Aspectual Classes and Scales of Change


Aspectual Classes and Scales of Change
Aspectual Classes and Scales of Change
John Beavers
The University of Texas at Austin
Standard models of aspectual classes focus on event decompositional or featural distinctions. However, such classifications often over- or under-generate,
and do not necessarily capture the temporal properties aspectual classifications are based on. I develop a predictive model of aspectual classes based on
theories of scalar change, taking two independently motivated properties of
scales as key: (a) how specific the predicate is about the theme’s final state on
the scale and (b) the scale’s mereological complexity. The resultant classification accommodates the standard Vendler dynamic classes, plus additional
classes that have proved difficult for prior approaches, and makes novel predictions about the relation of aspectual class and argument realization.
1. Introduction
Aspectual classes have been an important part of modern work in lexical semantics since at least Vendler (1957), with most researchers providing analyses for (or
arguing against) the following four aspectual classes:
a. States: love someone, know the answer, hear music
b. Activities: run (around), play in the garden, push a cart
c. Achievements: notice a painting, recognize a friend, die
d. Accomplishments: build a house, eat a pizza, paint a barn red
These classes are usually defined, or at least diagnosed, by their temporal properties. For example, as Rothstein (2004: 6–14) discusses, two properties that distinguish (1) are telicity — indicating an inherent endpoint to the event — and
having stages, i.e. describing events that have subevents that lead directly to other
subevents (Landman 1992: 22–24) (see Verkuyl 1993: 33–67 for an overview of
various such approaches). These temporal properties can be probed for by applying
aspectual diagnostics. For example, telic predicates are generally more acceptable
with in an hour than for an hour modifiers, while atelic predicates have the opposite pattern (Dowty 1979: 56–58). On this diagnostic, states and activities pattern
together as atelic, while accomplishments and achievements are telic, as in (2).
a. John knew the answer for/??in an hour.
b. John ran around for/??in an hour.
c. John noticed the error in/?for two minutes.
d. John built the shelves in/?for two hours.
(State, atelic)
(Activity, atelic)
(Achievement, telic)
(Accomplishment, telic)
Having stages is diagnosed by progressive aspect: in American English accomplishments and activities are acceptable in the progressive, but not states and achievements (though some achievements are better than others; Rothstein 2004: 36–58):
a. #John is knowing the answer.
(State, no stages)
b. John is running around.
(Activity, stages)
c. #John is noticing the error.
(Achievement, no stages)
d. John is building the shelves.
(Accomplishment, stages)
These cross-cutting diagnostics thus derive (1) via the binary features [±stages,±telic].
However, as Rothstein also notes, such a classification is inherently unexplanatory inasmuch as it does not explain why different predicates have the temporal
properties they do. Intuitively, achievements and accomplishments are telic because they specify particular result states that characterize the end of the event, unlike states and activities. Similarly, subevents of states are too homogeneous to constitute separate stages, and achievements are punctual and thus have no subevents
at all. Accomplishments and activities are durative and heterogenous enough to
have stages. A more explanatory analysis should take such factors into account.
Furthermore, a classification based on binary features is problematic in light of
the fact that there are predicates that do not neatly fit Vendler’s four classes, including semelfactives (Smith 1991: 29–30 and Beavers 2008) and degree achievements
(Dowty 1979: 88–90 and Hay et al. 1999) (see also Rothstein 2008):
a. Semelfactive: John kicked the car (once/repeatedly).
b. Degree achievement: John cooled the soup.
Semelfactives are like achievements in allowing punctual readings, but unlike achievements they also allow iterative readings (I reserve the term “semelfactive” for the
punctual reading). Degree achievements entail a result like accomplishments, but
are atelic like activities (though they may be telic in some contexts; I assume the
atelic reading is basic and the telic reading derived from it). No set of binary features will generate six classes without additional constraints.
An alternative analysis is that aspectual classes derive from the types of events
different predicates describe, commonly analyzed via lexical event decompositions, usually based on Dowty (1979: Ch.2) (though Dowty revised his own analysis in his third chapter). An example is given in (5), taken from Rappaport Hovav
and Levin (1998: 108), where a state is the predication of a state over an individual,
an activity is the predication of an action, an achievement is the coming about of a
state, and an accomplishment is an action that causes a state to come about. (Other
classes could be defined by other decompositions and/or event types.)
a. States: [ x < STATE > ]
b. Activities: [ x ACT<M AN N ER> ]
c. Achievements: [ BECOME [ x < STATE > ] ]
d. Accomplishments:
[ [ y ACT<M AN N ER> ] CAUSE [ BECOME [ x < STATE > ] ] ]
However, while event types and subevent structure are undoubtedly necessary
for aspectual classification, they alone are not sufficient to define a classification
that accounts for the temporal properties in (2) and (3). For example, BECOME
events may or may not have stages and/or give rise to telicity, as in (6) and (7)
respectively (though the degree achievement in [7b] can be telic in some contexts).
a. #The vase is breaking in an instant.
b. The water is evaporating slowly.
(BECOME without stages)
(BECOME with stages)
a. The vase broke in/?for five minutes.
(Telic BECOME)
b. The vase cooled for/in five minutes.
(Atelic BECOME)
CAUSE and ACT are similar. Thus standard subevent types alone do not define aspectual classes, since they do not determine the relevant diagnostic temporal properties (see also Rappaport Hovav 2008). But then what does?
It is now widely recognized that a predicate’s temporal properties also reflect
how certain of its arguments are expressed (Tenny 1994; Krifka 1998, inter alia),
which I refer to as “incremental arguments”. A standard example are patient objects
of consumption verbs (Dowty’s 1991: 567–568 “incremental themes”). When the
object is realized by a DP with quantized reference (no proper part of an entity in
its denotation is also in its denotation) the predicate is telic, otherwise it is atelic:
a. Mary drank a glass of wine in/?for an hour.
b. Mary drank wine for/??in an hour.
