Themes, Cumulativity, and Resultatives:
Comments on Kratzer 2003
Alexander Williams
Abstract. According to Kratzer (2003), the thematic relation Theme, construed
very generally, is not a “natural predicate.” She says that the “natural predicates”
are “cumulative,” and argues that Theme is not cumulative, in contrast to Agent. It
is therefore best, she concludes, to remove Theme from the palette of semantic analysis. Here I oppose this argument, relying especially on facts about the resultative
construction in Mandarin. These show that Theme and Agent are in fact on equal
footing, since neither has the property that Kratzer requires of a natural predicate.
Keywords. Thematic relations; cumulativity; event mereology; resultative construction; Mandarin Chinese.
1
Introduction
According to Kratzer (2003), the thematic relation Theme, construed very generally,
is not a “natural predicate.” She says that the “natural predicates” are “cumulative,”
and argues that Theme is not cumulative, in contrast to Agent. It is therefore best,
she concludes, to remove Theme from the palette of semantic analysis. Here I briefly
oppose this argument, relying especially on facts about the resultative construction
in Mandarin. I make my objection in section 5, after reviewing the substance of
Kratzer’s proposal in sections 2 through 4. I conclude in section 6.
2
Cumulativity and Naturalness
Kratzer proposes that “cumulativity” is a property of any “natural predicate.” What
does this mean?
For Kratzer a relation is “cumulative” when it is closed under summing of its
arguments, indicated here by ‘⊕.’ A one-place relation P is cumulative when (1)
holds, and a two-place relation Θ, when (2) does (compare Krifka 1992).
(1)
P (e1 ) ∧ P (e2 ) → P (e1 ⊕ e2 )
(2)
Θ(e1 , x1 ) ∧ Θ(e2 , x2 ) → Θ(e1 ⊕ e2 , x1 ⊕ x2 )
Summing of x and y yields a single individual x ⊕ y with x and y as improper
parts. The improper part relation, ⊑, is reflexive, transitive, and antisymmetric. An
individual with parts other than itself is complex. An individual that is not complex
is atomic. Following David Lewis, Kratzer takes summing to apply freely. Given any
1
two individuals, say Al Gore (a) and Marcus Junius Brutus (b), there exists a unique
complex individual that is their sum (a ⊕ b). Likewise for any two events. Al kissed
his wife in 2000 ad (e1 ), Brutus stabbed Caesar in 44 bc (e2 ), and there is a complex
event that is the sum of these two (e1 ⊕ e2 ). The parts of a sum needn’t stand in any
substantive relation.
Kratzer uses parts and sums in a semantic theory of sentences containing plurals,
one deriving in large part from Link 1983. Complex individuals serve as the extensions
of plural definites. And at least sometimes, summing interprets the conjunction of
expressions in type hei, such that the extension of “Al and Brutus” might be a ⊕ b.
In addition, predicates of events have complex events in their domain. But unlike
summing of entities, summing of events does not have very obvious morphological
expression.1
Given this theory of plurals, cumulativity helps validate certain inferences. Suppose, for example, that the (a) sentences in (3–5) have the logical forms in (b), and e1
and e2 are events that verify the first two sentences. Then cumulativity for the predicates Agent and dance ensures that (3) and (4) jointly entail (5), since he1 ⊕ e2 , a ⊕ bi
then satisfies Agent, and e1 ⊕ e2 satisfies dance.
(3)
(4)
(5)
a.
Al danced.
b.
∃e.Agent(e, a) ∧ dance(e)
a.
Brutus danced.
b.
∃e.Agent(e, b) ∧ dance(e)
a.
Al and Brutus danced.
b.
∃e.Agent(e, a ⊕ b) ∧ dance(e)
In sentences with more than one plural argument, a logical form that expresses
thematic relations in separate conjuncts becomes crucial (Krifka 1992, Schein 1993,
Kratzer 2000). Suppose two editors separately proof a manuscript riddled with errors.
There is an interpretation of (8a) under which it is implied by (6a) and (7a). Separate
expression of the Agent relation allows the subject and object quantifiers in (8) to
be independent. And now the inference from (6b) and (7b) is readily be captured by
presuming cumulativity, once again.
