6.4 Comparing the approaches
6.4.2 The strata-based approach
I will now argue that the strata-based approach provides a handle on the observa- tions presented in Section 6.2: that the sentenceJohn pushed carts to the storeis compatible with a temporalfor-adverbial; that this adverbial enforces an iterative interpretation; and that the sentence is not compatible with a spatialfor-adverbial. It will also be necessary to exclude irrelevant events, but this appeal to relevance does not undermine the approach because none of the parts of the sum event need to be considered irrelevant. The strata-based approach was illustrated in Figure 6.2a. The facts just mentioned are illustrated by example (5), repeated here: (30) a. John pushed carts to the store for fifty minutes.
b. *John pushed carts to the store for fifty meters.
I start with the first observation: the sentence is compatible with a temporal for-adverbial. Take any event in the denotation of (30) and call ite. As implemented in Dowty’s proposal, the strata-based approach checks if every subinterval of the runtime of e is the runtime of an event in the denotation ofJohn push carts to the store. This condition is of course problematic, because there are no infinitely short events that qualify as pushing events, let alone events of pushing carts to the store. However, Chapter 5 shows that the strata-based approach can be maintained in spite of this minimal-parts problem. My implementation of the strata-based approach checks if there is a way to divide up the sum event in (21) along the temporal axis into very short strata that are all in the denotation of the main clause predicate. What counts as very short depends on the length of the temporal interval associated with the measure phrase of thefor-adverbial. In the case of (21), “very short” means whatever counts as very short relative to fifty minutes – say,
five minutes.
(31) SRτ,ε(λt[minutes(t)=50])(JJohn push carts to the storeK)⇔ ∀e[e∈JJohn push carts to the storeK→
e ∈ ∗(λe0.ε(λt[minutes(t) = 50])(τ(e0)) ∧ e0 ∈
JJohn push carts to the storeK)]
(Every eventeinJJohn push carts to the storeKcan be divided into one or more parts, each of which is also in the denotation ofJJohn push carts to the storeKand has a very small runtime compared with fifty minutes.)
Because the strata-based approach does not quantify over all temporally shorter subevents, it places a weaker requirement on the main clause predicate than Krifka’s account does. We have seen that the sum event of (21),e, can be divided into two partse1 ande2 such thate1 does not qualify as an event in which John
pushed carts to the store. More specifically,e1represented the sum of all subevents
in which John pushed carts halfway towards the store. In other words, the existence of the partse1ande2 represents a way of dividing upealong the spatial axis. The
existence of e1 is without consequence for my proposal. All that needs to be
checked is whether there exists a way of dividing e into subevents along the
temporal axis, such that these subevents are each in the denotation of the main clause predicate. Once it has established that such a division exists, it does not matter whether or not there are also other ways of dividingeinto parts to which the main clause predicate does not apply.
To check whetherecan be divided up in the specified way, we need to check the scenarios with which (24) is compatible. Example (24) by itself does not specify whether John pushed carts to the store little by little (iteratively, that is, with many trips back and forth) or all at once, but as mentioned, adding a temporal for-adverbial as in (21) forces an iterative interpretation. On my proposal, this contrast is expected. A scenario in which John pushed the carts to the store little by little entails that the main clause predicate in (24) is true within many consecutive time intervals – whatever time it takes John to push a set of carts to the store and to go back to the origin. A scenario in which John pushed the carts to the store all at once is not compatible with such an entailment. This entailment is exactly the one that is also required byfor-adverbials on the strata-based approach.
The strata-based approach not only accounts for the acceptability and licensed entailments of (21). It also explains the contrast between the acceptability of the temporal interval in (21) and its spatial counterpart. This minimal pair is repeated here from (5):
(32) a. John pushed carts to the store for fifty minutes. b. *John pushed carts to the store for fifty meters.