One standard analysis is that the event is related to the object homomorphically
so that the endpoint of the event is known only if the object’s quantity is known.
If incremental arguments figure into the temporal properties that define aspectual
classes, aspectual classes should be defined directly or indirectly in terms of them.
In this paper, I propose such an analysis based on work on scalar change (Hay
et al. 1999; Wechsler 2005; Beavers 2008, 2011, in press, Kennedy and Levin 2008;
Rappaport Hovav 2008), where change is defined as some theme transitioning to
and maintaining a new value along some property scale, which is an incremental
argument. I show that temporal facts such as those in (2) and (3) arise from crossclassifying predicates by two independently motivated properties of the scale:
a. The specificity of the endpoint along the scale
b. The mereological complexity of the scale
I outline a version of the scalar analysis in Section 2, and discuss the factors in (9)
in Section 3. I show in Section 4 that the aspectual classes in (1b-d) plus those in
(4) arise from classifying predicates by the two factors in (9). In Section 5 I further
motivate this proposal by showing that it makes novel predictions about argument
realization that also correlate with the factors in (9). I conclude in Section 6. For
space reasons I ignore states and focus only on dynamic predicates. Thus having
stages reduces to durativity since only durative dynamic predicates have stages but
not punctual predicates (see above); I discuss durativity diagnostics in Section 3.2.
2. Scales of change as incremental arguments
It is often assumed that there are three types of incremental arguments (Tenny
1994: 15–18), sometimes thought to stand in different homomorphic relationships
to the event (Krifka 1998). For creation/consumption predicates (10a), the patient
is the incremental argument, as above. For motion predicates (10b), the path is
the incremental argument, and the predicate is telic only if it indicates an explicit,
reached goal. For change-of-state predicates (10c) a property of the patient is the
incremental argument, and the predicate is telic only if the result is fully specified.
a. John ate (the) sandwiches.
b. John walked (to the store).
c. John scrubbed the sink (clean).
Work on scalar change has instead unified these distinct types of incrementality under a single rubric, wherein all entities have properties — volume, location, color, etc. — that form scales along which they can transition. For example,
hℜ, >,WARMTHi is a scale consisting of a property dimension (WARMTH), a set
of values along that dimension (the real numbers ℜ), and an ordering > of those
values (Hay et al. 1999 and Kennedy and McNally 2005), and (11) describes a transition of the theme from some w ∈ ℜ in its WARMTH to w′ ∈ ℜ, where w′ > w.
The soup warmed.
On a scalar analysis, each predicate in (10) encodes a three-way relation between
an event, a theme, and a scale, and differ only in what the scale is. For changeof-state the scale is a property scale, for motion it is a directed path, and for creation/consumption it is the physical extent of the theme. I adopt the version of this
analysis of Beavers (2008), who builds on Krifka (1998: 222–230), where a scale
hR, >, δi of values R on dimension δ ordered by relation > is a mereologically
complex “path” s in set P H (the connected, directed paths), as in (12) (for any
domain U X , for entities x, y ∈ U X , x < X y means x is a proper part of y).1
a. For each r i ∈ R (1 ≤ i ≤ n) there is a unique si < H s;
b. The scale s is the join of all such si (s = i= n si );
c. If r i > r j then sj precedes si on s (sj ≪ H si )
Thus a scale is analyzed as a directed path leading from a source state to a final
state through all successive states in between (see also Verkuyl 1993 and Zwarts
2006 for related approaches).2 As sources are not ultimately relevant here I ignore
them, giving Neo-Davidsonian representations for the three predicate types in (10)
as in (13), where the first conjunct indicates the type of event and its participants
and the second its final state on s; result′ is defined as in (14) to indicate the goal
g on s in e and the existence of a specific, contextually-defined source b.
a. John walked to the cafe.
∃e∃s[walking′ (j, s, e) ∧ result′ (s, cafe, e)]
(s is a path scale)
b. John warmed the pie to 100◦ .
∃e∃s[warming′ (j, p, s, e) ∧ result′ (s, 100◦ , e)] (s is a warmth scale)
c. John ate the pie.
∃e∃s[eating′ (j, p, s, e) ∧ result′ (s, 0, e)]
∀s∀g∀e[result′ (s, g, e)
(s is an extent scale)
↔ [SOU RCE(s, b, e) ∧ GOAL(s, g, e)]]
The incremental effects of scales follow from the way predicates relate their
events to their scales via a single mereological homomorphic θ-relation in (15),
where the event is measured out by adjacent transitions along the scale.
Movement Relation (MR): each part of e corresponds to a part of s and
vice versa, temporal adjacency in e corresponds to spatial/scalar adjacency
in s, and the initial and final points in e are mapped uniquely to the initial
and final points in s respectively.
(adapted from Krifka 1998: 225, (71))
This MR preserves endpoints and adjacency, so that the event begins with the theme
at the source state, and as it progresses temporally the theme transitions along the
scale through successive, adjacent values until the event ends at the goal state.
I adopt the definition of telicity in (16), where an eventive predicate is telic iff
for any event it describes it does not describe any subevent not sharing the same
final point (following Beavers in press, slightly revising Krifka 1998: 207, (37)):
φ is telic iff for any event e it describes it describes no non-final e′ < E e.
From (15) and (16), telicity follows from overt boundedness of the scale, which
determines the bound on the event. For the motion predicate with an explicit goal
in (17), any e it describes is MR-related to a path s from some given source to the
cafe. By (15), any non-final e′ < E e is thus MR-related to some non-final s′ < H s.