(6)
(7)
(8)
a.
Editor 1 found errors 1 through 12.
b.
∃e.Agent(e, x1 ) ∧ find (e, y1)
a.
Editor 2 found errors 7 through 20.
b.
∃e.Agent(e, x2 ) ∧ find (e, y2)
a.
Exactly two editors found exactly twenty errors.
b.
∃e.[∃x : 2!(x)]Agent(e, x) ∧ [∃z : 20!(z)]find (e, z)
2
If e1 and e2 are events that verify (6b) and (7b), cumulativity ensures that he1 ⊕
e2 , x1 ⊕ x2 i satisfies Agent and he1 ⊕ e2 , y1 ⊕ y2 i satisfies find . (8b) must therefore be
true, since by assumption x1 ⊕ x2 comprises two editors and y1 ⊕ y2 , twenty mistakes.
To secure results like these, Kratzer pursues the conjecture that all event sortals
and thematic relations are uniformly cumulative—at least if they are “natural.” The
“natural predicates,” she writes, are “those that humans take to be candidates for
denotations of simple lexical items, spontaneously and without any explicit instruction
or definition” (2003: 7).2
Unfortunately Kratzer says little about why the cumulative predicates should be
most immediately acquired: does this express an arbitrary bias of the language faculty,
or rather something more general about the structure of thought and perception in
human children?3 Nor does Kratzer say whether the ontology of complex individuals
that her discussion of cumulativity presumes is “natural” itself. Do toddlers come
to presume, “spontaneously and without explicit instruction,” that any two objects
are part of a complex individual, even when there is no substantive relation between
them? Depending on the answers to these questions, the conjecture that “natural
predicates” are cumulative will be more or less plausible, prima facie.
In any case, if the conclusions I reach below are correct, one strong version of
Kratzer’s hypothesis is falsified empirically. We cannot maintain that thematic relations are cumulative, while also presuming that events can be summed freely.
3
Agent versus Theme
Kratzer argues that Theme is not cumulative, while Agent is. This conclusion is
presented in the context of a broader intuition:
Themes lack the conceptual independence of agents. Theme arguments
seem to be tightly linked to their verbs. Agents are different. Actions
seem to have agents independently of how we describe them. (Kratzer
2003: 4)
So for Agent but not for Theme, one can tell whether x bears the relation to e,
without knowing what other predicates hold of e.4
There are well-known objections to this optimism about agents (see e.g. Parsons
1990, Dowty 1991, Landman 2000, Schein 2002). Given an exchange of money for
goods, for example, one cannot say who its agent was except relative to a description
of the event as a buying or as selling. But let us imagine that Kratzer’s general idea
can be sustained despite such problems.
This allows Kratzer a further presumption. In testing for cumulativity, she feels
free to describe the sum event in any way that seems appropriate—exactly because
the applicability of the tested predicate should not depend on how we describe the
event of which it is predicated. In particular, the sum event need not be described
3
using a verb that applies equally to its parts. So Kratzer presumes what I will call
Variety, (9).
(9)
Variety
An event that satisfies V may have parts that do not.
For instance, Kratzer narrates the planting of a rose bush as in (10). Take e1 , e2
and e3 to be events verifying these three sentences. Suppose the planting of the bush,
e4 , involves just these three events. Then maybe the planting is simply identical to
their sum: e4 = e1 ⊕ e2 ⊕ e3 . In that case, the sum event is a planting, but it has
parts that are not, thus illustrating Variety.
(10)
a.
Al dug a hole.
b.
Bill inserted a rose bush.
c.
Carl covered the hole with soil.
Now the proposed difference between Agent and Theme emerges. If the planting
has a single agent, it seems right to assume that it is Al, Bill, and Carl together: a ⊕
b ⊕ c. So if e1 ⊕ e2 ⊕ e3 is identical with the planting, the agents of its three parts
sum to the agent of the whole. But consider the theme of the planting. It is not the
hole, the rose bush, and the soil together. What got planted was just the bush itself.
