The present work sees the Distributivity Constraint as applying to all distributive constructions. This leads to the prediction that all distributive constructions, and not just pseudopartitives, reject measure functions in the same way. In particular, both pseudopartitives andfor-adverbials are predicted to be unacceptable when they relate events to measure functions that are intensive on the sets denoted by their substance nominals and by their verbal predicates respectively. The following examples confirm this prediction:
(12) a. thirty hours of driving runtime
b. thirty miles of driving location
c. *thirty miles an hour of driving *speed
(13) a. drive for thirty hours runtime
b. drive for thirty miles location
c. *drive for thirty miles an hour *speed
While this observation is novel as far as I know, the general idea that there is a connection between measure adverbials and measurement is not new. Krifka (1998), Section 3.4, notes that for-adverbials are like nominal measure phrases “insofar as they introduce a quantitative criterion of application.” In his setup, the noun hourintroduces an extensive measure function for events. Schwarzschild (2006), Section 3.2, similarly points out that a formalization of telic-atelic opposition in the line of Dowty (1979) can be couched in terms of monotonicity. For example, in-adverbials can only combine with telic predicates because, as he puts it, runtime “is nonmonotonic on the relevant part-whole relation in the domain given by” that predicate. For Schwarzschild, runtime is a dimension that is monotonic on the part-whole relation that relates events to their subevents. While Schwarzschild
does not go into any formal detail, the intuition is the same as the present one. I will discuss Krifka’s and Schwarzschild’s proposals in Section 7.5.
I discussed the fact that English has not only temporal but also spatial for- adverbials in Chapter 6. In that chapter, I argued for including spatial aspect in the study of aspect. The question arises, which categories of aspect there might be besides temporal and spatial aspect. It turns out that not every measure function is associated with an aspect in the way runtime and location are:
(14) a. drive∅/for thirty hours runtime
b. drive∅/for thirty miles location
c. *drive∅/for thirty kilograms *weight
d. *drive∅/for thirty degrees Celsius *temperature
e. drive∅/*forthirty miles an hour *speed
To some extent, these gaps have independent explanations. Unlike typical pseudopartitives,for-adverbials measure events rather than substances. Common sense suggests that driving events do not have weights or temperatures, and we can assume that examples like (14c-d) are category mistakes. More formally, I assume that the measure functionsweightandtemperatureare partial functions (see Section 2.5.3) and do not have any driving events in their domains. What is surprising, however, is that (14e) is unacceptable with afor-adverbial but acceptable when the wordforis left out. This contrast shows that even though we can talk in principle about the speed of an event,for-adverbials reject speed as a Map. The example from Quine (1985), mentioned in Section 2.4.4, of a sphere rotating slowly and heating up quickly at the same time also suggests that speed is among the possible properties of events. We can avoid the undesirable conclusion that the sphere is both quick and slow by assuming that the rotating and the heating up are two separate events, and that each one has a different speed.
One might think that it is just an idiosyncratic fact aboutfor-adverbials that they reject speed as a measure function. However, we have seen above that speed is rejected as a Map by pseudopartitives as well. What is more, the following
example shows thatfor-adverbials are productive in the way they combine with
measure functions:
(15) I’m interested in fashion for five pages, not for eighteen pages!
This sentence was used by Tuğba Çolak in conversation with me on April 25, 2010. Its intended interpretation was roughlyI’m willing to read five pages but not eighteen pages of articles on fashion. Here, thefor-adverbial is used in connection with a measure function that can best be described as page length. Given thatfor- adverbials can be put to use spontaneously even with unusual measure functions
such as page length, it is remarkable that they resist measure functions such as temperature in examples such as the ones above.
I now propose an explanation of these facts in terms of strata theory. The measure functionsruntimeandlocationare acceptable both in pseudopartitives andfor-aderbials. They can both be regarded as nonintensive measure functions on events, because the runtime and location of a part of an event can be smaller than the one of the whole event. In contrast, there are driving events on which speed is intensive, that is, every part of the event has the same speed as the whole event. I assume that speed is intensive on driving events:
(16) Intensive(speed,drive)
Based on the background assumptions in Chapter 3, the constructions in (12) and (13) involve different measure functions: runtime, location, and speed. The Distributivity Constraint therefore requires stratified reference to hold of the predicatedrivewith respect to different Maps (measure functions). The specific conditions imposed on (12) and (13) are the following (respectively for the a, b, and c examples):
(17) a. Every driving eventecan be divided into one or more parts, each of
which is a driving event whose runtime is very small. (true)
b. Every driving eventecan be divided into one or more parts, each of
which is a driving event whose location is very small. (true)
c. Every driving eventecan be divided into one or more parts, each of
which is a driving event of very short speed. (false)
Condition (17c) fails because speed is intensive on driving events. This explains why (12c) and (13c) are unacceptable. In general, all measure functions that are intensive in the systems denoted by the substance nominal of the pseudopartitive are predicted to be unacceptable.
Since the Distributivity Constraint is relativized to the Share (the substance nominal of the pseudopartitive and the verbal predicate with which afor-adverbial combines), we expect different Shares to be compatible with different measure
functions. Consider the nouns fever and warming: A sum of two consecutive
one-degree fever bouts is a two-degree fever bout, and a sum of two consecutive one-degree warmings is a two-degree warming. Constrast this with the case of water: a sum of two water entities whose temperature is one degree does not equal a water entity whose temperature is two degrees. Generalizing from these examples, it is plausible to assume that the measure functiontemperatureis intensive on the setJwaterKand extensive on the setsJfeverKandJwarmingK. We can express this distinction by assuming the following meaning postulates:
(18) a. Extensive(temperature,fever) b. Extensive(temperature,warming) c. Intensive(temperature,water)
The postulate (18c) is repeated from (6b) above. The point here is that it is not in logical contradiction with the meaning postulates (18a) and (18b).
Based on these meaning postulates, we expect that measure functions like temperature should be acceptable in pseudopartitives and infor-adverbials as long as their Share satisfies stratified reference. This prediction is confirmed by the following examples (emphasis mine):
(19) a. Emilia was lying on her bed,with 41 degrees Celsius of fever.30
b. The scientists from Princeton and Harvard universities say justtwo
degrees Celsius of global warming, which is widely expected to occur in coming decades, could be enough to inundate the planet.31
c. The sample continued tocool for several degreesto point N and then suddenly increased to a temperature between the transition points of Form I and Form I1 with no indication of the presence of Form 111.32
These examples show that temperatureis an acceptable measure function in
pseudopartitives whose substance noun isfeverorwarming. We have seen above
that temperature is not acceptable in pseudopartitives whose substance noun is water. This provides additional motivation for the point made above: We cannot simply categorize measure functions as intensive or extensive per se. What matters is whether they are intensive or extensive on the set denoted by the substance noun of the pseudopartitive in which they appear.