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1.5.1.Tense
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This section discusses the binary tense system originally proposed by Te Winkel (1866) and briefly outlined above, which is based on three binary oppositions: present versus past, imperfect versus perfect, and non-future versus future. Te Winkel was not so much concerned with the properties ascribed to time in physics or in philosophy, which heavily influenced the currently dominant view that follows Reichenbach's (1947) seminal work, which is based on two ternary oppositions: (i) past—present—future and (ii) anterior-simultaneous-posterior. Instead, Te Winkel had a (surprisingly modern) mentalistic view on the study of language, and was mainly interested in the properties of time as encoded in the tense systems found in natural language. Verkuyl (2008:ch.1) compared the two systems and argued that Te Winkel's system is more successful in describing the universal properties of tense than the Reichenbachian systems for reasons that we will review after we have discussed the details of Te Winkel/Verkuyl's binary approach.

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[+]  I.  Binary tense theory: time from a linguistic perspective

Verkuyl (2008) refers to Te Winkel's (1866) proposal as the binary tense system, given that the crucial distinctions proposed by Te Winkel can be expressed by means of the three binary features in (229).

229
a. ±past: present versus past
b. ±posterior: future versus non-future
c. ±perfect: imperfect versus perfect

The three binary features in (229) define eight different tenses, which are illustrated in Table 9 by means of examples in the first person singular form.

Table 9: The Dutch tense system according to Verkuyl (2008)
  present past
synchronous imperfect simple present
Ik wandel.
I walk
simple past
Ik wandelde.
I walked
  perfect present perfect
Ik heb gewandeld.
I have walked
past perfect
Ik had gewandeld.
I had walked
posterior imperfect future
Ik zal wandelen.
I will walk
future in the past
Ik zou wandelen.
I would walk
  perfect future perfect
Ik zal hebben gewandeld.
I will have walked
future perfect in the past
Ik zou hebben gewandeld.
I would have walked

The features in (229) are in need of some further explication, which will be given in the following subsections. For clarity of presentation, we will focus on the temporal interpretations cross-linguistically attributed to the tenses in Table 9 and postpone discussion of the more special temporal and the non-temporal aspects of their interpretations in Dutch to, respectively, Section 1.5.2 and Section 1.5.4.

[+]  A.  The present-tense interval

Binary Tense theory crucially differs from the Reichenbachian approaches in that it does not identify the notion of present with the notion of speech time. Keeping the notions of speech time and present strictly apart turns out to offer important advantages. For example, it allows us to treat tense as part of a developing discourse: shifting of the speech time does not necessarily lead to shifting of the present. In a binary system, the present tense can be seen as not referring to the speech time n but to some larger temporal domain i that includesn. The basic idea is that the use of the present-tense form signals that the speaker is speaking about eventualities as occurring in his or her present even though these eventualities need not occur at the point of speech itself. This can be illustrated by the fact that a speaker could utter an example such as (230a) on Tuesday to express that he is dedicating the whole week (that is, the stretch of time from Monday till Sunday) to writing the section on the tense system mentioned in (230a). It is also evident from the fact that this example can be followed in discourse by the utterances in (230b-d), which subdivide the present-tense interval evoked by the adverbial phrase deze week'this week' in (230a) into smaller subparts.

230
a. Ik werk deze week aan de paragraaf over het tempussysteem.
present
  work  this week  on the section  about the tense system
  'This week, Iʼm working on the section on the tense system.'
b. Gisteren heb ik de algemene opbouw vastgesteld.
present perfect
  yesterday  have  the overall organization  prt.-determined
  'Yesterday, I determined the overall organization.'
c. Vandaag schrijf ik de inleiding.
simple present
  today  write  the introduction
  'Today, Iʼm writing the introduction.'
d. Daarna zal ik de acht temporele vormen beschrijven.
future
  after.that  will  the eight tense forms  describe
  'After that, I will describe the eight tense forms.'
e. Ik zal het zaterdag wel voltooid hebben.
future perfect
  will  it  Saturday  prt.  completed  have
  'I probably will have finished it on Saturday.'

