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Merging FeaturesComputation, Interpretation, and Acquisition$

José M. Brucart, Anna Gavarró, and Jaume Solà

Print publication date: 2009

Print ISBN-13: 9780199553266

Published to Oxford Scholarship Online: May 2009

DOI: 10.1093/acprof:oso/9780199553266.001.0001

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Homogeneity and flexibility in temporal modification *

Homogeneity and flexibility in temporal modification *

(p.235) 13 Homogeneity and flexibility in temporal modification*
Merging Features

Aniko Csirmaz

Oxford University Press

Abstract and Keywords

Following an overview of time intervals in the clause, this chapter tackles the appropriate characterization of divisibility, the requirement of durative adverbs which can measure any of these times. The flexible view of temporal modification offers a natural account of a variety of novel phenomena and a coherent view of earlier accounts of durative modification.

Keywords:   durative adverbs, time intervals, divisibility, stativity, maximal events

13.1 Introduction

A finite clause can contain a variety of time intervals, including the event time, reference time, speech time, and a variety of other times as well. Several temporal modifiers (though not all, cf. below and Csirmaz 2006b) show flexibility in time interval modification: for-adverbs, for instance, can modify most of these time intervals.1 These durative adverbs diagnose homogeneity: they require a homogeneous predicate of times to apply to the time interval measured. Building on different argument types and a variety of eventuality descriptions, this chapter explores how the properties of the distinct predicates of times are affected. It is argued that a sufficiently detailed inventory of times can accommodate the effects of the variation among eventuality descriptions as well as the interpretation of durative adverbs.

It is suggested that the interpretation of flexible, unrestricted durative adverbs is determined exclusively by their position within the clause—that is, by the position with respect to the time intervals that are available for modification. Semantic factors, described in more detail in sections 13.4 and 13.5, also play a role, since the durative adverbs impose specific semantic (p.236) requirements on their temporal predicate arguments. This view of durative adverbs is genuinely and extremely Minimalist (in the sense of Chomsky 2005, 2008, among others); it is devoid of the specific tools adopted for certain Minimalist implementations. In a strictly Minimalist system, the only restrictions should follow from interface conditions and virtual conceptual necessity.

Durative adverbs are a case in point. The maximal set of temporal intervals could be universally specified (arguably an instance of virtual conceptual necessity), with the specific time intervals available in a given language possibly varying according to the temporal (including aspectual) operators available in the lexicon of that language. The interpretation of a given occurrence of a durative adverb is trivially determined by the interpretive LF/C‐I component, by relying on the (external merge) position of the adverb and on the time interval measured (for specific details, see section 13.5).

It is not necessary to assume any solution or tool specific to any Minimalist implementation. The generality and triviality of the approach suggests that it is on the right track, since the formulation of the analysis will stay unvarying even with different formulations of the Minimalist Program.

13.2 Time intervals and interpretation

A finite clause may contain several distinct time intervals and predicates applying to these. I reserve the term “eventuality description”, based on Bach 1986, to refer to the entire clause, containing all the times and the predicates applying to them. Adopting a Reichenbachian approach (Reichenbach 1947), the time intervals which are obligatorily present in finite clauses are the event time, the reference time, and the speech time. The event time is the duration of the eventuality (that is, of the event or state in question) and the speech time is the time of utterance. With respect to the reference time, I follow Reichenbach 1947, Klein 1994, Iatridou et al. 2003, and Stechow 2002 in interpreting that time as the time interval under discussion. The reference time can be related to event time in two ways, determined by the viewpoint aspect specification of the eventuality description. In a perfective description, the reference time contains the event time; in an imperfective description, the event time contains the reference time. Concerning the position of these times, I assume that the event time is associated with vP, the reference time with AspP, and the speech time with TP.

Among these time intervals, it is only the speech time that cannot be modified. As noted by Hornstein 1990, speech time is deictic and, similarly to other deictic expressions, it resists modification. The modification of the other (p.237) two intervals is illustrated below, with the additional material in parentheses clarifying the intended interpretation.


  1. a. Event time modification

    Tracy ran t o t he shed [in ten minutes]

    Tracy ran [for ten minutes]

  2. b. Reference time modification

    Tracy was running to the shed [for ten minutes] (but then decided to head to the house)

A clause may also contain other time intervals in addition to these times. I assume, for concreteness, that the result time is present whenever a distinct result state arises as the result of a culminated event; the other times are introduced by optional operators. The time intervals in question include the result time, iterative time, habitual time, perfect time, and modal time.2 The modification of each of these time intervals is illustrated below.3


  1. a. Result time (the time at which the result state holds)

    Tracy opened the window [for two hours]

  2. b. Iterative time (the time during which an event is iterated)

    Tracy coughed [for ten minutes]

  3. c. Habitual time (the time during which an event habitually occurs)

    Tracy biked to work [for a whole year]

  4. d. Perfect time (the time interval which extends before the reference

    time (Iatridou et al. 2003, Pancheva and von Stechow 2004))