But s′ , being a non-final proper part of s, cannot itself be a path to the cafe and thus
cannot be the path in (17). Therefore (17) cannot describe e′ , making (17) telic.
John walked to the cafe in/?for an hour.
∃e∃s[walking′ (j, s, e) ∧ result′ (s, cafe, e)]
But if the goal is unspecified as in (18), then some non-final s′ < H s will match
(18), since for any s leading to some arbitrary goal there are non-final subpaths that
lead to an arbitrary goal (e.g. to the location just prior to the goal on s). Thus e′ and
e are both described by (18), which is therefore atelic (note that all translational
motion has a goal, as encoded in [18], though due to looping it may be the source).
John walked for/??in an hour.
∃e∃s∃g[walking′ (j, s, e) ∧ result′ (s, g, e)]
The crucial distinction is between predicates that specify the exact goal reached,
and those that simply say that a goal exists.
This analysis works for change-of-state as in (19) and creation/consumption
predicates in (20), where the formal properties are identical and all that differs is
the scale type. (As per Section 5, consumption verbs with unspecified results are
reflected in the conative oblique, e.g. some pie was eaten, but no given amount.)
a. John warmed the pie to 100◦ in/?for an hour.
∃e∃s[warming′ (j, p, s, e) ∧ result′ (s, 100◦ , e)]
b. John warmed the pie for/??in an hour.
∃e∃s∃g[warming′ (j, p, s, e) ∧ result′ (s, g, e)]
a. John ate the pie in/?for an hour.
∃e∃s[eating′ (j, p, s, e) ∧ result′ (s, 0, e)]
b. John ate at the pie for/??in an hour.
∃e∃s∃g[eating′ (j, p, s, e) ∧ result′ (s, g, e)]
I now outline two previously motivated scalar properties — specificity of the goal
and mereological complexity — by which we can analyze aspectual classes.
3. Properties of scales of change
3.1. Degree of affectedness as specificity of transitions
I first discuss the different ways a predicate can specify what transition occurred
along a scale, recapping Beavers (2011). Scalar change is a type of affectedness,
but affectedness is generally assumed to be a matter of degree (Hopper and Thompson 1980: 252–253). Consider (21), where intuitively the apple is increasingly less
affected from (21a) to (21d): with peel it is completely de-skinned, with cut it is
cut but not to a specific degree (in half, in many pieces, etc.), with hit it is impinged
but no change need obtain, and with see there is not necessarily any impingement.
a. John peeled the apple.
b. John cut the apple.
c. John hit the apple.
d. John saw the apple.
These degrees of affectedness are not just intuitionistic; they are distinguished
linguistically. Together (21a-c) take what Rappaport Hovav and Levin (2001: 786–
787) call “force recipients” objects, i.e. participants which take the brunt of the
force of an action and might change as a result, satisfying the What happened to X
is Y test (see also Cruse 1973: 13, Jackendoff 1990: 125–130):
a. What happened to the apple is that John peeled/cut/hit it.
b. #What happened to the apple is that John saw it.
Further, only (21a,b), a subset of force recipient predicates, entail an actual result:
a. #John peeled/cut the apple, but nothing is different about it.
b. John hit/saw the apple, but nothing is different about it.
Finally, only (21a) is telic:
a. John peeled the apple in/?for five minutes.
b. John cut/hit/saw the apple for/#in five minutes.
(on intended reading)
Crucially, these three diagnostics group the predicates in (21) into a subset relation,
where predicates satisfying n tests are a subset of those satisfying n − 1:
Change entailed
What happened to X is Y
peel x
cut x
hit x
see x
Beavers (2011) analyzes these facts in a scalar model in terms of how specific the predicate is about the theme’s progress on the scale. Theme x undergoes
a quantized change on scale s in event e described by predicate φ iff φ entails that
x reaches a specific state gφ on s, while x undergoes a non-quantized change iff
all that is entailed is that some result state g obtains. To model impingement for
impact and contact predicates, Beavers proposes that x has potential for change:
it is associated by the predicate with a scale — there is some specific set of possible changes that could occur due to the type of action the predicate describes —
but there is not necessarily any change, meaning no incremental MR relation need
obtain (cp. the latent aspectual structure of Tenny 1992: 20, (42)). For example,
Beavers notes that impact predicates like kick tend to occur in resultative constructions indicating damage and motion (see Boas 2003: 321–340; Appendix A), in
line with the sort of action they describe. Finally, x is unspecified for a change if
it simply is an event participant. These degrees of affectedness are summarized in
(26) (where θ is the role of the theme).
a. x undergoes quantized change iff φ → ∃e∃s[θ(x, e) ∧ result′ (s, gφ , e)]
(scale is bounded, e.g. peel, break, shatter x)
b. x undergoes non-quantized change iff φ → ∃e∃s∃g[θ(x, e) ∧ result′ (s, g, e)]
(scale is unbounded, e.g. cut, widen, lengthen x)
c. x has potential for change iff φ → ∃e∃s∃θ′ [θ(x, e) ∧ θ′ (s, e)]
(latent scale, no MR, e.g. hit, wipe, scrub, rub x)
d. x is unspecified for change iff φ → ∃e[θ(x, e)]
(no scale, e.g. see, smell, play (as children), ponder x) (cf. Beavers 2011: (60))
As defined in (26), these degrees of affectedness form the implicational Affectedness Hierarchy in (27): a quantized change entails a non-quantized change,
which entails potential for change, which entails being in the event.