The sequence of utterances in (230) thus shows that what counts as the present for the speaker/hearer constitutes a temporal domain that consists of several subdomains, each of them denoted by a temporal adverbial phrase that locates the four eventualities expressed by (230b-e) more precisely within the interval denoted by deze week'this week' in (230a). Following Verkuyl (2008) the global structure of a present domain is depicted in Figure 6, in which the dotted line represents the time line, n stands for the speech time, and i for the time interval that is construed as the present for the speaker/hearer. The role of the rightward shifting speech time n is to split the present-tense intervali into an actualized part ia (the present preceding n) and a non-actualized part i (the present following n).

Figure 6: The present-tense interval i

It is important to realize that present-tense interval i is contextually determined. In the discourse chunk in (230), it may seem as if the present i is defined by the adverbial phrase deze week'this week', but (231) shows that the present-tense interval can readily be stretched by embedding (230a) in a larger story in the present tense.

231
We werken nu al jaren aan een grammatica van het Nederlands. De eerste delen zijn al afgerond en we beginnen nu aan het deel over het werkwoord. Deze week werk ik aan de paragraaf over het temporele systeem. [continue as in (230b-d)]We werken nu al jaren aan een grammatica van het Nederlands. De eerste delen zijn al afgerond en we beginnen nu aan het deel over het werkwoord. Deze week werk ik aan de paragraaf over het temporele systeem. [continue as in (230b-d)]
'We have been working for years on a grammar of Dutch. The first volumes are already finished and we are beginning now with the part on verbs. This week I am working on the section on the tense system. [....]'

Example (232) in fact shows that we can stretch the present-tense interval i indefinitely, given that this sentence involves an eternal or perhaps even everlasting present.

232
Sinds de oerknal breidt het heelal zich in alle richtingen uit en waarschijnlijk zal dat voortduren tot het einde der tijden.
  since the Big Bang  expands  the universe  refl  in all directions  prt.  and probably  will  that  continue  until the end thegen times
'Since the Big Bang the universe is expanding in all directions and probably that will continue until the end of time.'

Ultimately, it is the shared extra-linguistic knowledge of the speaker and the hearer that determines what counts as the present-tense interval, and, consequently, which eventualities can be discussed by using present-tense forms. This was already pointed out by Janssen (1983) by means of examples such as (233); the extent of the presumed present-tense interval is determined (i) by the difference between the lifespan of, respectively, planets and human individuals, and (ii) by the fact that "being a stutterer" and "being ill" are normally construed as, respectively, an individual-level and a stage-level predicate.

233
a. De aarde is rond.
  the earth is round
b. Jan is een stotteraar.
  Jan is a stutterer
c. Jan is ziek.
  Jan is ill

      Following Verkuyl (2008), we can define Te Winkel's binary oppositions by means of the indices i and n, which were introduced previously, and the indices j and k, which pertain to the temporal location of the eventuality (state of affairs) denoted by the main verb, or, rather, the lexical projection of this verb. We have already mentioned that the defining property of the present domain is that it includes speech time n, which is expressed in (234a) by means of the connector "○". Verkuyl assumes that the present differs from the past in that past-tense interval i precedes speech time n, as indicated in (234b); we will see in Subsection C, however, that there are reasons not to follow this assumption.

234
The feature ±past (to be revised)
a. Present: i ○ n
i includes speech time n
b. Past: i < n
i precedes speech time n

The index j will be taken as the temporal domain in which eventuality k is located. In other words, every eventuality k has not only its running time, but it has also its own present j, which may vary depending on the way we talk about it. In the examples in (230), for instance, the location of the present j of k is indicated by means of adverbial phrases; in example (230d), for instance, the adverbial phrase daarna restricts j to the time interval following Tuesday, and the semantic representation of (230d) is therefore as schematically indicated in Figure 7, in which the line below k indicates the actual running time of the eventuality.

Figure 7: Eventuality k and its present j

It is important to note that, due to the use of the present-tense form in (230d), the notion of future is to be reduced to the relation of posteriority within the present domain. The difference between non-future and future is that in the former case the present j of eventuality k can synchronize with any subpart of i, whereas in the latter case it cannot synchronize with any subpart of the actualized part of the present, that is, it must be situated in the non-actualized part i of what counts as the present for the speaker/hearer. This is expressed in (235) by means of the connectors "≈" and "<".