    Tracy has lived in Alaska [for two years]


    (for a time span extending two years before the speech time to the speech time, Tracy has lived in Alaska)

  5. e. Modal time modification (the time where the modal is evaluated;

    also Stowell 2004, citing Zagona 1990)

    [For half an hour,] Tracy could have escaped

    (for a 30‐minute time interval, it was possible for Tracy to escape;

    outside of that interval, the possibility did not exist anymore)

13.3 Durative adverbs

The discussion in the remainder of this chapter will focus on the relation between adjuncts that measure the duration of a time interval and the properties of predicates applying to these intervals. Before turning to a more detailed discussion of the modification of times, let us consider homogeneity, a property relevant for durative adverb modification. The duration of a time interval, for example that of an event time, can be measured by a for‐ or an in‐adverb:


  1. a. Tracy ran/was sick for an hour

  2. b. Tracy painted the shed in a day

As noted by Vendler 1967 and discussed extensively in the literature, the choice between the two adverb types is determined by homogeneity. For‐adverbs appear with homogeneous predicates of times, and in‐adverbs appear if the predicate lacks homogeneity. I suggest, in line with Bennett and Partee 1972, Dowty 1979, Link 1998, and others, that the property of homogeneity should be seen as divisibility and offer an argument for this claim in section 13.4. In addition, I assume that divisibility, the relevant notion of homogeneity, is relevant for predicates of times. Thus, a given time interval can be measured by a for‐adverb if the predicate that applies to the time interval is divisible. I adopt the following definition of divisibility (Bennett and Partee 1972, Dowty 1979, Link 1998, among others)4:

(4) A predicate P is divisible iff whenever P(x) for an argument x, then for allx′ ⊂ x, P(x′)

The homogeneous event time predicates, which license the for‐adverb measure of the event time, are divisible. Whenever the event time predicate Tracy run is true for a time interval, it also holds for all (contextually relevant) parts of that time interval, even though it fails to hold for atomic subintervals. With (p.239) lexically stative predicates, no such qualification is necessary: given a time for which Tracy sick is true, it is also true at all parts of that time interval. Divisibility fails to hold for non‐homogeneous event time predicates. If Tracy paint the shed holds for a 24‐hour interval, it fails to hold for all subintervals; for instance, for the first several hours of the day.

In adopting divisibility as the relevant homogeneity condition, I deny that cumulativity plays a role in identifying homogeneous predicates. This view of homogeneity contrasts with Krifka 1992, 1998, Rothstein 2004, Moltmann 1991, and Tenny 1994; these works assume that cumulativity plays some role in determining homogeneity, possibly in addition to divisibility.

13.4 Homogeneity and negation

Durative adverbs can give rise to ambiguous interpretations. I assume that the variable interpretation arises because of structural ambiguity (as explored, among others, in Iatridou et al. 2003, Thompson 2005 for adverbial modification of a more restricted set of times). Specifically, durative adverbs can be externally merged in a position local to a variety of time intervals. The adverb is interpreted as measuring the duration of the time interval that is sufficiently local to the adverb.5 This view of durative adverbs predicts a degree of flexibility in interpretation which is attested by a number of situation descriptions, including negated descriptions, explored below.

The wide range of time intervals as well as the structural and interpretational flexibility of temporal modifiers provide a handle on the properties of eventuality descriptions. This section considers some properties of negated descriptions, focusing on the homogeneity and temporal modification licensed by negation. It is argued that negation yields a homogeneous predicate that applies to the reference time.

As noted above, durative adverbs are sensitive to the homogeneity of predicates of times. For‐adverbs, unlike in‐adverbs, require the predicate applying to the time interval measured to be homogeneous (5). The difference between the affirmative descriptions disappears under negation (6).


  1. a. Tracy crossed the street [in ten minutes] / # [for ten minutes]

  2. b. Tracy walked along the street [for ten minutes] / # [in ten minutes]


  1. a. Tracy didn't cross the street [for ten minutes]

  2. b. Tracy didn't walk along the street [for ten minutes]

There have been two kinds of accounts offered for the difference between negated and affirmative eventuality descriptions. One approach argues that (p.240) negation is an aspectual operator which converts all eventuality descriptions into states. Proponents of this view, including Bennett and Partee 1972, Dowty 1979, and Verkuyl 1993, maintain that both sentences below are stative.


  1. a. Tracy didn't cross the street [for half an hour]

  2. b. Tracy slept [for half an hour]

The alternative treatment, which I label the homogeneity account, is advocated in some form by Zucchi 1991, Moltmann 1991, and Kamp and Reyle 1993. This approach maintains that negated eventuality descriptions are homogeneous, but not stative. Under this view, negation is not an aspectual operator and fails to affect the aspectual properties of the eventuality description. The negated description is homogeneous, however: intuitively, a negated predicate of times (such as Tracy not crossing the street) holds for a time argument and all subintervals of that time interval as well.