So the themes of the parts do not sum to the theme of the whole. We can derive this
result by assuming that Agent is cumulative but Theme is not. Then (10), plus the
assumption that e1 ⊕ e2 ⊕ e3 is a planting, entails (11) but not (12).
(11)
Al, Bill, and Carl planted something.
(12)
Al, Bill, and Carl planted a hole, the rose bush, and soil.
The asymmetry vanishes, however, whenever the events do not exhibit Variety.
Themes then sum as well as agents do. Let’s say that Al wrote a poem and Bill drew
a picture. We can describe the sum of these events by saying that Al and Bill created
a poem and a picture.
(13)
(14)
a.
Al wrote a poem.
b.
Bill drew a picture.
Al and Bill created a poem and a picture.
But the same description, create, also applies to the writing and the drawing, which
are the parts of the sum event. So in this case we don’t see Variety. The description
of the whole applies equally to its parts. And correspondingly, both participants sum.
The agent of the complex event is the sum of Al and Bill, while its theme is the sum
of the poem and the picture.
Let us therefore distinguish two ‘kinds’ of cumulativity, one that does not depend
of the description provided by the verb, and one that does.
4
(15) Independent Cumulativity
Cumulative, under any description of the sum event.
(16) Dependent Cumulativity
Cumulative, at least under a description of the sum event which also applies
to its parts.
In excluding Theme from the family of natural predicates, Kratzer is interested
only in the first kind of cumulativity. She thinks that Agent has this property but
Theme does not. Yet we will see in section 5 that Agent is not independently cumulative either.
4
Uniqueness and Devolution of Relations
Sentence (17) does not say merely that there was a lifting whose agent (or agents)
included Al, and whose theme (or themes) included the piano. If it did, (18) would
be enough to make it true. But in fact (18) does not entail (17), since (18) allows
that Al did nothing at all to the piano.
(17)
Al lifted the piano.
(18)
Al and Bill lifted the piano and the harpsichord.
Rather, (17) makes the stronger statement that there was a lifting whose only
agent was Al, and whose only theme was the piano. For this reason it entails that Al
lifted the piano (Schein 1993).
Semantic theories need to ensure this result. Those which presume an ontology
of complex individuals, like Kratzer’s, do this with a principle like (19); see Carlson
1984, Dowty 1989, Parsons 1990, Landman 2000, Kratzer 2001.5
(19)
Thematic Uniqueness
For any thematic relation Θ and event e (possibly complex), there is at
most one individual d (possibly complex) such that Θ(e, d).
So if (17) implies an Agent relation between Al and a lifting, there can be no other
individual so related.
Given Thematic Uniqueness, cumulativity has a further consequence, (20). Thematic relations to e devolve to e’s parts (Kratzer 2001: 29).
(20)
Devolution
If Θ is cumulative and Θ(e, d), then for any part e′ of e, if there is a d′ such
that Θ(e′ , d′ ), then d′ is either identical to, or part of, d itself.
For if e′ is a part of e, e′ ⊑ e, their sum is just e again, e′ ⊕ e = e. The sum of their
agents is d′ ⊕ d. But by assumption the complete agent of e is just d. So it must be
that d′ ⊕ d = d, hence that d′ ⊑ d.
5
In case the agent d of event e is an atomic individual, therefore, d must also be
the agent of any part e′ that has an agent.
Kratzer (2003: 4) notices a problem in causatives like (21). This sentence seems
to describe an event of making Bill vote, one which has a voting as a part, and whose
agent is just Al alone. But then the agent of voting too would have to be Al, and
this is wrong.
(21)
Al made Bill vote.
To squelch the challenge, Kratzer revises her interpretation for (21). Al is not the
agent of a making vote. Rather he is the agent of some event which itself is in the
make relation to Bill’s voting.
I will now discuss a similar case, namely resultative constructions like (22). Here
I think the facts overwhelm the parry Kratzer makes in response to (21), and uproot
a number of wrong assumptions.
(22)
5
Al pounded the cutlet flat.
Agent is not Independently Cumulative
In a resultative, an adverb that modifies the verb phrase as a whole does not ipso facto
modify its main verb. (23) does not entail (24), for example, under either placement
of the adverb; as a consequence, (25) is in no way odd or contradictory.