For all x, φ, quantized → non-quantized → potential → unspecif ied
This captures the subset relation in (25) once we define What happened to X is Y
and entailment diagnostics by the weakest truth conditions they pick out:
a. What happened to x is φ is felicitous iff φ is felicitous and entails x has
potential for change.
b. φ, but nothing is different about x is infelicitous if x undergoes nonquantized change in φ. (Beavers 2011: (65), (64))
Due to the implicational nature of (27), if What happened to X is Y picks out potential change it also picks out (non-)quantized change, since these entail potential
change, and similarly for entailing change. Most relevant, only quantized change
ensures telicity (see Section 2). Thus affectedness is modeled as how specific a
predicate is about the result on the scale, and (a)telicity is one consequence of this.
3.2. Durativity and mereological complexity
Scales are also known to come in two types, evidenced by the existence of two
types of terms that describe values on scales (Kennedy 1999: xiii–xv). Non-gradable
scalar terms describe values on scales that consists of just two values, φ and ¬φ, and
resist comparative morphology. Gradable scalar terms describe values on scales
that have more than two values, and are acceptable with comparative morphology:
a. Non-gradable: dead, #more dead, pregnant, #more pregnant
b. Gradable: clean, cleaner/more clean, polished, more polished
Similarly, durativity has to do with the mereological complexity of the event (Engelberg 1999, 2000), diagnosable by temporal modifiers. Punctual predicates are
acceptable with in-modifiers only on an after reading, while durative predicates
allow both an after and a during reading (Kearns 2000: 206):3
a. The settler will cross the border in ten days.
(after ten days)
b. The settler will cross the desert in ten days.
(after/during ten days)
The smallest dynamic events — punctual events — have exactly two atomic parts,
a beginning and an end, the minimum number of points in time needed to tell a
change or action occurred (Dowty 1979: 168–173, Beavers 2008: 248). Durative
events have more than two parts, including also a middle. Thus both scales and
events come in two key mereological types: two atomic parts, or more than two.
Crucially, durativity mirrors scalar gradability as outlined in (31): crossing a
path consisting of just two points — a border as in (30a) — determines a punctual
event, while crossing a more complex path determines a durative event, as in (30b).
a. non-gradable scale ≈ punctual event
b. gradable scale ≈ durative event
As Beavers (2008: 254–260) discusses, this correlation follows directly from the
MR between the scale and the event, assuming the following three complexity
types for all objects (for x, x′ ∈ U X , x ⊕ X x′ is their join):
a. Strict atom (STM) (no proper parts): ∀x[ST M (x) ↔ ¬∃y[y < X x]]
b. Simplex (SMP) (just two proper parts):
∀x[SM P (x) ↔ ∃y∃z[(x = y ⊕ X z) ∧ (y 6= z) ∧ ST M (y) ∧ ST M (z)]]
c. Complex (CMP) (>2 proper parts): ∀x[CM P (x) ↔ ∃y[y < X x ∧ SM P (y)]
By the MR a transition along a simplex scale requires all and only two points
in time, and thus a simplex event, whereas a complex scale requires a complex
event, giving us (31) (see Beavers for details). Furthermore, punctual predicates
are always telic because they describe events that have exactly two atomic proper
parts, and neither of these two parts will satisfy the predicate, thus satisfying (16).
Thus we have now defined two key temporal diagnostics of dynamic predicates —
telicity and durativity — in terms of two properties of the scale. I show next that we
can use these two properties to define a comprehensive set of aspectual classes.4
4. The interaction of affectedness and scalar complexity
Above I defined four affectedness types formally — four degrees to which a predicate can be specific about what transition along a scale occurred — and two mereological complexity types. Cross-classifying dynamic predicates by these two properties produces the eight-way system in (33) that I show subsume all of the Vendler
classes, albeit cross-cutting one of them, and provides a natural home for degree
achievements and two types of semelfactives, totaling seven predicate classes. The
eighth theoretical possibility I argue below is independently ruled out. In the top
two rows of (33), an MR necessarily holds, thus event and scalar complexity are
correlated and not distinguished. In the lower two rows no MR necessarily holds
(even if there is a latent scale), and thus the predicates are classified solely on the
basis of whether the events they describe are independently simplex or complex.
Simplex scale (and/or event)
break a vase, kill Bill
hit (once), slap (once)
cough (once)
Complex scale (and/or event)
load the wagon, eat the apple
cool the soup
beat, pummel
watch TV
Each cell in (33) represents predicates whose denotations have various formal properties defined in Section 3, thus predicting specific aspectual properties, and these
give rise to the aspectual classification.
In the upper left are predicates that describe changes along simplex scales —
simple, binary transitions — and the change is quantized. These predicates are
therefore both telic and punctual, and thus are achievements. In the upper right we
have essentially the same properties, save that here the event and scale are complex.
These predicates are telic and durative, and thus are accomplishments. In the lower
right are two classes where there is no necessary transition along a scale, and thus
the predicates are atelic. Here the event is complex (due to non-scalar factors; see
below), so that these predicates constitute Vendler’s activity class. The difference
between the two types of activities is potential for change, which is irrelevant for
temporal properties (and thus indicated by a dotted line) but will be relevant for
linking aspectual classes to argument realization in Section 5. Thus these classes
correspond to Vendler’s dynamic classes, with activities split into two.
In addition, (33) provides a natural analysis for two more classes. Semelfactives are defined in the lower left. Like activities, they do not entail scalar change,
and there is again a temporally irrelevant distinction between those that do and
do not carry potential for change. However, the events semelfactives describe are
simplex, and thus they are punctual and telic (this is often obscured by the possibility of iterativity; modification by once may rule this out). Fundamentally, then,
the difference between activities and semelfactives boils down to whether — for
whatever reason — the events they describe are naturally simplex or complex. This
may follow from the types of actions or manners encoded in specific predicates as
discussed by Beavers (2008: 260–262), and/or what Rothstein (2008: 186) calls
“natural atomicity” — whether minimal events described by the predicates are
“perceptually salient and given by the world”, something that gives rise to what
a reviewer calls their “precise countability” (see also Rothstein 2004: 183–187).