235
The feature ±posterior
a. Non-future: i ≈ j
i and j synchronize
b. Future: ia < j
ia precedes j

The difference between imperfect and perfect tense pertains to the relation between eventuality k and its present j. In the latter case k is presented as completed within j, whereas in the former case it is left indeterminate whether or not k is completed within j. Or, to say it somewhat differently, the perfect presents k as a discrete, bounded unit, whereas the imperfect does not. This is expressed in (236) by means of the connectors "≼" and "≺".

236
The feature ±perfect
a. imperfect: k ≼ j
k need not be completed within j
b. Perfect: k ≺ j
k is completed within j

[+]  B.  The four present tenses defined by Binary Tense Theory

The following subsections will show that the four present tenses in Table 9 in the introduction to this subsection differ with respect to (i) the location of eventuality k denoted by the lexical projection of the main verb within present-tense interval i, and (ii) whether or not it is presented as completed within its own present-tense interval j. Recall that we will focus on the temporal interpretations cross-linguistically attributed to the tenses in Table 9 and postpone the discussion of the more special temporal and the non-temporal aspects of their interpretations in Dutch to Section 1.5.4.

[+]  1.  Simple present

The simple present expresses that eventuality k takes place during present-tense interval i. This can be represented by means of Figure 8, in which index j is taken to be synchronous to the present i of the speaker/hearer ( j = i) by default. The continuous part of the line below k indicates that the preferred reading of an example such as Ik wandel'I am walking' is that eventuality k overlaps with the moment of speech n.

Figure 8: Simple present ( Ik wandel'I am walking')

In many languages, including Dutch, the implication that k holds at the moment of speech n can readily be canceled by means of, e.g., adverbial modification: the simple present example (237) with the adverbial phrase morgen'tomorrow' can be used to refer to some future eventuality k.

237
Ik wandel morgen.
  walk  tomorrow
'Iʼll walk tomorrow.'

This is, of course, to be expected on the basis of the definition of present in (234a), which states that the present-tense interval i must include speech time n, but does not impose any restrictions on j or k. Although we will briefly return to this issue in Subsection 5, we will postpone a more thorough discussion of this to Section 1.5.4, where we will show that this use of the simple present is a characteristic property of languages that do not express the future within the verbal tense system but by other means, such as adverbials.

[+]  2.  Present perfect

The default reading of the present perfect is that eventuality k takes place before speech time n, that is, eventuality k is located in the actualized part of the present-tense interval ia ( j = ia). In addition, the present perfect presents eventuality k as a discrete, bounded unit that is completed within time interval j that therefore cannot be continued after n; this is represented in Figure 9 by means of the short vertical line after the continuous line below k.

Figure 9: Present perfect ( Ik heb gewandeld'I have walked')

A sentence like Ik heb gisteren gewandeld'I walked yesterday' can now be fully understood: since neither the definition of present in (234a) nor the definition of perfect in (236b) imposes any restriction on the location of j (or k) with respect to n, the adverb gisteren'yesterday' may be analyzed as an identifier of jon the assumption that yesterday is part of a larger present-tense interval i that includes speech time n. This explains the possibility of using the present-tense form heeft'has' together with an adverbial phrase referring to a time interval preceding n.
      In many languages, including Dutch, the implication that k takes place before speech time n can readily be canceled by means of, e.g., adverbial modification: the present perfect example (238) with the adverb morgen'tomorrow' can be used to refer to some future eventuality k. Again, this is to be expected given that neither the definition of present in (234a) nor the definition of perfect in (236b) imposes any restriction on the location of j (or k) with respect to n; we will return to this issue in Section 1.5.4.

238
Ik heb je paper morgen zeker gelezen.
  have  your paper  tomorrow  certainly  read
'Iʼll certainly have read your paper by tomorrow.'

      In the literature there is extensive discussion about whether perfect-tense constructions should be considered temporal or aspectual in nature. The position that individual linguists take often depends on the specific tense and aspectual theory they endorse. Since the characterization of the perfect tense in the binary (and the Reichenbachian) tense theory does not appeal to the internal temporal structure of the event, this allows us to adopt a non-aspectual view of the perfect tense. The non-aspectual view may also be supported by the fact that the use of the perfect tense does not affect the way in which the internal structuring of eventuality k is presented; it is rather the interaction of perfect tense and Aktionsart (inner aspect) that should be held responsible for that. This will become clear when we consider the contrast between the atelic (states and activities) and telic (accomplishments and achievements) eventualities in (239). We refer the reader to Section 1.2.3 for a discussion of the different kinds of Aktionsart.