(23)
Al (slowly) pounded the cutlet flat (slowly).
(24)
Al (slowly) pounded the cutlet (slowly).
(25)
Striking it rapidly for hours, Al slowly pounded the cutlet flat.
It follows that the verb phrase is a predicate of an event e1 , distinct from the event
e2 of its primary subpredicate. Abstracting from many details, the verb phrase in (22)
has a meaning something like (26), for some relation K. Presumably the proposition
K(e1 , e2 , e3 ) requires at least that e1 is a change achieved by means of e2 and ending
with e3 (see Williams 2007a).
(26)
J pound the cutlet flat K
= . . . λe1 ∃e2 ∃e3 .K(e1 , e2 , e3 ) ∧ pound (e2 , . . .) ∧ flat(e3 , . . .) . . .
Yet if it’s right to assume that events can have parts, and parts that needn’t
satisfy the same description as the whole, then it would also seem right to say that a
pounding flat has a pounding as a part, and necessarily so. It seems safer than saying
that a planting has a digging as a part. Every pounding flat involves a pounding, but
not every planting involves a digging.
Suppose then (at the moment, just for the sake of argument) that (22) says Al is
the agent of the pounding flat (compare McCawley 1971, Green 1972). Given that
6
poundings too have agents, Al must then be the agent of the pounding as well, by
Devolution.
This seems unproblematic, since (22) in fact entails that Al pounded the cutlet.
Indeed in English, the underlying subject in a resultative always identifies the agent
of the event of its main verb (the ‘means event’), a fact that theories of the English
resultative generally try to capture.
But things are different in Mandarin. Sometimes, as in (27), Mandarin looks like
English. The underlying subject is naturally understood as referring to the agent of
the event of the first verb, the one describing the means of change.
(27)
Tā tı̄ duàn -le nàtiáo mùbǎn.
3s kick snap -pfv that wood plank
‘S/he made the plank snap from kicking.’6
(More naturally: ‘S/he kicked the plank in two.’)
But not always (Lü 1986, Ma 1987, Li 1990, Huang 1992, Ren 2001, Williams 2005).
In other cases the subject is most naturally taken to refer to the theme of the means
event, (28), or to an individual with no thematic relation to that event at all, (29).7
(28)
a. Yı̄fú xı̌
lèi -le jiějiě.
clothes wash tired -pfv elder sister
‘The clothes made big sister tired from [her] washing [them].’
(Ren 2001: 326, translation aw)
b. Nà pı́ng jiǔ hē
zuı̀
-le wǒ.
that bottle wine drink drunk -pfv 1s
‘That bottle of wine made me drunk from drinking.’
(Huang 1992, translation aw)
(29)
a. Zhèjiàn shı̀
kū hóng le Lı̌sı̀-de yǎnjı̄ng.
this
matter cry red pfv L-’s
eyes
‘This matter made Lisi’s eyes red from crying.’
(Huang 1988: 296, translation aw)
b. Chı̄ jı̌
dùn miàntiáo yě chı̄ bu
qióng tā.
eat several meal noodle also eat neg.pot poor 3s
‘Eating a few meals of noodles won’t make him poor from eating.’
(Lü 1986:7, citing Jiang Zilong, Weichi Hui Chang, translation aw)
The latter type of example is important. It shows what the defender of Independent Cumulativity would want to deny—and what we assumed provisionally for
English (22). The subject is indeed assigned a thematic relation to the event of
change associated with the whole verb phrase, independent of any additional relation
to the events of its component predicates. In particular, it is necessarily construed as
referring to the initiator of that event, its agent (see Li 1990, Gu 1992, Huang 1992,
7
Williams 2007b). And yet this thematic relation does not devolve to the subevents,
as cumulativity requires. (29b), for example, talks about an event of change, one
that ends in poverty and is brought about by eating. The initiator or agent of this
change is an eating of noodles. But this eating of noodles is not the agent of the
event described by the first verb in the main verb phrase. That event, an eating, has
different agent, presumably the referent of the pronominal direct object.