The reason for the contrast between these two sentences is easily explained on the strata-based approach, given any background theory that makes the uncon- troversial prediction that the PPto the storeis only true of events whose spatial extent ends at the store. The idea is this: While the temporalfor-adverbial in (32a) tests whether the main-clause predicate is true within every very short temporal interval that is a part of the fifty minutes in question, the spatial for-adverbial in (32b) tests whether the main-clause predicate is true within every very short spatial subinterval of the fifty meters in question (see Figure 6.3). Some of these
subintervals will not spatially contain the location of the store, that is, they will not contain the endpoint of the spatial interval at which the sum event is located. Any event that is located in such a subinterval will not qualify aspush carts to the store, that is, it will not be in the denotation of the main-clause predicate. This
means that there is no way of dividing up a sum event denoted byJohn pushed
carts to the storealong the dimension of the spatialfor-adverbial in (32b) that would be conform to the requirements of thefor-adverbial. This reasoning applies both to Krifka (1998) and to the strata-based approach. In other words, both theories rule out (32b). However, only the strata-based approach can explain the contrast of (32b) with (32a). As we have seen, Krifka (1998) would rule out both sentences.
Figure 6.3: Ruling out*John pushed carts to the store for fifty meterson the strata-
based approach STORE STORE STORE STORE STORE ru n ti m e
extent along path = 50 meters
5
5
5
5 4
6.5
Summary
Temporal and spatialfor-adverbials impose analogous constraints on the predicates with which they combine. Any theory of telicity should therefore account for temporal as well as spatialfor-adverbials. Since the two kinds of adverbials differ in their distribution, any theory of telicity should be able to classify a given predicate as temporally telic but spatially atelic or vice versa. This situation supports a parametrized notion of the telic-atelic opposition, where the parameter is set either to time or to a spatial dimension.
The parametrized nature of aspect is expected within the general picture of this work. As argued in Chapter 4, the fact that a predicate can be distributive on its agent “dimension” without being distributive on its theme “dimension” or
vice versa supports a parametrized view of distributivity. In connection with measurement, I have argued in Chapter 4 that the singular-plural and count-mass distinctions that are operational in the pseudopartitive construction need to be parametrized to a “dimension” like width or diameter. The concept of stratified reference subsumes this picture. The dimension parameter of stratified reference gives us a handle on the distinction between spatial and temporal aspect.
I have argued that subinterval-property based or “strata-based” approaches to atelicity, modified as in Chapter 5, generalize to the spatial case in a better way than approaches which are based on divisive reference do. On strata-based approaches, an atelic predicate is one that holds of subevents which are constrained in size along the dimension with respect to which the predicate is atelic, but not along other dimensions. Approaches based on divisive reference impose too strong conditions because they also require the predicate to hold of subevents whose size is small along all dimensions. Once again, the picture is subsumed by the concept of stratified reference. According to this concept as applied in Chapter 4, a predicate that is distributive on its agent “dimension” is not required to apply to subevents that are constrained on their theme dimensions – that is, it is not required for an agent-distributive predicate to be distributive on its theme as well.
Chapter 7
Measure functions
7.1
Introduction
This chapter considers the formal properties of measure functions and the way in which distributive constructions constrain these properties. I start by describing the relevant constraint in relation with the extensive-intensive opposition known from physics. In line with the unified picture presented in this work, I show that this opposition is not only operative in pseudopartitives, but also infor-adverbials. As in Chapters 4 and 6, I draw attention to circumstances involving several dimensions. In this case, the dimensions correspond to different measure functions. I show that the constraint on measure functions only applies along one dimension at a time. I suggest that this behavior has the same source as the atelicity constraint in for-adverbials and the distributivity constraint in adverbial-eachconstructions.
My background assumptions on pseudopartitives and measure functions are laid out in Sections 2.5.3 and 3.2. Section 2.5.2 has also introduced trace functions, and Section 3.2 has assumed htat event pseudopartitives involve trace functions. Measure functions relate individuals and events to their degrees on various scales, while trace functions relate events to their runtimes and locations. The rest of this work distinguishes them from measure functions mainly for technical reasons, for example because they have different types. Trace functions behave analogously to measure functions with respect to the facts I will discuss here. Therefore, this chapter does not distinguish between measure functions and trace functions.