239
a. Jan heeft zijn hele leven van Marie gehouden.
state
  Jan has  always  of Marie  loved
  'Jan has loved Marie always.'
b. Jan heeft vanmorgen aan zijn dissertatie gewerkt.
activity
  Jan has  this.morning  on his dissertation  worked
  'Jan has worked on his PhD thesis all morning.'
c. Jan is vanmorgen uit Amsterdam vertrokken.
achievement
  Jan is  this.morning  from Amsterdam  left
  'Jan left Amsterdam this morning.'
d. Jan heeft de brief vanmorgen geschreven.
accomplishment
  Jan has  the letter  this.morning  written
  'Jan wrote the letter this morning.'

All examples in (239) present the eventualities as autonomous units that (under the default reading) are completed at or before speech time n. This does not imply, however, that eventualities cannot be continued or resumed after n. This is in fact quite natural in the case of atelic verbs: an example such as (239a) does not entail that Jan will not love Marie after speech time n as is clear from the fact that it can readily be followed by ... en hij zal dat wel altijd blijven doen'and he will probably continue to do so forever'. Likewise, example (239b) does not imply that Jan will not continue his work on his thesis after speech time n as is clear from the fact that (239b) can readily be followed by ... en hij zal daar vanmiddag mee doorgaan'... and he will continue doing that in the afternoon'. The telic events in (239c&d), on the other hand, do imply that the events have reached their implied endpoint and can therefore not be continued after speech time n. The examples in (239) thus show that the internal temporal structure of the eventualities is not affected by the perfect tense but determined by the Aktionsart of the verbs/verbal projections in question. From this we conclude that the perfect is not aspectual in nature but part of the tense system; see Verkuyl (2008:20-27) for a more detailed discussion.

[+]  3.  Future

The future expresses that eventuality k takes place after speech time n, that is, eventuality k is located in the non-actualized part of the present-tense interval ( j = i).

Figure 10: Future ( Ik zal wandelen'I will walk')

The implication of Figure 10 is that eventuality k cannot take place during ia, but example (240) shows that this implication can be readily cancelled in languages like Dutch. In fact, this will be one of the reasons for denying that willen functions as a future auxiliary in Dutch. We will return to this in Sections 1.5.2 and 1.5.4.

240
Jan zal je paper lezen. Misschien heeft hij het al gedaan.
  Jan will  your paper  read  maybe  has  he  it  already  done
'Jan will read your paper. Maybe he has already done it. '
[+]  4.  Future perfect

The interpretation of the future perfect is similar to that of the future, but differs in two ways: (i) it is not necessary that the eventuality k has started after n and (ii) it is implied that the state of affairs is completed before the time span ihas come to an end.

Figure 11: Future perfect (Ik zal hebben gewandeld 'I will have walked')

The implication of Figure 11 is again that eventuality k cannot take place during ia, but example (241) shows that this implication can be readily cancelled in languages like Dutch by means of, e.g., adverbial modification. We will put this non-future reading aside for the moment but return to it in Sections 1.5.2 and 1.5.4.

241
Jan zal je paper ondertussen waarschijnlijk wel gelezen hebben.
  Jan will  your paper  by.now  probably  prt  read  have
'Jan will probably have read your paper by now.'

      The main difference between the future and the future perfect is that in the former the focus is on the progression of the eventuality (without taking into account its completion), whereas in the latter the focus is on the completion of the eventuality k in j. This difference is often somewhat subtle in the case of states and activities but transparent in the case of telic events. Whereas the future tense in example (242a) expresses that the process of melting will start or take place after speech time n, the future perfect example in (242b) simply expresses that the completion of the melting process will take place in some j that is positioned in i; the future perfect leaves entirely open whether the melting process started before, after or at n.

242
a. Het ijs zal vanavond smelten.
  the ice  will  tonight  melt
  'The ice will melt tonight.'
b. Het ijs zal vanavond gesmolten zijn.
  the ice  will  tonight  melted  be
  'The ice will have melted tonight.'

In (243), similar examples are given with the accomplishment die brief schrijven: (243a) places the entire eventuality after the time n, whereas (243b) does not seem to make any claim about the starting point of the eventuality but simply expresses that the eventuality will be completed after n (but within i).