Building on Csirmaz 2005, 2006a, 2007, I adopt the homogeneity account. As noted above, the derived homogeneity affects the reference time predicate but leaves the properties of the event time predicate—including stativity— intact.

13.4.1 Diagnosing stativity

Stativity diagnostics support the homogeneity account, since they consistently identify negated event descriptions as dynamic rather than stative. There are two environments where states—stative event time predicates and imperfectives—behave alike.6 First, discourse structure distinguishes states and dynamic eventuality descriptions (Dowty 1986, Kamp and Reyle 1993). Stative descriptions do not advance the narration but provide an elaboration of the background (8a). A dynamic description advances narration and has a consecutive interpretation (8b).


  1. a. Tracy looked around. She felt sad/She was smiling

  2. b. Tracy looked around. She smiled

Negated event descriptions pattern with their affirmative counterparts. The negated imperfective in (9a) fails to advance narration. The negated perfective event description, in contrast, does advance narration: the expected reaction of smiling, following Tracy's looking around, did not happen (9b). (p.241)


  1. a. Tracy looked around. She wasn't smiling

  2. b. Tracy looked around. She didn't smile

The interpretation of present‐tense forms also identifies some negated event descriptions as nonstative. An eventuality description with present tense morphology has either an ongoing or a habitual interpretation, depending on the stativity of the description. A stative description has an ongoing interpretation (10a), while a dynamic description has a habitual interpretation (10b).


  1. a. Tracy is sad/Tracy is smiling

  2. b. Tracy smiles

Once again, the contrast between the perfective and imperfective event descriptions survives under negation. The negated imperfective event description has an ongoing interpretation, and the negated perfective description is interpreted as a habitual description.


  1. a. Tracy is not smiling

  2. b. Tracy does not smile

If negated event descriptions are not necessarily stative, then the definition of stativity cannot extend to these descriptions either. This consideration forces the abandonment of a homogeneity‐based definition of stativity (Vendler 1967, Dowty 1979, Comrie 1976, Smith 1991, Rothstein 2004, among others), which maintains that only states are (strongly) homogeneous and lack atomic subintervals. A negated event predicate is (strongly) homogeneous (it holds for all subintervals of the time measured by the for‐adverb), and yet it is not stative.

Since homogeneity cannot reliably identify states, a different property should be adopted as distinguishing states from dynamic predicates. In addition to homogeneity, dynamicity was also suggested to identify states. Comrie 1976 and subsequently Smith 1991 note that states—in contrast with events— are non‐dynamic; that is, they are not “continually subject to a new input of energy” (Comrie 1976: 49). It may be possible then to define states in terms on non‐dynamicity rather than as homogeneous predicates. A more detailed discussion is, however, outside of the scope of this chapter.

13.4.2 Modification of the reference time

The homogeneity licensed by negation affects the reference time rather than the event time. The properties of the event time predicate are not affected, which is shown by the paraphrase in (12b). The two durative adverbs in (p.242) (12c) also indicate that the event time predicate is not homogeneous under negation, since it can be measured by an in‐adverb.7


  1. a. [For an hour,] Tracy did not cross the street

  2. b. There was a time interval which is an hour long, and during which there was no event of Tracy crossing the street

  3. c. [For an hour,] Tracy did not cross the street [in five minutes]

Under the structural ambiguity account sketched above, the different interpretations of the durative adverb can be explained by assuming that the durative adverb which measures the reference time (the for‐adverb in (12a,c)) is merged locally to the reference time, while the in‐adverb in (12c), which measures the event time, is merged in a position local to the event time.

Finally, a few remarks concerning the position and interpretation of the adverb are in order. In the clause‐initial position, the for‐adverb unambiguously modifies the reference time rather than the event time. In a clause‐final position, as given below, the adverb is ambiguous:

(13) Tracy did not cross the street [for an hour]

The for‐adverb in (13) can modify either the reference time or an iterative time interval. This correlation between the adverb position and the interpretation is consistent with the approach to temporal modification in Thompson 2005. Discussing punctual adverbials, Thompson argues that the adverbs which modify the lower event time cannot move to a clause‐initial position. This movement is banned by economy considerations, since the same numeration allows a derivation with a shorter movement—with the adverb moving from the position where it measures the structurally higher reference time. On the (reasonable) assumption that the iterative time is lower than the reference time, the difference among possible readings follows.

In addition to disambiguating the interpretation, the clause‐initial position of the durative adverb also gives rise to a contrastive implicature. These adverbs function as contrastive topics and implicate that the eventuality in question holds for some interval following the reference time. For (12a), the implicature is that the event culminates following the reference time.8

(p.243) 13.5 Homogeneity and reference time modification elsewhere

In addition to negation, other environments can also yield homogeneity for perfective telic eventuality descriptions. In this section I address the effects of decreasing quantifiers and only, building on Csirmaz 2005, 2006a, and 2007.