However, the reviewer also suggests that there may be more to semelfactives,
including “resettablity” (Talmy 2000: 63–64), i.e. at the end of the event things
have returned to their prior state (Talmy gives #The beacon flashed and then went
off). This of course ties into the iterability of semelfactives and lack of this for
achievements, which is easily accommodated on the approach outlined here: achievements necessarily require result states that must be explicitly and separately undone
for iteration to obtain, and semelfactives do not require this (and if the reviewer is
right in fact require resetting) and thus immediate iteration is possible. That said,
I disagree that all semelfactives require resetting; it is no contradiction (to me) to
say I hit the car (once), but my hand got stuck so I never pulled it away. However,
if resettability is part of even some semelfactives, they would thus require more
than two points, e.g. an event of John winked (once) requires a minimum of three
moments to be instantiated: the eye is open, it is closed, and then it is open again.
Any subset would be just a closing, just an opening, or just stasis. In this case John
winked (once) is in fact a short activity, belonging in the lower right side of (33),
as opposed to the hit example above, which requires just two points and is in the
lower left (and, as the reviewer notes, so do verbs like cough). In this case the set
of things traditionally termed “semelfactives” might include what I have labeled
semelfactives in (33) plus some short activities, although the cell of truly two-point
semelfactives is both predicted and attested. Nonetheless, I leave open what other
factors are relevant for defining and distinguishing semelfactives and activities.
Finally, in the second row, righthand column, are predicates that (a) entail
change, (b) are atelic since the change is non-quantized, and (c) are durative. These
are exactly the properties of degree achievements. Thus (33) provides a natural
analysis for all of the Vendler dynamic classes plus the additional classes mentioned in Section 1, and correctly predicts their aspectual properties. However, a
predicate may be vague as to one or more of these properties, and thus may sit in
several of the cells in (33), unless context fills in the relevant factors. For example, canonical degree achievements such as The soup cooled entail non-quantized
change, but this just means they are vague about what change occurred. As Hay
et al. (1999: 136–138) note, in a specific context (e.g. the soup is always cooled
to a certain temperature), degree achievements may behave like accomplishments.
Still further, for many such predicates the scale may be reduced or reconceptualized as simplex (see also Beavers 2008: 251–252), in which case the interpretation
becomes that of an achievement (e.g. The soup cooled slightly/a minimal amount
(from its original temperature)). Likewise, while semelfactives describe events that
are naturally simplex, they may be iterated. Thus the same predicate may be durative in context (on the iterative reading), i.e. it may also be a de facto activity.
Interestingly, one class in (33) is unattested: simplex, non-quantized changes.
I argue that this class is uninstantiated because it is truth-conditionally equivalent
to simplex, quantized changes, i.e. achievements. To see why, consider why the
contrast between quantized and non-quantized change along a complex scale is
semantically contentful. A quantized change along a complex scale as in (34) is
a change from some initial state b to some final state g through all intermediate
states, represented by the top arrow in (34). A non-quantized change, however, is
a transition from some initial state b to some other state on si , which could be any
state leading up to and including g, as indicated by the bottom arrows in (34).
b ⊕H s ⊕H s ... ⊕H sn− ⊕H sn ⊕H g
Thus on a complex scale quantized and non-quantized change are semantically
distinct. But on a simplex scale as in (35), there are only two possible states, b and
g. A quantized change, indicated by the top arrow, indicates a transition from the
one state to the other. For non-quantized change, the theme left state b and entered
some other state. But on a simplex scale, the only other possible state is g, as per
the bottom arrow, leading to the exact same meaning as a quantized change.
b ⊕H g
I therefore suggest that no predicate ever directly instantiates a simplex, non-quantized
change, since it would be semantically indistinguishable from an achievement, explaining why (33) has only seven distinct classes. Thus we have an analysis of
aspectual classes based on the scale’s complexity and the specificity of its endpoint
that predicts exactly the right number of classes and their temporal properties. I
turn next to an additional prediction of this analysis that further supports it.
5. Argument realization and aspectual classes
Beavers (2010) has employed the theory of affectedness reviewed in Section 3.1 to
model certain argument realization facts, and I now show that the analysis of aspectual classes in the previous section is further motivated by a significant interaction
with these data. My core example is the English conative alternation (Guerssel
et al. 1985; Levin 1993; van der Leek 1996; Broccias 2003). A standard analysis
of the conative is that it indicates the contrast between an actual change of state vs.
an attempted (though still possibly realized) change of state (Levin 1993: 41–42):
a. Marie cut the rope, #but nothing is different about it.
b. Marie cut at the rope, but nothing is different about it.
This also explains why verbs that do not entail change, such as touch, do not show
the conative. However, not all transitive change-of-state verbs permit the conative:
a. John broke/bent/curved/polished/cleaned the razor.
b. *John broke/bent/curved/polished/cleaned at the razor.
Guerssel et al. (1985: 58–60) explain this by proposing that only verbs where the
agent manipulates an instrument show conatives, giving the final analysis in (38).
a. Object: The agent manipulates some instrument and moves it into contact with the patient, effecting a change on the patient.
b. Oblique: The agent manipulates some instrument and attempts to move
it into contact with the patient in order to effect a change on the patient.
This rules out all of (37), since arguably none of these verbs require an instrument.