243
a. Jan zal vanavond die brief schrijven.
  Jan will  tonight  that letter  write
  'Jan will write that letter tonight.'
b. Jan zal vanavond die brief geschreven hebben.
  Jan will  tonight  that letter  written  have
  'Jan will have written that letter by tonight.'

For the moment, we will ignore the difference between future and future perfect with respect to the starting point of the state of affairs, but we will return to this in Section 1.5.2, where we will challenge the claim that zullen is a future auxiliary.

[+]  5.  The need to distinguish i and j

In the tense representations given in the previous subsections, we made a distinction between the present i of the speaker/hearer, on the one hand, and the present j of eventuality k, on the other. Although the latter is always included in the former, it can readily be shown that the distinction need be made. This may not be so clear in examples such as (244a), in which j seems to synchronize with the entire present-tense interval i of the speaker/hearer. Adverbial phrases of time, however, may cause j to synchronize to a subpart of i: the adverb vandaag'today' in (244b) refers to a subpart of i that includes n, and morgen'tomorrow' in (244c) refers to a subpart of i situated ini.

244
a. We zijn thuis.
  we  are  at.home
  'We are at home.'
b. We zijn vandaag thuis.
  we  are  today  at.home
c. We zijn morgen thuis.
  we  are  tomorrow  at.home

That it is j and not the present-tense interval i that is affected by adverbial modification is also clear from the fact that it is possible to have present-tense examples such as (245), in which the two adverbial phrases refer to two subdomains within i.

245
We zijn vandaag thuis en morgen in Utrecht.
  we  are  today  at.home  and tomorrow  in Utrecht

Entailments are furthermore computed on the basis of j and not the present-tense interval i. Example (244b), in which j synchronizes with a subpart of i that includes n, does not say anything about the whereabouts of the speaker yesterday or tomorrow, even when these time intervals are construed as part of present-tense interval i. That entailments are computed on the basis of j and not i is even clearer in example (244c), in which j synchronizes with (a subpart of) i; this example does not say anything about the whereabouts of the speaker at speech time n, which clearly shows that the state of affairs does not have to hold during the complete present-tense interval i. It is only in cases such as (244a), without a temporal modifier, that we conclude (by default) that the state of affairs holds for the complete present-tense interval i.

[+]  C.  The past-tense interval

The examples in (246) show that, like the present tense, the past tense involves some larger time interval, which can be divided into smaller subdomains. A speaker can utter an example such as (246a) to report on Els' activities during the past-tense interval evoked by the adverbial phrase vorige week'last week'. This utterance can be followed in discourse by the utterances in (246b-d), which subdivide this past-tense interval into smaller subparts in a fashion completely parallel to the way in which the present-tense examples in (230b-d) subdivide the present-tense interval evoked by the adverbial phrase deze week'this week' in (230a).

246
a. Els werkte vorige week aan de paragraaf over het temporele systeem.
past
  Els worked  last week  on the section  about the tense system
  'Last week, Els was working on the section on the tense system.'
b. Op maandag had ze de algemene opbouw vastgesteld.
past perfect
  on Monday  had  she  the overall organization  prt.-determined
  'On Monday, she had determined the overall organization.'
c. Op dinsdag schreef ze de inleiding.
simple past
  on Tuesday  wrote  she  the introduction
  'On Tuesday, she wrote the introduction.'
d. Daarna zou ze de acht temporele vormen beschrijven.
future in past
  after.that  would  she  the eight tense forms  describe
  'After that, she would describe the eight tense forms.'
e. Ze zou het zaterdag wel voltooid hebben.
future perfect in past
  she  would  it  Saturday prt  completed  have
  'She probably would have finished it on Saturday.'

The striking parallelism between the four present-tense forms and the four past-tense forms makes it possible to assume that the mental representations of the past tenses are similar to the ones for the present tenses except for n. To account for the striking parallelism between the four present tenses and the four past tenses, we will assume that the past tenses are defined by means of a virtual "speech-time-in-the past", which we will refer to as n'. To make this a bit more concrete, assume that the speaker of the discourse chunk in (246) is telling about a conversation he has had with Els. We may then identify n' with the moment that the conversation took place; the speaker is repeating the information provided by Els from the perspective of that specific point in time. This leads to the representation in Figure 12, in which the dotted line represents the time line, index i stands for the time interval that is construed as the past (that is, the then-present) for the speaker/hearer, ia for the actualized part of the past at n', and ifor the non-actualized part of the past at n'.