An eventuality description can always be modified by a for‐adverb if it contains a decreasing quantifier or only. The description in (14a) is not homogeneous, and thus cannot be modified by a for‐adverb (a possible iterative interpretation is disregarded here, and is ascribed to the availability of an iterative operator). Negation, as noted above, yields a divisible reference time predicate and permits modification by a for‐adverb (14b). The effect of decreasing quantifiers and only is illustrated in (14c,d). The relevant interpretation for (14c) is distributive with respect to the participants: the intended interpretation is that during a year‐long time span, there was a total of fewer than five events of a tourist climbing the Mulhacén.


  1. a. (#For a year) Tracy climbed Mulhacén (#for a year)9

  2. b. (For a year) Tracy didn't climb Mulhacén

  3. c. (For a year) fewer than five tourists climbed Mulhacén

  4. d. (For a year) only Tracy climbed Mulhacén

The account of negation extends straightforwardly to decreasing quantifiers. If these quantifiers have narrow scope within a predicate of times, then the resulting predicate is homogeneous. I suggest that the time interval measured in (14c) is the reference time, just as in the case of (14b). Under this view, (14c) asserts that during the time interval under discussion, which is a year long, there were fewer than five events of a tourist climbing Mulhacén. This reference time predicate is homogeneous, since it is true for all subintervals of the reference time. In absence of a decreasing quantifier, the reference time predicate is not homogeneous, and consequently no for‐modification is possible, as predicted:


  1. a. (For a year) fewer than five tourists climbed Mulhacén

  2. b. #(For a year) five tourists climbed Mulhacén

  3. c. #(For a year) more than five tourists climbed Mulhacén

Once again, a possible iterative reading (where the same tourists climb the mountain on more than one occasion) or a marginally available, coerced (p.244) non‐culminating reading (where the mountain top was not reached) are not relevant for this discussion. These readings yield a homogeneous iterative and event time predicate respectively—independently of the presence of the decreasing quantifier.

As illustrated above, only also allows for‐adverbial modification. Similarly to negation and decreasing quantifiers, neither a coerced non‐culminating interpretation nor iteration is enforced. The eventuality description (16a) holds if within a year‐long time interval Tracy climbed Mulhacén (either once or on multiple occasions), but no one else did. (16c) is true if within a yearlong interval the only mountain that Tracy climbed was Mulhacén—again, she could have climbed the mountain only once or several times.


  1. a. (For a year) only Tracy climbed Mulhacén

  2. b. #(For a year) Tracy climbed Mulhacén

  3. c. (For a year) Tracy climbed only Mulhacén

Unlike decreasing quantifier phrases, only cannot be treated as parallel to negation. A predicate of times containing only is not divisible according to the definition adopted earlier: if the description only Tracy climbed Mulhacén is true for a time t, it does not hold for all subintervals of that time. For those time intervals that do not contain an appropriate event, the predicate is false.

In order to account for the similarity between the behavior of only and that of decreasing quantifiers, Csirmaz 2005, 2006a, 2007 appeals to the notion of Strawson entailment (Fintel 1999). Fintel argues that the downward‐entailing property of only can be captured by assuming that entailment is only checked for those conclusions that have a semantic value defined. Adopting the treatment of Csirmaz 2005, 2006a, 2007,I assume that this modified view of downward entailment can also be adapted to divisibility, as given below.

(17) A predicate P is Strawson‐divisible iff whenever P(x) for an argument x, then for all x′ ⊂ x, such that the predicate is defined at x′, P(x′)

A predicate of times that contains only will be Strawson‐divisible, since the predicate only needs to hold for the subintervals where the predicate is defined. For (16a), this amounts to the requirement that only Tracy climb Mulhacén be true for all intervals that contain an event time of Tracy climbing Mulhacén, which conforms to the intuitions. A predicate of times containing only is thus Strawson‐divisible. If for‐adverbs measure times that are arguments of Strawson‐divisible predicates (rather than arguments of divisible predicates) then the behavior of all the previous examples is accounted for.

(p.245) The effect of decreasing quantifiers and only on predicates of times is handled straightforwardly in the present account, by appealing to the divisibility or Strawson divisibility of the resulting predicate of times. The effect of decreasing quantifiers also provides support for the view of homogeneity as divisibility. If homogeneity were defined in terms of cumulativity, then the predicates containing a decreasing quantifier would not count as homogeneous: given two reference time intervals, where the predicate fewer than five tourists climbed Mulhacén is true for both intervals, the predicate does not necessarily hold for the sum of those intervals.

13.6 Restricted distribution of durative adverbs

In the preceding discussion it was shown that for‐adverbs are flexible and they can measure the duration of any time interval, as long as the predicate applying to that time interval is (Strawson‐)divisible. This flexibility does not extend to all durative adverbs—neither within English nor cross‐linguistically.

As noted by Csirmaz 2005, 2007, and independently by Morzycki 2004, English bare durative adverbs can only modify a limited range of time intervals. These adverbs can only measure the duration of the event time, but not that of the result, iterative, or any other time interval, as shown below.



