in all possible worlds, but we ignore this for the moment for simplicity.

    Figure 23: Future reading of zullen'will'

    If zullen is an epistemic modal, on the other hand, we would expect that its present-tense forms are also possible if the split-off point precedes n and eventuality k is located in the actualized part ia of the present-tense interval, as in . Since the examples in (288) in the introduction to this subsection have already shown that in certain examples with zullen eventuality k may overlap with speech time n, the discussion below will focus on whether k may also precede n.

    Figure 24: Epistemic reading of zullen'will'

    The representation in Figure 24 is essentially the one that we gave in Figure 22 for example (282) with epistemic moeten'must'; the main difference involves the fact not indicated here that whereas moeten is truly a universal quantifier, the use of zullen does not imply that the speaker asserts that eventuality k will take place in all possible worlds. This means that we can easily test whether zullen can be used epistemically by considering the result of replacing moeten in (282) by zullen, as in (295).

    Example 295
    Mijn huis zal deze week instorten. Mogelijk is het al gebeurd.
      my house  will  this week  prt.-collapse  possibly is  it  already  happened
    'My house will collapse this week. Possibly it has already happened.'

    Now, assume the same context as for (282): there has been a storm last week and on Sunday the speaker inspected his weekend house and saw that it was seriously damaged. Since it has remained stormy, the speaker has worries about the house and on Tuesday he expresses these worries by means of uttering sentence (295). In this context, this sentence would be considered true if the house had already collapsed on Monday, as in world 1 of Figure 24, and we can therefore conclude that zullen indeed exhibits the semantic hallmark of epistemic modals.
          As in the case of moeten and kunnen, the unambiguous future readings in Figure 23 should be seen as the result of pragmatics. This will become clear when we replace the modal moeten in example (283) by zullen, as in (296a). The proximate demonstrative dit in dit huis'this house' suggests that the speaker is able to evaluate the actual state of the house at speech time n. It now follows from Grice's (1975) maxim of quantity that (296a) can only be used if the house is still standing: if the house is already in ruins at n, the speaker could, and therefore would have expressed this more accurately by using the perfect-tense construction in (296b).

    Example 296
    a. Dit huis zal deze week instorten.
      this house  will  this week  prt.-collapse
      'This house will collapse this week.'
    b. Dit huis is deze week ingestort.
      this house  has  this week  prt.-collapse
      'This house has collapsed this week.'

    In the situation just described, a simple present sentence such as (297) would also receives a future interpretation for the same pragmatic reason; if the house is already in ruins at n, the speaker again could have expressed this more accurately by the perfect-tense construction in (296b). This shows that the future reading of (296c) is independent of the use of the verb zullen.

    Example 297
    Dit huis stort deze week in.
      this house  collapses  this week  prt.
    'This house will collapse this week.'

          Note, finally, that the speaker who uttered sentence (295) could also have used the sentence in (298) given that the two examples express virtually identical meanings; compare the discussion of moeten in sentences like (282) and (285).

    Example 298
    Mijn huis zou deze week instorten. Mogelijk is het al gebeurd.
      my house would  this week  prt.-collapse  maybe  is  it  already  happened
    'My house would collapse this week. Maybe it has already happened.'

    The possibility that the house still stands at speech time n is not only left open in (295), but also in (298). This is due to the fact that speech time n can be included in past-tense interval i; see the definition of +past in Section 1.5.1, sub C, example (249b). The two examples differ, however, in the perspective from which the information about eventuality k is presented. In (295) the information is presented from the perspective of the actual speech time n of the speaker/hearer, as is clear from the fact that it can be followed by the present-tense clause … zo is mij verteld'so I am told'. In (298), on the other hand, the information is presented from the perspective of the virtual speech-time-in-the pastn', as is clear from the fact that it can only be followed by a past-tense clause: … zo werd mij verteld'so I was told'. This suggests that the choice between present and past tense is determined by the wish to speak about eventuality k on the basis of information available within, respectively, a specific present-tense interval i or a specific past-tense interval i.
          That eventuality k can precede speech time n can also be illustrated by means of non-telic predicates; see Janssen (1983). An example such as (299) is three ways ambiguous when it comes to the location of eventuality k. First, if the speaker and hearer know that Jan has already departed, the speaker can use (299) to express his expectation that Jan has already travelled for three hours at the moment of speech ( k < n). Second, if the speaker and hearer know that Jan has departed one hour earlier, the speaker can use (299) to express his expectation that Jan will arrive in two hours ( n is included in k). Third, if the speaker and hearer know that Jan has not yet departed, (299) can be used to express the speaker's expectation that Jan will undertake a future journey that lasts three hours ( n < k).