Figure 12: The past-tense interval i

In what follows we will show that the four past tenses in Table 9 differ with respect to the way in which they locate the eventuality k in past-tense interval i. Before we start doing this, we want to point out that the present proposal diverges in one crucial respect from the proposal in Verkuyl (2008). In Figure 12, we placed speech time n external to i and Verkuyl indeed claims that this is a defining property of the past-tense interval i, as is clear from his definition of present and past tense given in Subsection A, which is repeated here as (247).

247
The feature ±past (to be revised)
a. Present: i ○ n
i includes speech time n
b. Past: i < n
i precedes speech time n

The idea that the past-tense interval must precede speech time n does not seem to follow from anything in the system. There is, for example, no a priori reason for rejecting the idea that, like the present-tense interval, the past-tense interval can be stretched indefinitely, and is thus able to include speech time n. In the subsections below, we will in fact provide empirical evidence that inclusion of n is possible. For example, the future in the past and future perfect in the past examples in (248) show that eventuality k can readily be placed after speech time n.

248
a. Marie zou morgen vertrekken.
  Marie would  tomorrow  leave
  'Marie would leave tomorrow.'
b. Marie zou oma morgen bezocht hebben.
  Marie would  grandma  tomorrow  visited  have
  'Marie would have visited Grandma tomorrow.'

In order to formally account for the acceptability of examples such as (248), Broekhuis & Verkuyl (2014) adapted the definition in (247b) as in (249b). Note that the examples in (248) also have a modal meaning component; we will ignore this for the moment but return to it in Section 1.5.2.

249
The feature ±past (adapted version)
a. Present: i ○ n
i includes speech time n
b. Past: i ○ n'
i includes virtual speech-time-in-the-past n'

The definitions in (249) leave the core of the binary tense system unaffected given that they maintain the asymmetry between the present and the past but now on the basis of an opposition between the now-present (characterized by the inclusion of n) and the then-present (characterized by the inclusion of n'). The now-present could be seen as the time interval that is immediately accessible to and directly relevant for the speaker/hearer-in-the-present, whereas the then-present should rather be seen as the time interval accessible to and relevant for some speaker/hearer-in-the-past; see Janssen (1983:324ff.) and Boogaart & Janssen (2007) for a review of a number of descriptions in cognitive terms of the distinction between past and present that may prove useful for sharpening the characterization of the now- and then-present proposed here. The definition of past in (249b) is also preferred to the one in (247b) for theoretical reasons: first, it formally accounts for the parallel architecture of the present and the past and, second, it solves the problem that n' did not play an explicit role in the definition of the three binary oppositions given in Subsection A, and was therefore left undefined.

[+]  D.  The four past tenses defined by Binary Tense Theory

The following subsections will show that the four past tenses in Table 9 in the introduction to this subsection differ with respect to (i) the location of eventuality k denoted by the lexical projection of the main verb within present-tense interval i, and (ii) whether or not it is presented as completed within its own past-tense interval j. Recall that we will focus on the temporal interpretations cross-linguistically attributed to the tenses in Table 9 and postpone the discussion of the more special temporal and the non-temporal aspects of their interpretations in Dutch to Section 1.5.4.

[+]  1.  Simple past

The simple past expresses that eventuality k takes place during past-tense interval i. This can be expressed by means of Figure 13, in which the continuous line below k refers to the time interval during which the eventuality holds. The continuous line below k indicates that the default reading of an example such as Ik wandelde'I was walking' is that eventuality k takes place at n'.

Figure 13: Simple past ( Ik wandelde'I was walking')

By stating that j = i, Figure 13 also expresses that the simple past does not have any implications for the time preceding or following the relevant past-tense interval i: the eventuality k may or may not hold before/after i. Thus, an example such as (250) does not say anything about the speaker's feelings on the day before yesterday or today. This also implies that the simple past cannot shed any light on the issue of whether speech time n can be included in past-tense interval i.