Tracy slept [an hour]

(event time)


Tracy opened the door [#(for) an hour]

(result time)


Tracy coughed [#(for) an hour]

(iterative time)

Bare adverbs are, in fact, generally dispreferred as modifying reference, habitual or possibly iterative time; this restriction can be observed, among others, in Russian, Spanish, Korean, and Hungarian as well as in English.

13.6.1 A transparent restriction&

Morzycki 2004, and separately Csirmaz 2005, 2007, suggested that the restricted distribution of bare adverbs follows from an independent factor, namely the locality restrictions on case licensing. Under this view, bare adverbs must bear a structural accusative case and case licensing must obey locality restrictions. If the adverb is merged too high in the structure—measuring the habitual or reference time—then its case cannot be licensed. In contrast, the case of a bare adverb measuring the event time can be licensed by the appropriate head, whether it is assumed to be v or AgrO. The range of times that a bare adverb can modify is therefore not intrinsically restricted, but follows from the independent requirement of case licensing.

(p.246) 13.6.2 A lexical restriction

Csirmaz 2006b provides arguments against the view that case licensing constrains the behavior of bare adverbs (or that of structurally case‐marked adverbs elsewhere). First, if case licensing was the only source of restriction on the distribution and interpretation of bare adverbs, it would be unexpected that these adverbs cannot modify the result time.

(19) Tracy opened the door for ten minutes / #Tracy opened the door ten minutes

The result time is usually assumed to be located below the event time (cf. Levin and Rappaport Hovav 2005, Ramchand 2008, among others), thus the locality of case licensing should not prove problematic: the AgrO/v accusative licensing head should be able to license case on the adverb that modifies the result time.

Second, bare adverbs and structurally case‐marked adverbs show a cross‐ linguistic variation in the times they can modify—a difference that is unexpected if neither the position of times nor (accusative) case licensing varies across the languages in question. Bare adverbs differ with respect to iterative times: they cannot measure an iterative time in English, but this is possible in Hungarian:


a. #Tracy knocked ten minutes

b. Tracy tíz percet kopogott


T‐nom ten minute‐acc knocked

‘Tracy knocked for ten minutes.’

Given these considerations, case licensing cannot account for the range of time intervals modified by bare adverbs. I assume that the times that these adverbs can measure is independently restricted, by lexically encoding the range of time intervals each adverb can modify.

On the assumption that bare durative adverbs are case‐marked constituents (and are thus parallel to other durative adverbs in those languages where accusative case marking is overt), lexical specification of the distribution appears to be the only option available. The syntactic component, the computational C HL cannot restrict the distribution of these adverbs appropriately. As noted above, a locality restriction on case checking or licensing (a natural assumption) derives the fact that the durative adverbs in question cannot modify time intervals that are located above the case licensing head in the tree. The variable acceptability with respect to the lower iterative time interval, and the impossibility of result time modification, however, remain unexpected under a purely syntactic account.

(p.247) Let us assume, given lack of evidence to the contrary, that the interpretation of durative adverbs is identical to that of for‐adverbs (when they measure the same time interval). If this is true, then the restricted distribution of bare dura‐ tive adverbs cannot be derived from factors relevant at the interpretational, C‐I interface. It appears implausible to assume that the PF interface is responsible for the different behavior of the two types of adverbs; there is no (PF‐) feature that could reasonably constrain the distribution as desired.

The sole remaining option is to assume that an arbitrary, lexical specification is also at play, possibly in addition to independent restrictions imposed— for instance, by the independent locality constraint on case checking. For concreteness, let us assume that is possible to explicitly specify the range of time intervals modified in the lexical entry for a durative adverb (or in the head of the durative adverb). The lexical entry for the bare adverb in English will specify that it can measure the event time only, while the lexical entry for accusative durative adverbs in Hungarian specifies the event time and the iterative time as those intervals that can be measured by this adverb.

Note that the conclusion that lexical specification is at the heart of different adverb distributions is supported by the fact that languages exhibit differences in this respect. On the standard Minimalist expectation that crosslinguistic variation is located in the lexicon, the varying behavior of English and Hungarian bare/accusative adverbs points strongly at a lexical account of the differences—and thus of restricted adverb distribution in general.10

13.6.3 Restricted distribution elsewhere

Further support for this type of approach is offered in Csirmaz 2006b, which offers a survey of Hungarian durative adverbs. It is shown that the four types of Hungarian for‐adverb equivalents (three of which are postpositional, rather than accusative adverbs) show significant variation in the range of time intervals they can modify. It is suggested that the range of times modified fails to follow straightforwardly from either the form or the interpretation of the adverbs, and must be independently constrained in the lexicon, as also noted above.