However, there are several problems with this analysis. First, the constraint
that the object variant entails a change is too strong. Impact predicates show the
conative but do not entail an effect in the object variant:
a. Marie hit/kicked DeFarge, but nothing is different about her.
b. Marie hit/kicked at DeFarge, but nothing is different about her.
Second, the constraint that the oblique entails merely attempted change is also too
strong. Some consumption verbs (e.g. eat, drink, sip, gnaw) also show conatives:5
a. He continued to think on it as he slowly ate at his fries. Chomping them
into his mouth without thinking about it since his mind was somewhere
else entirely. (
b. Then he shivered and smoked and drank at his beer, and hunched his
shoulders against the South Dakota cold. (
c. Nate stared over the rim of his coffee–content enough to simply sip at
his drink and watch the man finish off the last of his chicken sandwich.
For at least some of these verbs, change is entailed in both variants as in (41), since
both entail that some of the object is consumed (as noted also by Broccias 2003:
301–303), although only in the object variant must all of the patient be consumed,
or at least some contextually-determined portion of it, as in (42).
a. ... he ate his fries, #but none of them were eaten.
b. ... he ate at his fries, #but none of them were eaten.
a. ... he ate his fries, #but left nearly all of them behind.
b. ... he ate at his fries, but left nearly all of them behind.
One could save (38) by arguing that the relevant “attempted” change is complete
consumption, regardless of other changes entailed by both variants. However, the
oblique variant does not necessarily entail an attempt to eat all of the patient. One
can eat at something just to nibble it, with no notion to eat it all. Thus the very
notion of “attempted change” is not consistently a part of the oblique variants.
This is also shown for a related class discussed for German by Frense and
Bennett (1996: 309–310), which (despite their claims), occur in English as well,
namely conatives of verbs of creation, including write, build, and (as a reviewer reminds me) knitting verbs like knit and sew. For most of these verbs the appropriate
preposition in the oblique variant is on (the reviewer notes that at works as well,
though perhaps on an intensive reading as per He knitted (away) at his sweater).6
a. Im not in the mood to write on my dissertation today so I thought Id talk
about how we are getting on at Inferno, ... (
b. She knitted on her scarf for awhile and decided that she wanted to
try the crochet projects out that she had brought. (crochetsoiree.
c. Legend has it that Mrs. Winchester was told by a psychic that in order to appease the spirits that killed her husband and newborn daughter, she had to build on her house continuously for the rest of her life.
Both variants require change, the object variant further requiring complete change:
a. She built her house, #but it is not (entirely) built/none of it is built.
b. She built on her house, but it is not (entirely) built/#none of it is built.
Again one cannot say the semantics of the oblique variant is attempted complete
change, since one could knit or build on something without a goal of ever really
finishing it. (The Winchester House example in [43c] is apt in this regard.)
Third, the instrument condition does not always obtain; while hit/kick arguably
involve an instrument (if a body part can be counted as such), eat does not (unless,
as a reviewer notes, the mouth/teeth are viewed as an instrument, though for Guerssel et al. an instrument is wielded and moved towards the patient). However, it is
surely the case that some manner condition obtains. For example, Broccias (2003:
309–322) suggests that conatives fall into three classes he refers to as allative, ablative, and allative-ablative, the first for motion towards the patient such as hit/cut
at (i.e. the instrument class above), the second for motion that takes things away
such as eat/chip at, and the third for a criss-cross of the two such as tear at.
Thus the generalization seems to be that the conative (a) has different effects
for different verbs, which often has some correlation with affectedness, provided
(b) some manner condition obtains. For present purposes I set the manner condition
aside and focus just on what affectedness contrasts obtain and why. Beavers (2010)
proposes an analysis wherein the semantic effect is that the object variant entails
some verb-specific degree of affectedness n on the Affectedness Hierarchy in (27)
(repeated here), and the oblique variant encodes degree of affectedness n − 1:
quantized → non-quantized → potential → unspecif ied
On this analysis, the eat/write conatives represent a contrast between quantized and
non-quantized change (exactly as analyzed in Section 2), as exemplified in (41) and
(42), which show that (a) some change occurs in both variants but (b) only in the
object variant is a specific change entailed (and telicity ensured). For cut conatives
the object variant entails non-quantized change, but the oblique variant entails only
potential for a change, as shown by the What happened to X is Y test:
a. John cut the rope for/??in an hour, #but nothing changed about it.
b. John cut at the rope for/??in an hour, but nothing changed about it.
c. What happened to the rope is John cut (at) it. (Beavers 2010: 838, (45))
A reviewer suggests that the oblique necessarily requires contact, which explains
the potential for change (and thus the What happened to X is Y facts). However, my
intuitions are that a miss is possible, as in (47) (and ?What happened to his face
was that I slash at it, though I narrowly missed is still relatively acceptable to me).
She slashed at his face but James ducked and Gatomon flew over him and
hit the ropes. (
Furthermore, potential change is not technically defined by contact and thus does
not necessarily require it, though that may give rise to it. That there is still potential for change in (46c) without it may be because the described action is such
that if contact were made, the likelihood of a change is very great, as suggested
by Beavers (2010: 835), who adopts a slightly different analysis of potential for
change as not just a latent scale but also change along that scale in some possible world (in which appropriate test conditions obtain for verifying that change,
building on Cross 1986). Finally, for verbs that entail only potential for change in
their object variants, such as hit/kick, the oblique variant entails no potential for
change. The idea that hit at does not entail potential change is perhaps hard to see
intuitively, but What happened to X is Y demonstrates this:
a. What happened to the rope is John hit it.
b.??What happened to the rope is John hit at it. (Beavers 2010: 838, (48))
The analysis, summarized in (49) (Beavers 2010: 839, Table 3), captures the fact
that while decreased affectedness is part of the conative, the effect is verb-specific.7
However, given the aspectual classification outlined in Section 4, there is an
alternative conception of (49). In particular, once scalar complexity is taken into
account, the Affectedness Hierarchy also determines an aspectual classification of
predicates. On these grounds we can can recast (49) not simply as a decrease in
affectedness, but as an aspectual class shifting operation that “moves” a predicate
of one aspectual class in (33), repeated here, “down” one.