250
Ik was gisteren erg gelukkig.
  was  yesterday  very happy
'I was very happy yesterday.'
[+]  2.  Past perfect

The default reading of the past perfect is that eventuality k takes place before n', that is, k is located in the actualized past-tense interval ia ( j = ia). In addition, the past perfect presents the eventuality as a discrete, bounded unit that is completed within time interval j, that is, cannot be continued after n'; this is again represented by means of the short vertical line after the continuous line below k. Given that k precedes n' and n' precedes n, k also precedes n, which implies that examples of this type cannot shed any light on whether speech time n can be included in the past-tense interval i.

Figure 14: Past perfect ( Ik had gewandeld'I had walked')

[+]  3.  Future in the past

The future in the past expresses that the eventuality k takes place after n', that is, k is located in the non-actualized part of the past-tense interval ( j = i).

Figure 15: Future in the past ( Ik zou wandelen'I would walk')

The future in the past examples in (251b&c) show that speech time n can be included in the past-tense interval. We have already seen above that this refutes the definition of past in (247b) and supports the revised definition in (249b).

251
a. Els zou gisteren wandelen.
  Els would  yesterday  walk
b. Els zou vandaag wandelen.
  Els would  today  walk
c. Els zou morgen wandelen.
  Els would  tomorrow  walk
[+]  4.  Future perfect in the past

The interpretation of the future perfect in the past is similar to that of the future in the past, but requires the state of affairs to be completed within time span i.

Figure 16: Future perfect in past (Ik zou hebben gewandeld'I would have walked')

The difference between the future in the past and the future perfect in the past is parallel to the difference between the future and the future perfect discussed in Subsection A: in future in the past examples such as (252a) the focus is on the progression of the eventuality, which is placed in its entirety after n', whereas in future perfect in the past examples such as (252b) the focus is on the completion of the eventuality and no particular claim is made concerning the starting point of the event.

252
a. Het ijs zou gisteren smelten.
  the ice  would  yesterday  melt
  'The ice would melt yesterday.'
b. Het ijs zou gisteren gesmolten zijn.
  the ice  will  yesterday  melted  be
  'The ice would have melted yesterday.'

Similar examples with the achievement die brief schrijven are given in (253): the future in the past in (253a) locates the entire eventuality after n', whereas the future perfect in the past in (253b) does not seem to make any claim about the starting point of the eventuality but simply expresses that the eventuality will be completed after n' (but within i).

253
a. Jan zou gisteren die brief schrijven.
  Jan would  yesterday  that letter  write
  'Jan would write that letter yesterday.'
b. Jan zou gisteren die brief geschreven hebben.
  Jan would  yesterday  that letter  written  have
  'Jan would have written that letter yesterday.'

The examples in (254) with the adverbial phrase morgen'tomorrow' show that the future perfect in the past provides evidence in favor of the claim that speech time n can be included in the past-tense interval. We have already seen that this refutes the definition of past in (247b) and supports the revised definition in (249b).

254
a. Het ijs zou morgen gesmolten zijn.
  the ice  will  tomorrow  melted  be
  'The ice would have melted tonight.'
b. Jan zou morgen die brief geschreven hebben.
  Jan would  tomorrow  that letter  written  have
  'Jan would have written a letter tomorrow.'
[+]  E.  The choice between present and past: a matter of perspective

So far, we have discussed the three binary features in (255) assumed within Te Winkel/Verkuyl's binary tense theory: these features define four present and four past tenses, which were exemplified in Table 9.

255
a. ±past: present versus past
b. ±posterior: future versus non-future
c. ±perfect: imperfect versus perfect

Subsections A and C discussed the default interpretations assigned to these present and past tenses by Verkuyl (2008). We also discussed Verkuyl's formalizations of the features in (255) and saw that there was reason to somewhat adapt the definition of +past. This resulted in the set of definitions in (256).

256
a. Present: i ○ n
i includes speech time n
a'. Past: i ○ n'
i includes virtual speech-time-in-the-past n'
b. Non-future: i ≈ j
i and j synchronize
b'. Future: ia < j
ia precedes j
c. Imperfect: k ≼ j
k need not be completed within j
c'. Perfect: k ≺ j
k is completed within j

An important finding of the previous subsections is that in principle the present and past interval can be indefinite, with the result that the past-tense interval may include speech time n. This means that the present and the past do not refer to mutually exclusive temporal domains and, consequently, that it should be possible to discuss eventualities both as part of the past and as part of the present domain. This subsection provides evidence in favor of this position and will argue that the choice between the two options is a matter of perspective, that is, whether the eventuality is viewed from the perspective of speech time n or the virtual speech time in the past n'.