A similar, yet independent restriction may be invoked for the distribution of in‐adverbs in English. These adverbs require the predicate of times measured to be non‐homogeneous, a property which can hold for event and for reference time predicates as well. The event time predicate of a telic eventuality description and the reference time predicate of a perfective eventuality (p.248) description is thus expected to permit in‐adverbial modification. This expectation is not borne out; in‐adverbs can only measure the event time predicate:



Tracy ran to the stop in an hour

(non‐homogeneous, indivisible event time)


#Tracy ran in an hour

(homogeneous, divisible event time)


#Tracy slipped in ten minutes

(non‐homogeneous reference time)

The eventuality description appearing with in‐adverbs must be telic, as shown in (21a,b); the non‐divisibility of the reference time predicate does not suffice for in‐adverb modification. (21c) also shows that the in‐adverb measures the event time, since it enforces a durative interpretation for the punctual event time predicate. The sensitivity of homogeneity of predicates of times is thus not sufficient to restrict the distribution of durative adverbs; it appears to be necessary to explicitly constrain the times these adverbs can measure.

13.7 Homogeneity elsewhere

As argued above, the property of homogeneity—as relevant for durative adverb modification—should be seen as (Strawson) divisibility. Divisibility can be licensed, among others, by an appropriate operator, negation, or a decreasing quantifier. The relation between homogeneity and arguments in an eventuality predicate have been explored in numerous works. Here I briefly consider the relevant claims put forth in two papers, contrasting them with the present observations. The discussion only focuses on broad aspects of the issues of homogeneity, and cannot fully explore all the issues addressed there.

13.7.1 Quantifiers and iteration

The preceding discussion emphasized that homogeneity should be defined as divisibility, a conclusion enforced by the effect of decreasing quantifiers on adverbial modification. Moltmann 1991 also discusses, among others, the effect of quantifiers on homogeneity and for‐adverbs. I show that her data, in spite of initial appearances, can be easily integrated into the system of adverbial modification advocated in this chapter.

Moltmann 1991 notes that for‐adverbial modification is always possible in the presence of a vague quantifier. Two sets of examples ((43) and (44) in Moltmann 1991) are reproduced below. Vague quantifiers are italicized and absolute quantifiers are underlined. (p.249)


  1. a. For several years John took a lot of pills / few pills

  2. b. #For several years John took those pills / all the pills


  1. a. For several years John had a lot of success / little success

  2. b. #For several years John had that success / all success

Moltmann 1991 notes that (22a) is homogeneous, since it is true for every (contextually relevant) part of the interval that there are a lot of/few pills that John took. Crucially, the relevant quantities of pills (a lot of/few pills) are determined with respect to subintervals of the larger event, which lasts several years.

The relevance of subintervals is also shown by a possible interpretation of (22b) and (23b), not discussed in Moltmann 1991. If the absolute quantifier expressions are interpreted as types, then for‐adverbial modification is gram matical. In (22b), for instance, the relevant interpretation states that John took certain types of pills, or that he took pills of all types respectively.

The relevance of vague quantifiers and type interpretations shows that for‐ modification in these examples crucially differs from the earlier cases. In the examples at hand, the quantifiers have a non‐cumulative interpretation; they are interpreted with respect to contextually relevant subintervals. In the earlier examples, in contrast, quantifiers are interpreted cumulatively, with respect to the maximal interval. In light of earlier discussion, Moltmann's examples can be described as involving modification of the iterative or habitual time. The distinction between vague and absolute quantifiers is related to the availability of an iterative or habitual interpretation. Vague quantifiers—since they can be interpreted with respect to the event time, which is iterated—easily permit iteration of the event time predicate. Absolute quantifiers resist a similar interpretation; hence the necessity of a type interpretation if the event is iterated or recurs habitually.

In this approach, the difference between vague and absolute quantifiers in Moltmann 1991 is on a par with the difference that arises in the presence of a frequency adverb. A frequency adverb (sometimes, often, etc.) requires a habitual or iterative eventuality description. If no such interpretation is possible, then a frequency adverb is ungrammatical. This is borne out; as before, a type interpretation of the absolute quantifiers is required with frequency adverbs.


  1. a. John sometimes/often took a lot of pills

  2. b. #John sometimes/often took those pills

Both Moltmann 1991 and the present chapter address the relevance of quantifiers with respect to for‐adverbial modification, but concern different times. Moltmann 1991 shows that vague and absolute quantifiers pattern differently (p.250) with respect to for‐adverbs. I suggested that the difference is tied to the availability of iterative or habitual interpretation of the description, and the for‐ adverbs measure the iterative or habitual time in these examples. Decreasing quantifiers, when interpreted cumulatively, yield a divisible predicate of times and thus permit measurement by a for‐adverb. As suggested above, these for‐ adverbs modify the reference time.

13.7.2 Maximality and homogeneity

Zucchi and White 2001 address a different aspect of durative adverbial modification. They focus on incremental themes and discuss how homogeneity is affected by these arguments. Their discussion reveals the role of maximality in determining homogeneity. Based on Csirmaz 2005, I propose that the examples of maximality discussed in Zucchi and White 2001 are only relevant to events and the event time, and have no bearing on the predicates applying to other time intervals. The maximality effects are thus another source of difference in the homogeneity of the various predicates of times.