Elsewhere (Williams 2005, 2007a, 2007b) I have argued that the logical form of
resultatives always involves, not only an Agent for the event of the complex predicate,
but a Theme as well.8 This relation is assigned to the underlying object. So the logical
form of (22) is something like (30).
(30)
J Al pound the cutlet flat K
= ∃e1 ∃e2 ∃e3 .K(e1 , e2 , e3 ) ∧ Agent(e1 , JAlK) ∧ Theme(e1 , Jthe cutletK)
∧ pound (e2 , . . .) ∧ flat(e3 , . . .) . . .
We just saw that the Agent relation does not devolve from the event of the complex
predicate to the event of its means verb. Nor does the Theme relation. Mandarin
(31) describes an event of change, ending in dullness and brought about by cutting.
The theme of the change is the cleaver: it is what changes. But the cleaver is not the
theme of the cutting: it’s not what’s cut.
(31)
Tā haı́ qiē dùn -le nı̌de caı̀dao.
3s also cut dull -pfv your food knife
‘S/he also made your cleaver dull by cutting.’
English examples like He shouted his throat hoarse make the same point, still presuming that the object identifies the theme of the event of change associated with the
complex predicate. But the Mandarin example has more force, since here the means
verb describes a type of event, cutting, which more clearly has a ‘highly affected’
theme itself, like the superordinate event of change (Williams 2007a).
Thus resultatives show that thematic relations do not devolve to the parts of their
event, and hence that neither Agent nor Theme is independently cumulative.
I see only one response to this challenge, consonant with the presumption of
Independent Cumulativity. One must assume that the thematic relations assigned to
the subject and object in a resultative, those that relate their referents to the event
of change, are not the general Agent and Theme relations. They are some other
relations, let’s call them Causer and Causee.
Then, even if these new relations are cumulative, they devolve to the subevents
only if those subevents themselves have causers or causees. For example, the causer
of an event of drinking someone drunk—see (28b)—is the causer of its component
drinking only if drinkings have causers. And why not say that they don’t? Often
enough, the verbs that occupy resultatives are activity verbs, not causatives, and
presumably activities don’t have causers.
8
One might fuss over cases where the verb describing the means of change may
itself be causative, like when it means ‘cut.’ But the effort is unnecessary, since the
suggested resolution of the challenge is weak enough as it is. If Agent is to be a natural
and basic predicate, one should it hope that it applies at least to both activities and
events of caused change. To say instead that the actor in an activity and the initiator
in a change do not share a thematic relation makes the theory weaker, and much less
interesting.
More particularly, it vitiates the project of summing subjects. Al and Bill can
participate in the cleaning up of a tabletop, Al by clearing it of plates and Bill by
wiping it.
(32)
a.
Al clears the tabletop of plates.
b.
Bill wipes the tabletop.
c.
Al and Bill clean up the table.
The clearing and the cleaning are both changes, and changes are supposed to have
causers. Given that the clearing is part of the cleaning up, cumulativity therefore
tells us that Al is among the cleaners. But not so Bill, even when the wiping is part
of the cleaning up too. Wiping is an activity, and activities have agents, not causers,
by hypothesis.
And yet, cumulativity would tell us that Bill is among the cleaners if he had not
merely wiped the tabletop, but dried it off. For then Bill, as the drier, would be a
causer, since drying off is a change.
(32b′ )
Bill dries off the tabletop.
This asymmetry seems strange. If there are general semantic principles that force
us to put Bill among the cleaners given (32b′ ), they should do the same given (32b),
it seems to me. So while dividing subjects into causers and agents saves Independent Cumulativity from the causative and resultative data, it lessens the descriptive
coverage of that doctrine. Now subjects can be summed only when they share the
thematic relation of the subject in the description of the sum event. And the result
is an unintuitive loss of generality.
6
Remainders
Resultatives, and causatives more generally, show that thematic relations are not
independently cumulative. But resultatives pose no challenge to the idea that natural
predicates are dependently cumulative. Then arguments sum only when the predicate
that characterizes the sum event holds equally for its parts. This never happens in
any sort of causative: a voting is not a making vote, and a pounding is not a pounding
flat.