Simplex scale (and/or event)
break a vase, kill Bill
hit (once), slap (once)
cough (once)
Complex scale (and/or event)
load the wagon, eat the apple
cool the soup
beat, pummel
watch TV
Thus the conative turns accomplishments like eat/write into eat at/write on, which
are atelic but entail some result, and thus are de facto degree achievements (having
the same temporal properties as canonical degree achievements like cool). It also
turns a (de facto) degree achievement like cut into a potential change activity cut
at as in (51a). However, due to the type of action described the oblique also allows
a semelfactive reading (one quick movement of the blade) as in (51b).
a. Aldous turns to his meal and cuts at it slowly as he listens to Ethan.
b. Derek cuts at him once, twice, and draws blood both times. (bigbadron.
Finally, potential change activities/semelfactives (hit/kick on either reading) become unspecified change activities/semelfactives (hit/kick at on either reading).
That hit/kick (at) instantiate both semelfactive and activity conatives is exemplified
by the fact that they can occur in both variants in both contexts:
a. Then they spit on him and took the stick and hit him repeatedly on his
head. (
b. Anomen hit at him repeatedly with an urgent rage, each brutal hit of
Crom Faeyr making the undeads body clench under the physical pain
and the burning of the lightning arching through his body. (www.shsforums.
a. Finally, hit him once in the belly when he returns from taking a few steps
b. The boy hit at her once more, grazing her shoulder, and she brought
her fist back, taking a step forward and planting it on his nose. (s3.
That said, an alternative is that potential to unspecified conatives are only possible as either semelfactives or activities, and the appearance of the other type is
subsequently derived from the allowed one by (de-)iteration of the variants (as I
suggested above for semelfactive cut at derived from activity cut at). However, this
would require additional constraints to rule one type out. The simpler assumption
is that conatives are possible for both activities and semelfactives, and thus every
possible aspectual class contrast defined by one degree of affectedness in (50) is
instantiated in the conative for attested classes.8
So far, however, this is just the same operation as proposed by Beavers (2010),
albeit also taking an additional formal property, mereological complexity, into ac17
count. However, there is a crucial property of the English conative virtually unnoticed in the literature that supports the relevance of this additional feature to
the operation, namely that the conative rarely applies to categorical achievement
predicates (see Rosales Sequeiros 2005 for a similar observation on Galician):
a. John pierced/punctured/pricked/cracked/broke/split the tire.
b. *John pierced/punctured/pricked/cracked/broke/split at the tire.
The instrument/manner condition (however defined) may explain the lack of an
oblique variant with some of the verbs in (54) such as break (as above). However,
verbs like pierce, puncture, and prick meet Guerssel et al.’s instrument condition,
and fall into Broccias’s allative class, and yet still do not show the conative, suggesting that another explanation is necessary. It cannot be a ban on punctual oblique
variants, since these are possible (see [53b]). So what is the explanation?
Crucially, recall that the predicate class of non-quantized, simplex change in
(50) — the class “below” achievements — is independently ruled out, since it is
semantically indistinguishable from achievements. This fact gives us a very simple
account of the data in (54): if the conative involves shifting the aspectual class of
a predicate by reducing the entailed degree of affectedness by one, then any transitive achievement to which the conative is applied will result in a predicate that
entails non-quantized change along a simplex scale. But this would be a semantically vacuous operation, since the output would be a marked way of expressing
what the transitive variant of the predicate already encodes and which no verb ever
lexicalizes on its own. Thus I suggest that for this reason the operation is simply
blocked for achievements, explaining the data in (54) in one single generalization
that builds on an independently motivated gap in the paradigm. Further support for
this analysis comes from creation/consumption predicates, which normally show
conatives, that are made punctual by virtue of taking themes that have minimal
volume/extent, thus reducing the volume/extent scale to a simple “exists” vs. “nonexists” contrast. In this case the conative becomes less acceptable:
a. She puzzled over this as she prepared herself for bed and drank a tiny
drop of the potion he had provided for her. (
b.??She drank at a tiny drop of potion.
The possibility of this analysis only arises when we view aspectual classes as we
did in the previous section, as a cross-classification by scalar properties. But since
the same properties also figure into argument realization, we might expect a significant interaction, which is exactly what we find, further supporting this analysis.
This in turn means the conative is an indicator of aspectual class: predicates that
undergo it are not achievements. I discuss some further issues in the next section.
6. Conclusion
I have argued that a scalar model of change provides a way to generate a full suite
of aspectual classes, including the traditional Vendler dynamic classes plus others. The relevant properties are two independently motivated factors that pertain to
constraints the predicate places on the scale argument:
a. Four types of specificity of the endpoint along the scale
b. Two types of mereological complexity of the scale
The resultant classification accommodates all of the Vendler dynamic classes, plus
others that go beyond this classification, and is supported by correlating argument
realization facts that rely on the same two properties. This analysis thus further
supports and motivates the scalar analysis of change, providing an additional case
study for its utility and correlating predictions.