Incremental themes are often described as determining aspectual properties of the eventuality description. In present terms, these themes affect the properties of the event time predicate. A divisible incremental theme appears in a divisible event time predicate, and a non‐divisible theme in a non‐divisible predicate. The incremental theme argument of eat, for instance, determines the divisibility of the event time predicate, and therefore also the adverb that modifies the event time:


  1. a. Tracy ate a sandwich in ten minutes

  2. b. Tracy ate sandwiches for ten minutes

Zucchi and White 2001 note that several nominals behave unexpectedly under this correlation. Certain nominals are divisible, but can appear as incremental themes of non‐divisible event time predicates. The exceptional nominals include a sequence, a quantity (of milk), twig or bush. A sequence, for instance, is divisible, since a sequence is composed of smaller sequences. Contrary to expectations, these nominals can appear as incremental themes in both divisible and non‐divisible predicates of times (26). Decreasing quantifiers also appear in both divisible and non‐divisible event time predicates (27).

(26) Tracy wrote a sequence of numbers in a few minutes / for a few minutes

(27) Tracy ate fewer than ten sandwiches in ten minutes / for ten minutes

It appears that the correlation between divisibility of the incremental theme and that of the event time predicate breaks down: divisible incremental themes do not always enforce a divisible event time predicate. The correlation cannot (p.251) be upheld in the other direction either, because divisible event time predicates may have a non‐divisible incremental theme (Hay et al. 1999). The non‐ divisible theme can appear in a divisible predicate if the theme has a non‐ maximal interpretation. The incremental theme is only partially affected in this case:

(28) Tracy ate a sandwich for a few minutes (but then she stopped munching on it)

Zucchi and White 2001 argue against the apparent breakdown and propose an account to ensure a non‐divisible interpretation of the surprising incremental themes. The proposed account ensures that (a) the predicate containing decreasing quantifiers is not divisible and (b) the predicate containing a nominal such as sequence can be non‐divisible.

For decreasing quantifiers, Zucchi and White 2001 build on a proposal of Krifka 1992 and make use of the notion of maximal events. They suggest that the event with a decreasing quantifier, such as that of Tracy eating fewer than ten sandwiches, can be of two types (29). Either the sum of all sandwiches eaten must be fewer than ten, or the maximal event (which includes all events occurring at the subintervals of the event time) cannot contain an event of eating sandwiches.

(29) Tracy ate fewer than ten sandwiches

Neither of these events are divisible, thus the event time predicate in (29) is non‐divisible as well. By adopting the notion of maximal event from Krifka 1992, Zucchi and White 2001 ensure that the incremental theme is non‐ divisible. The event time predicate can thus be either non‐divisible or divisible, depending on whether the theme has a maximal or non‐maximal interpretation, respectively.

Zucchi and White 2001 offer two possible accounts for the behavior of exceptional indefinites such as a sequence. Only one of these accounts, the maximality approach, will be presented here, since it allows a uniform treatment of exceptional indefinites and other non‐divisible nominals. Zucchi and White 2001 note that, if the incremental theme has a maximal interpretation, then the theme is non‐divisible—and therefore a non‐divisible interpretation is also possible for the event time predicate. Under this approach, the event of writing a sequence at the event time t is the event whose theme is maximal among the sequences written in t. The non‐divisibility interpretation is thus available with a maximal interpretation. As before, divisible event time predicates can arise because of a non‐maximal interpretation of the event and the incremental theme.

(p.252) As Zucchi and White 2001 show, event time predicates with decreasing quantifiers and exceptional indefinites show a dual behavior. They can be either divisible or non‐divisible, depending on whether the maximal interpretation of the theme or event is enforced or not.

In contrast with event times, it appears that maximality plays no role in reference time predicates. For example, the reference time of Tracy ate fewer than ten sandwiches can either (a) contain a time of an event of Tracy eating a total of fewer than ten sandwiches or (b) not contain the time of Tracy eating a sandwich at all. The restriction of maximality effects to the event time is expected if maximality is tied to the presence of events, as in Krifka 1992, and as described above. Events are not relevant for the reference time predicate, hence no maximality effects are expected to arise within those predicates. The difference between the homogeneity properties of the event time and reference time predicates can thus be simultaneously upheld: Zucchi and White 2001 and the previous discussion address distinct predicates of times.

13.8 Time intervals, homogeneity, and modification

Let us summarize the main points of discussion. Finite clauses can contain a variety of time intervals. As shown, most of these times—except for the deictic speech time—can be modified. This flexibility of temporal modifiers easily accommodates the different interpretations of durative adverbs such as the English for‐adverb, which can measure the duration of any time interval. The different interpretations arise as a consequence of the different external merge positions; a durative adverb measures the time interval that is local to the merge position.

Durative adverbs impose a homogeneity requirement on the predicate that applies to the time interval measured. It was argued that homogeneity should be defined as divisibility—specifically as Strawson divisibility to accommodate the effects of decreasing quantifiers and only on adverbial modification. Concerning the relevance of homogeneity for aspectual properties, I argued that while homogeneity is relevant for telicity, it is independent of the property of stativity.