    Example 299
    Jan zal in totaal drie uur onderweg zijn.
      Jan will  in total  three hours  on.the.road  be
    'Jan will be on the road for three hours.'

    Note, however, that the three readings of (299) differ in their implications for the duration of Jan's travel. The first reading ( k < n) can be used if the speaker knows the complete journey will take longer than three hours, whereas under the second and third reading the speaker expresses that the journey will take three hours. We assume that this is a side effect of the fact that the first reading implies some evaluation time that is identical to speech time, which could be made explicit by means of the adverb nu'now'. When we overrule this default evaluation time by adding an adverbial phrase like morgenmiddag om drie uur'at 3:00 p.m. tomorrow', the future reading ( k < n) of this example will also allow the reading that the journey will take longer than three hours. If we put this side effect aside, we can conclude that the three way ambiguity of (299) with respect to the location of k shows that examples with zullen can have the temporal representation in Figure 24, and, hence, that zullen is not a future auxiliary.
          This subsection has shown that the interpretation of simple present/past-tense constructions with the verb zullen proceeds in a way similar to the interpretation of simple present/past constructions with the epistemic modals moeten'must' and kunnen'may'. This means especially that in both cases inferences about the precise location of eventuality k (that is, whether it is situated before or after speech time n) are made along the lines sketched in (286) in Subsection I. We take this to be a conclusive argument for assuming that zullen is not a future auxiliary; see Janssen (1983) for a similar line of reasoning.

    [+]  C.  The meaning contribution of zullen

    Now that we have established that zullen is not a future auxiliary, we can conclude that it is an epistemic modal verb. This subsection tries to establish more precisely what its meaning contribution is.

    [+]  1.  No quantificational force

    It seems that zullen'will' differs from epistemic modal verbs like moeten'must' and kunnen'may' in that it does not have any inherent quantificational force. This will be clear from the examples in (300), in which the quantificational force must be attributed to the modal adverbs: zeker'certainly' expresses universal quantification over possible worlds, mogelijk/misschien'possibly' expresses a low degree of probability, and waarschijnlijk'probably' expresses a high degree of probability.

    Example 300
    a. Dit huis zal deze week zeker instorten.
    universal
      this house  will  this week  certainly  prt.-collapse
      'This house will certainly collapse this week.'
    b. Dit huis zal deze week mogelijk/misschien instorten.
    low degree
      this house  will  this week  possibly/maybe prt.-collapse
      'Possibly/Maybe, this house will collapse this week.'
    c. Dit huis zal deze week waarschijnlijk instorten.
    high degree
      this house  will  this week  probably prt.-collapse
      'This house will probably collapse this week.'

    If zullen were inherently quantificational, we would expect the examples in (300) to be degraded or at least to give rise to special effects (which is indeed the case in various degrees when we replace zullen by moeten or kunnen). For example, if zullen were to inherently express universal quantification, the modal adverb zeker in (300a) would be tautologous and the adverbs mogelijk and waarschijnlijk in (300b&c) would be contradictory. And if zullen were to inherently express existential quantification, mogelijk and waarschijnlijk in (300b&c) would be tautologous. Nevertheless, it should be noted that examples like (295) and (296a), which do not contain any element with quantificational force, are normally used if the speaker has strong reason for believing that eventuality k will occur in all possible worlds; high degree quantification therefore seems to be the default reading of sentences with zullen.