However, the classification presented here is of course preliminary — it is
likely that there are further subclasses of the predicate types discussed here. I
briefly discuss three potentially problematic points and some conclusions. First,
although I based the notion of accomplishment on a notion of affectedness that
involve entailments of change, there are some accomplishments that do not entail
change, including in particular performance verbs such as play or perform:
The troupe performed the play in/?for exactly five hours.
Despite the fact that the predicate is telic there are no entailments of change: nothing is different about the troupe of performers or the play at the end of the event.
This might suggest that there are other types of accomplishments not based on
a notion of change. However, Tenny (1994: 73) suggests that performance predicates can be analyzed metaphorically as motion predicates, where the performer
is a “theme” and the piece performed is the “path”, based on the fact that in such
predicates the performer progresses incrementally through the piece in an adjacent
fashion. Thus such predicates are amenable to a scalar analysis, though we would
have to say that the scale is a type of scale that does not correspond to lasting
physical change. What other types of scales may exist is a matter of future work.
A second remaining issue is that, as Rothstein (2004: 36–58) notes, some
achievements are better than others in the progressive, which as noted in Section 1
is a diagnostic for having stages, which in turn presupposes durativity:
a. #John is noticing his friend in the corner.
b. John is arriving at the station just now.
However, a reviewer points out that achievements and accomplishments differ in
the progressive: the former allow that the actual change is not in progress but the
latter do not (giving Flight 5 is arriving now and will arrive at Gate 7 in two minutes vs. **John is reading the letter and will read it in another minute.; judgment
his/hers). I concur; my reading of the reviewer’s data with achievements is something like “just about to”, i.e. the result is viewed as imminent and inevitable. This
suggests that the progressive may not diagnose durativity in all cases, meaning (58)
are not a problem per se, though I leave open what the progressive is in fact doing.
Finally, as noted in Section 1, I have only addressed dynamic predicates in
this paper, leaving states aside. It is clear that the proposed aspectual classification
offers no room for states. Thus another parameter of some sort altogether must be
proposed, and I leave aside what it is, though this is not to say that some of the
parameters above regarding properties of states may not be relevant as well, since
stative terms may also be more or less clear about what specific state is predicated,
and may also predicate states along gradable and non-gradable scales. (And indeed,
there may well be notions of incrementality in the domain of statives; see Gawron
2009 and Koontz-Garboden 2010 on changes along spatial dimensions.)
For reasons of space, here and in Section 3 I give relatively brief, informal sketches of this
implementation and the motivations for it. Please see the references cited for further details. However,
this model is a simplification in one respect: while it assumes that scales are incremental arguments
(as below), themes are also often incremental arguments, so that Water flowed to the button of the
hill/turned red/was drunk are atelic despite having specified results. Beavers (2011, in press) discuss
such facts extensively and argue that they can be accommodated straightforwardly under an extension
of the analysis assumed here by first decomposing the event by parts of the theme into subevents that
stand in incremental relations to the scale. For space reasons I set themes aside and focus only on
the role of scales in aspectual properties, though the approach I outline can be easily expanded to
accommodate themes by introducing this additional dimension of variation.
This model also gives us “subscales” qua subpaths, i.e. for each Rj ⊂ R there is sj < H s
corresponding to the join of all si < H s corresponding to all r i ∈ Rj .
For some reason this diagnostic produces the clearest results when there is a modal or temporal
auxiliary, although it works in the simple past as well. For durative atelic predicates, the appropriate
diagnostic is acceptability with a for-temporal modifier; this is not relevant here.
A reviewer asks if this model has consequences for possible types of resultative constructions,
as discussed by Gehrke (2008). In fact the Krifka-based approach cited here was developed partly
to deal with constraints on resultatives (as in Wechsler 2005; Beavers 2008), and there may well be
connections with Gehrke, though a discussion of this is beyond the scope of this paper.
These are not always acceptable to all speakers, and not all verbs in classes that allow the conative will actually show it for speakers who accept conatives in general. My ultimate goal here is to
examine the properties of the alternation having to do with affectedness when it does arise, although
some facts about which predicate classes do and do not allow conatives will be relevant below.
As Frense and Bennett note, German also makes a prepositional distinction, where at conatives
translate with nach and on with an. In Danish nearly all conatives use på except consumption verbs,
which use af (Line Mikkelsen, Pia Quist, p.c.). In Galician (the only Romance language I am aware
of that has conatives) all conatives use en (Rosales Sequeiros 2005). These facts suggest that English
at and on conatives are variants of the same operation (as also suggested by Levin 1993: 42).
There are also predicates which seem to show no contrast at all in the alternation, such as gnaw
the steak vs. gnaw at/on the steak, something that is also problematic on most previous approaches.
Beavers’s (2010) analysis is that semantic contrasts are not obligatory in object/oblique alternations
(depending on the verb), but when they do occur, they must conform to (49).
On a related note, a reviewer suggests that the reading of cut x as an accomplishment (e.g. cut
the cloth into some particular pattern) does not allow the conative. However, it is again not obvious
to me that such a reading is ruled out, and the following may exemplify it:
(i) A few times within the last 3 months, the Lord has shown me a place or rather a room where
there is a large table, and I see a pair of extraordinary hands cutting a long piece of cloth on
this table. The first time I saw it, the hands were cutting a pattern out of the cloth. I watched
those hands for awhile, and they were beautiful. They cut at that cloth with such loving care.
However, since cut at as a potential change predicate could take on a number of readings in context
(due to its very unspecified nature) the use in (i) could actually be derived from that. Nonetheless, the
simpler assumption is again that accomplishment cut does allow a conative, and I assume that here.
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John Beavers
Department of Linguistics
The University of Texas at Austin
1 University Station, B5100
Austin, TX 78712-0198
[email protected]

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