It was also noted that different quantifiers and argument types affect the homogeneity of predicates of times differently. On the one hand, maximality (of events and incremental themes) can affect the event time predicate; on the other, the contrast between vague and absolute quantifiers is relevant for iterative and habitual time predicates. Building on the effect of negation on adverbial modification, I noted that the for‐adverb licensed in this case—as well as in eventuality descriptions with decreasing quantifiers and (p.253) only—measure the reference time. A sufficiently detailed view of times can thus accommodate the distinct ways arguments affect homogeneity.

Finally, I suggested that the flexibility of for‐adverbs does not extend to all durative adverbials. Some equivalents of these adverbs, similarly to in‐adverbs, need to be explicitly constrained in terms of the time intervals they can measure—that is, the positions where they can be externally merged must be restricted to positions local to specific times. This restriction on times, which is independent of the homogeneity requirements, can occasionally mask the flexibility of durative adverb interpretation.


* I gratefully acknowledge the comments and help of Kai von Fintel, Danny Fox, Irene Heim, Sabine Iatridou, David Pesetsky, Katalin É. Kiss, Chris Piñón, and those of the audiences at the 30th Penn Linguistics Colloquium, the GLOW 29 Workshop on Adjuncts and Modifiers, the 16th Colloquium of Generative Grammar, and of NELS 37. All errors are mine.

(1) This approach differs crucially from the conclusions of Rákosi (this volume) about dative constituents. Concerning datives, mostly of experiencer and benefactive/malefactive interpretation, Rákosi argues for diversification; he argues that three types of constituents must be distinguished: dative arguments, theta-marked dative adjuncts, and (non-theta-marked) dative adjuncts. In contrast, I argue that durative adverbs are largely homogeneous, and the variable interpretation arises simply because of the various time intervals measured. A number of durative adverbs can, however, appear only in a limited type of environment; it is argued in section 13.6 that this restriction must be seen as being lexically determined.

(2) I assume (in agreement with most descriptions of aspectual systems, including Dahl 1985, de Swart 1998, and contrary to Michaelis 2004 and van Geenhoven 2005) that the iterative and habitual operators, as well as the times introduced by them, are distinct. While habitual eventuality descriptions may involve iteration (if the event which occurs habitually occurs more than once), they do not necessarily do so. It is possible for a habitual event to not occur even once, a property they share with generic descriptions. Likewise, iterative eventuality descriptions do not necessarily involve the lawlike regularity that is characteristic of habitual eventualities. I identify the operator responsible for habitual interpretation as HAB, but tentatively assume (following Krifka et al. 1995, Giorgi and Pianesi 1997) that it is a generic GEN operator which binds a temporal variable. In contrast with Krifka et al. 1995, I do not identify the temporal variable bound as the event time. Rather, I maintain that the operator can also bind the iterative time, whenever that is present—as in For ten years, Tracy played this song every afternoon, where the habitually occurring happening can be the repeated, iterative rendering of the song.

(3) The proposed range of time intervals is a collection of various times that have been argued for and adopted in several descriptions of aspect and tense. The inventory of times and the relevance of operators in introducing times is reminiscent of van Geenhoven 2005, who enumerates a number of aspectual operators that play a role in West Greenlandic. While the basic approach is shared between van Geenhoven 2005 and the present description as well as Csirmaz 2006b, there are some differences between the two approaches. Among others, the inventory of operators is distinct, and van Geenhoven 2005 appeals to cumulativity as the relevant property of homogeneity.

(4) In Csirmaz 2005, 2006b, I argue that divisibility should be defined differently, following the definition given in Hinrichs 1985. For present purposes, however, this definition is sufficient (though it will be modified later).

(5) The specific characterization of locality does not concern us here.

(6) Occasionally, agentivity diagnostics are also invoked to identify stativity (e.g. Smith 1991), building on the observation that states lack an agent argument. These diagnostics (which include imperatives, modification by agentive adverbs and grammaticality when heading the complement of force or persuade) also fail to support the stativity account. The diagnostics show that a negated agentive event predicate can have an agent argument, which is only expected under the homogeneity account.

(7) In fact, modification by in‐adverbs can be grammatical in the scope of negation while being marked in absence of negation (The line hasn't / # has moved in an hour). The polarity nature of these adverbs is explored in Hoeksema 2005.

(8) The implicature arises because the adverb appears as a contrastive topic. The in‐adverb measures the event time in (i), and, as a contrastive topic, it also gives rise to a contrastive implicature. In this case the adverb can be fronted because it cannot measure the topic time, hence the economy considerations do not block movement.

(i) [In one hour,] Tracy did not bike to work

(9) Following standard convention, (#xxx) indicates that the overt appearance of the material surrounded by parentheses leads to ungrammaticality; #(xxx) indicates that the omission of that material is marked.

(10) Note that the same problem arises if it is assumed, as in Emonds (this volume), that bare durative adverbs have a null P head. Under this assumption, it is the restricted distribution of null P‐headed adverb (or the licensing of a null P head) that is a problem.