[+]  1.  Supratemporality

The use of adverbial phrases of time in sentences with a past tense may introduce a so-called supratemporal ambiguity; cf. Verkuyl (2008:118-123). This ambiguity is especially visible when the adverbial phrase occupies the first position of the sentence, as in (257).

257
a. Om vijf uur ging Marie weg.
  at 5 oʼclock  went  Marie away
  'Marie would leave at 5 oʼclock.'
b. Een uur geleden had Marie nog zwart haar.
  an hour ago  had Marie still  black hair
  'An hour ago Marie still had black hair.'

The two sentences in (257) have a run-of-the-mill "real event" interpretation in the sense that the sentence is about Marie's departure or about Marie having black hair at the time indicated by the adverbial phrase; in such cases the adverbial phrase functions as a regular temporal modifier of the time interval j that includes eventuality k. There is, however, also a supratemporal interpretation in which the eventuality itself does not play any particular role apart from being the topic of discussion. On this interpretation, the speaker of (257a) expresses that his most recent information about Marie's departure goes back to five o'clock. This means that the adverbial phrase om vijf uur'at five oʼclock' thus does not pertain to the location of the eventuality on the time axis but to the speaker: "according to my information at five oclock, the situation was such that Marie would be leaving". In a similar way, (257b) may be interpreted as a correction of a mistake signaled by the speaker in, e.g., a manuscript; the sentence is not about the character Marie but about information about the character Marie: "An hour ago, I read that Marie is black-haired (but now it is mentioned that Jan is fond of her auburn hair)".
      Past-tense clauses are compatible with future eventualities on a supratemporal reading. Consider a situation in which the speaker is discussing Els' plans for some time interval after speech time n. He may then compare the information available at two different moments in time: sentence (258a), for example, compares the information that the speaker had yesterday with the information that he has just received. The first conjunct of (258a) also illustrates that past-tense clauses with a supratemporal reading are compatible with locating the eventuality k after speech time; the speaker's talk is located in the speaker's future. Example (258b) in fact shows that it is even possible to make the future location of k explicit by means of a second adverbial phrase like morgen'tomorrow', particularly when adding the particle nog right behind gisteren'yesterday'; see Boogaart & Janssen (2007) for similar examples.

258
a. Gisteren zou Els mijn lezing bijwonen, maar nu gaat ze op vakantie.
  yesterday  would  Els my talk  attend  but  now  goes she on holiday
  'As of yesterday, the plan was that Els would attend my lecture but now I have information that sheʼll be going on holiday.'
b. Gisteren (nog) zou Els morgen mijn lezing bijwonen, maar nu gaat ze op vakantie.
  yesterday   prt  would  Els tomorrow  my lecture  attend but  now  goes  she  on holiday
  'As of yesterday, the plan was that Els would attend my talk tomorrow but now I have information that sheʼll be going on holiday.'

That the past tense in the first conjunct of the examples in (258) is compatible with locating the eventuality after speech time n and that the adverbs gisteren'yesterday' and morgen'tomorrow' can be used in a single clause is exceptional. However, that this is possible need not surprise us when we realize that speech time n can be included in the past-tense interval. As is illustrated in Figure 17 for example (258b), the first conjuncts in sentences such as (258) give rise to completely coherent interpretations. The notation used aims at expressing that the adverbial phrase gisteren is a supra-temporal modifier of the virtual speech-time-in-the past n', whereas the adverbial phrase morgen'tomorrow' functions as a regular temporal modifier of j.

Figure 17: Supratemporal interpretation of future in the past

[+]  2.  Sequence of tense

The claim that speech time n may be included in the past-tense interval also has important consequences for the description of the so-called sequence of tense phenomenon, that is, the fact that the tense of a dependent clause can be adapted to concord with the past tense of the matrix clause. Sequence of tense is illustrated by means of the two examples in (259): example (259a) is unacceptable if we interpret the adverb morgen'tomorrow' as a temporal modifier of the eventuality k, whereas example (259b) is fully acceptable in that case.

259
a. $ Jan vertrok morgen.
  Jan left  tomorrow
  'Jan was leaving tomorrow.'