Caudal and Nicolas (2005)

Caudal and Nicolas propose a degree-based aspectual alternative to the approaches by Kennedy and Levin, Krifka, and Verkuyl, hence it is relevant to the present discussion. Although they make a number of useful observations and aim to account for a wide range of facts, their proposed alternative is problematic in terms of its conceptual and formal development. My comments will be comparatively brief, and I will focus on their analysis of John eat an apple (again, ignoring tense), because the treatment of this kind of example brings their discussion closest to the present one:

This formula states that there is an individual x, an event e, and a degree d such that e is an eating to degree d, the event type “eat” is a becoming, the quantity of x is d, the agent of e is John, and the patient of e is x, which is an apple. Setting aside the two thematic relations agent and patient,¹ the crux of the matter comes down to the interpretation of eat, become, and quantity in order to understand the formula in (1). In this connection, it is also vital to ask about Caudal and Nicolas’ conception of telicity and how the formula in (1) captures the telic reading of the sentence in question.

Beginning with eat, how does this predicate relate events to degrees? For Caudal and Nicolas (p. 287), in the case of non-atomic predicates such as eat, degrees are taken from the set of positive real numbers. However, Caudal and Nicolas do not say what the maximal degree is in this case, and even more crucially they do not indicate how degrees are supposed to be assigned to eating events.² Yet suppose that we have an eating event e: how is it determined what degree is assigned to e? For example, when would the degree assigned to e be 1 and when would it be 2 and when would it be 102? If there is any eating at all, why is the degree not maximal? Unfortunately, since Caudal and Nicolas do not address such questions, it is unclear what eat actually measures in the end.³ Alternatively, if the degree assigned to e should also depend on what is eaten in e, then it would be more expedient to treat eat as a two-place function on events and individuals, yet this is not what Caudal and Nicolas do.

The clause become(eat) in (1) is unproblematic once eat is accepted. In prose, it says that there is a one-to-one mapping between initial subevents of eating events and degrees such that if eat yields d for e, then every initial subevent of e is mapped to a unique degree lower than d (but higher than 0), and every degree lower than d (but higher than 0) is mapped to a unique initial subevent of e. In other words, degrees steadily increase in the course of eating events. Although there is something intuitively correct and attractive about this, it is still unclear what exactly eat is measuring.

Turning to quantity, the problem is similar as for eat: it is unclear what is being measured. Does quantity count atomic individuals, or does it measure the mass of an individual with respect to some unit of measure? And what is the maximal degree for quantity?⁴ It is easy to imagine that the clause quantity(x)(d) in (1) counts apples, but then why not specify d to be 1 in this case? It is also unclear what the motivation is for identifying the degree argument of quantity with that of eat in (1). Caudal and Nicolas do not model telicity in terms of quantization but instead offer a new definition:

Not immediately obvious is that this notion of telicity applies to relations between degrees and events and not to one-place event predicates, as quantization does. Consequently, this definition has to be applied to the relation between degrees and events underlying the formula in (1):

Firstly, however, it is not evident that this relation specifies a maximal degree, and even if d were specified as 1 (assuming that individual apples are counted), it is unclear why this would be a maximal degree (how about the case of two apples?). But even if it were deemed that d is maximal in this case, it is hard to see why d should not also be maximal in the following formula (which presumably underlies the analysis of John eat applesauce), because presumably the particular quantity x of applesauce at issue also has a maximal value:

However, this formula should be atelic, in contrast to the formula in (3),

which should be telic. Secondly, the definition in (2) is global in an uncanny way, because it presupposes that we can tell, given an arbitrary relation between degrees and events, whether the verbal predicate buried inside (if there is one) satisfies become. However, on the usual assumptions of a compositional semantics, this information will in general no longer be accessible.⁵

In sum, it is difficult to view Caudal and Nicolas’ account in its present state as a serious contender to either Kennedy and Levin’s or Krifka’s. Although they suggest a number of ideas which are intuitively attractive (e.g., a monotonic increase of degrees as a component of incrementality – even if they do not quite put it this way), their account needs significant work to cohere as it should.

1 At the same time, it is unclear what principles Caudal and Nicolas assume for patient. Do Krifkastyle mapping properties hold for patient and, if not, how are parts of the patient argument related to parts of the event? Caudal and Nicolas recite (note 15) two of Krifka’s (1998a) mapping properties, but it is unclear to what extent they are committed to them.

2 Although Caudal and Nicolas do not state explicitly that eat is functional with respect to its degree argument, I assume that it is.

3 A reasonable but unintended interpretation for eat would be that it measures temporal length with respect to some unit of measurement (e.g., seconds), but Caudal and Nicolas clearly do not have this interpretation in mind.

4 Caudal and Nicolas’ axiom for quantity in their (56) presupposes a maximal degree.

5 Caudal and Nicolas may have in mind a kind of representational approach, but then they should clarify this up front, and needless to say it would place their analysis in a different ballpark and accordingly make direct comparisons between their account and those by Kennedy and Levin, Krifka, and Verkuyl (not to mention the present account) more difficult to make.