9
Nor do resulatives and causatives pose a challenge if we reject Variety. Then any
part of a V event must itself be a V event. So a making vote cannot have a voting as
a part, and a pounding flat cannot have a pounding as a part. Whatever the relation
is between the two events, it is not the relation of whole to part.
So Kratzer must reject Variety, or settle for Dependent Cumulativity. So far as I
can tell, neither of these compromises will undermine the other uses to which Kratzer
puts cumulativity, within her theory of plurals.9
But both will efface the alleged asymmetry between Agent and Theme. It may
still be true that “themes lack the conceptual independence of agents.” But evidence
for this is no longer to be found in cumulativity. The only feasible kind of cumulativity is Dependent Cumulativity, and this is shared by Agents and Themes equally.
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Department of Linguistics
University of Maryland
1401 Marie Mount Hall
College Park, MD 20742
[email protected]
Notes
1
Following Davidson 1967, sentences are existential quantifications over events, not directly referring descriptions or names. So conjunction of sentences does not straightforwardly express summing
of events. Perhaps conjunction of event nominals expresses summing of events, but only if such
nominals actually denote events (Parsons 1990), rather than entities uniquely correlated with events
(Chierchia 1984).
2
The restriction to “simple lexical items” does not much weaken the definition, since Kratzer
keeps the semantic contributions of syntactic relations to a minimum. Syntax introduces only application, conjunction, and perhaps something like composition of functions. All content beyond these
operations, the substantive content, must come from the primitive items combined in syntax (i.e. the
lexical items), and these may be silent. The natural predicates are therefore the initial candidate
denotations for every minimal pairing of substantive content and syntactic form in the analysis of
the sentence—with one exception. If a lexical item is not “simple” it might not immediately find a
denotation among the natural predicates. This is a wild card for Kratzer, but here we can ignore it.
11
3
The latter possibility would seem to be more reasonable in this case. At the very least, it should
not be that predicates we acquire “spontaneously” lead immediately to thoughts and percepts that
require “explicit instruction.”
4
Thus Agent has the property that Dowty (1989: 82) calls “Independence”: “The properties in
an L-thematic role type must be characterizable independently of the relations (denoted by natural
language verbs) that entail them.” Roughly this means that, if Θ is a legitimate thematic relation,
one must be able to describe when x bears Θ to e, without knowing what verb is being used to
characterize e.
5
See Schein 1993, Schein 2002, and Pietroski 2005 for theories which deal with thematic relations
but do not presume that plurals denote complex individuals. Instead of (19), these theories presume
that a plural argument in a position assigned a Θ relation to a predicate P is constrained to identify
all and only the Θ participants in the events e1 , . . . , en that satisfy P.
6
In order to avert certain confusions, I impose a uniform scheme of translation: ‘Subject made
Object Verb-2 from Verb-1’ing.’ The resulting formula is meant to convey only the general content
of the sentence, not its grammatical structure. The Mandarin construction involves no verb meaning
‘make,’ the two verbs are no separately inflected, and the first verb is not contained within an adjunct
prepositional phrase. Interlinear glosses use these abbreviations: 1s ‘first person singular pronoun,’
3s ‘third person singular pronoun,’ neg.pot ‘negative potential infix,’ pfv ‘perfective.’
7
Not all relations to an event that satisfies the description of a verb V are thematic relations. I
count only those which are imposed on the interpretation of some argument in a simple clause whose
predicate is V. So if Al made Bob cry, Al has some relation to the crying—he made it happen—but
not a thematic relation, since this sort of relation to a crying is imposed on neither argument in the
sentence He cried tears.
8
I prefer to use the term Patient. But here I will stick with Kratzer’s preferred labels.
9
Oddly, while Kratzer (2003) clearly presupposes Variety in distinguishing Theme from Agent,
she appears to reject it in Kratzer 2001 (pg. 25): “[W]henever e is a reading, eating, building,
pushing, or petting of something, and e′ is a subaction of e, then e′ is a reading, eating, building,
pushing, or petting of something as well.”
12