    [+]  2.  Subjective assessment

    In order to describe the meaning contribution of zullen'will', we have to discuss a meaning aspect of epistemic modality that has only been mentioned in passing. Epistemic modality stands in opposition to what is known as metaphysical modality, in which objective truth is the central notion and which is part of a very long philosophical tradition concerned with the reliability of scientific knowledge. Epistemic modality, on the other hand, concerns the degree of certainty assigned to the truth of a proposition by an individual on the basis of his knowledge state (note in this connection that the notion epistemic is derived from Greek episteme'knowledge'). Epistemic modal verbs like moeten'must' and kunnen'can', for example, do not express a degree of probability that is objectively given, but one that results from the assessment of the situation by some individual on the basis of the knowledge available to him. The difference between a declarative clause without a modal verb such as (301a) and a declarative clause with a modal verb such as (301b) is thus that in the former case the proposition that Marie is at home is merely asserted "without indicating the reasons for that assertion or the speaker's commitment to it" (Palmer 2001:64), whereas in the latter the modal verb indicates "that a judgment has been made or that there is evidence for the proposition" (Palmer 2001:68).

    Example 301
    a. Marie is nu thuis.
      Marie is now  at.home
      'Marie is at home now.'
    b. Marie moet/kan nu thuis zijn.
      Marie must/may  now  at.home  be
      'Marie must/may be at home now.'

          In his Kritik der reinen Vernunft(1781) Immanuel Kant already distinguished three types of epistemic modality, which he called problematical, apodeictical and assertorical modality. Palmer (2001) makes essentially the same distinctions in Section 2.1; he refers to the three types as speculative, deductive and assumptive modality. Illustrations are given in (302).

    Example 302
    a. Marie kan nu thuis zijn.
    problematic/speculative
      Marie may  now  at.home  be
    b. Marie moet nu thuis zijn.
    apodeictical/deductive
      Marie must  now  at.home  be
    c. Marie zal nu thuis zijn.
    assertorical/assumptive
      Marie will  now  at.home  be

    By uttering examples such as (302), the speaker provides three different epistemic judgments about (his commitment to the truth of) the proposition Marie is at home. The use of kunnen'may' in (302a) presents the proposition as a possible conclusion: the speaker is uncertain whether the proposition is true, but on the basis of the information available to him he is not able to exclude it. The use of moeten'must' in (302b) presents the proposition as the only possible conclusion: on the basis of information available the speaker concludes that it is true. The use of zullen'will' in (302c), finally, presents the proposition as a reasonable but uncertain conclusion on the basis of the available evidence; see also Droste (1958:311) and Janssen (1983/1989). Palmer (2001) further suggests that the evidence involved may include experience and generally accepted knowledge as in Het is vier uur; Marie kan/moet/zal nu thuis zijn'It is 4.00 p.m.; Marie may/must/will be at home now'. Note that contrary to what Palmer (2001: section 2.1.2) suggests, we believe that (at least in Dutch) this holds not only for assumptive but for all types of epistemic modality.
          The claim that epistemic modality involves some subjective assessment is completely compatible with our earlier claim that epistemic modality introduces a set of possible worlds. The term possible world in fact only makes sense if such a world is accessible, that is, if one can, in principle, enter it from the one that counts as the point of departure. Thus, the creation of a point of perspective is—however metaphorically expressed—an essential ingredient of the notion of possible world; "Suppose now that someone living in w1 is asked whether a specific proposition, p, is possible (whether pmight be true). He will regard this as the question as to whether in some conceivable world (conceivable, that is, from the point of view of his world, w1), p would be true …" (Hughes & Cresswell 1968:77).
          That we are dealing with subjective assessments is clear from the fact that examples such as (303a) are definitely weird; the modals moeten and kunnen express that the suggested probability of the sun rising is just the result of an assessment by the speaker, who thereby suggests that the alternative view of the sun not rising tomorrow might in principle also be viable. Example (303b) shows that the modal zullen likewise gives rise to a weird result; examples like these are only possible if stating the obvious has some rhetoric function as in Maak je niet druk, de zon zal morgen ook wel opkomen'Donʼt get upset, the sun will rise tomorrow just the same'. Janssen (1983) suggests that the markedness of the examples in (303) follows from Grice's maxim of quantity; the expression of doubt makes the utterances more informative than is required.

    Example 303
    a. $ De zon moet/kan morgen op komen.
      the sun  has.to/may  tomorrow  up  come
      'The sun must/may rise tomorrow.'
    b. $ De zon zal morgen op komen.
      the sun  will  tomorrow  up  come
      'The sun will rise tomorrow.'

    That epistemic modals imply an assessment by some individual may also be supported by the fact that examples like (304a&b) are completely acceptable if uttered by an amateur astronomer who has calculated for the first time in his life the time of the rising of the sun on a specific day; in these cases the possibility that the sun rises at some other time than indicated is indeed viable, as the speaker may have made some miscalculation. The expression of doubt in these examples is thus in accordance with the maxim of quantity.

    Example 304
    a. De zon moet morgen om 6.13 op komen.
      the sun  has.to  tomorrow  at 6:13  up  come
      'The sun must rise at 6:13 a.m. tomorrow.'
    b. De zon zal morgen om 6:13 op komen.
      the sun  will  tomorrow  at 6.13  up  come
      'The sun will rise at 6:13 a.m. tomorrow.'

    That subjective assessment is an essential part of the meaning of epistemic modal verbs is perhaps clearer in English than in Dutch given that epistemic clauses require that a modal verb be used in the English, but not the Dutch, simple present. This difference can be formulated as in (305): English obeys the material implication in (305a), from which we can derive (305a') by modus tollens (the valid argumentation form in propositional logic according to which we may conclude from P → Q and ¬Q that ¬P); Dutch, on the other hand, has the material implication in (305b), from which we cannot derive the statement in (305b') as that would be a formal fallacy.

    Example 305
    Distribution of epistemic modals in the present tense
    a. English: subjective assessment → modal present
    a'. no modal present → no subjective assessment
    valid inference
    b. Dutch: modal present → subjective assessment
    b'. no modal present → no subjective assessment
    invalid inference

    From this difference it follows that the Dutch simple present can be used in a wider range of "future" constructions than the English simple present. Comrie (1985:118) has claimed that the English simple present construction can only be used to refer to future states of affairs if we are dealing with what he calls scheduled events (such as the rising of the sun, the departure of a train, etc.). Under the reasonable assumption that scheduled events do not involve a subjective assessment, this is correctly predicted by the valid inference in (305a').

    Example 306
    a. * Jan leaves tomorrow.
    b. The train leaves at 8.25 a.m.

    The invalidity of the inference in (305b'), on the other hand, expresses that Dutch is not restricted in the same way as English, but can freely use clauses in the simple present to refer to any future event; see Section 1.5.4 for further discussion.

    Example 307
    a. Jan vertrekt morgen.
      Jan  leaves  tomorrow
      'Jan will leave tomorrow.'
    b. De trein vertrekt om 8.25 uur.
      the train  leaves  om 8.25 hour
      'The train leaves at 8.25 a.m.'

          Although the presence of an epistemic modal is not forced in contexts of subjective assessment in Dutch, the discussion above has shown that subjective assessment is an inherent part of the meaning of epistemic modals. Note that the person whose assessment is given can be made explicit by means of an adverbial PP. In accordance with the generalizations in (305) such PPs normally require an epistemic modal verb to be present in English present-tense constructions (Carole Boster, p.c.), whereas in Dutch they can also be used without such a modal.

    Example 308
    a. Volgens Jan komt de zon morgen om 6.13 uur op.
      according.to Jan  comes  the sun  tomorrow  at 6.13 hour  up
      'According to Jan the sun will rise at 6.13 a.m. tomorrow.'
    a'. *? According to John the sun rises at 6.13 a.m. tomorrow.
    b. Volgens Jan zal