FORTALEZAS 1 Existe disposición por parte de los

The minimal-parts problem occurs in the domains of verbal and nominal predicates (Taylor 1977; Dowty 1979). I discuss each of them in turn.

5.2.1

The minimal-parts problem for verbal predicates

As discussed in Section 4.5.2, the entailment properties of atelic predicates with respect to a large range of other phenomena can be represented as a first approxi- mation in terms of the subinterval property (Bennett and Partee 1972; Dowty 1979). A predicate P has the subinterval property if and only if whenever it holds at an interval, it also holds at every one of its subintervals. The minimal-parts problem consists in the fact that the subinterval property only applies to certain atelic predicates if we are willing to disregard subintervals below a certain threshold. For example,waltzis an atelic predicate, but waltzing takes at least three steps, and there is no consensus on whether or not a given event whose runtime is substantially shorter than this three-step threshold still qualifies as waltzing. For this reason, it is difficult to know whether the subinterval property applies towaltz, and it is not clear whether this property is really an adequate characterization of atelicity. We can perhaps already conclude from this fact that the subinter- val property must be given up. This conclusion is sometimes objected to on the grounds that that the problem is not part of linguistics and should be ignored. Such an objection assumes that we do not really know what kinds of events occur at instants or even at very short subintervals, or in any case that these events should be seen as irrelevant for the purposes of semantics because they do not enter our daily experience. Once such events are excluded the subinterval property can still technically be assumed to hold of all atelic predicates.

I think this kind of objection misses the point. There is no benefit in choosing the underlying assumptions of semantic theory with the sole purpose of being able to continue using the subinterval property, because one might as well avoid the problem by using a different property than the subinterval property to begin with. The extent to which our intuitions about short events would have to be changed in order to maintain that atelic predicates have the subinterval property is considerable. For example, in order to give the predicate pass on in (1) the subinterval property, even generations would have to be considered as having minimal time:

(1) The Chinese people have created abundant folk arts, such as paper-cuttings, acrobatics, etc., passed on from generation to generation for thousands of years.16

It does not seem practical to maintain that the predicatepass on from generation to generationreally has the subinterval property, but it is clearly atelic since it can 16_{Attested example (http://www.twinbridge.com/detail.aspx?ID=315). Accessed}

be modified by afor-adverbial. I conclude that atelic predicates do not necessarily have the subinterval property. This conclusion is not new. As we will see, Dowty (1979) already recognized that the subinterval property is an idealization, and many subsequent authors have avoided using this property in their formalizations (see Section 5.3 below).

5.2.2

The minimal-parts problem for mass nouns

An analogous concept to the subinterval property, divisive reference, is sometimes used following Cheng (1973) as a defining semantic propety of mass nouns: any part of something denoted by a mass noun is assumed to be denoted by the same mass noun. The definition of divisive reference is repeated here from Section 2.3.2:

(2) Definition: Divisive reference

DIV(P)=def ∀x[P(x)→ ∀y[y < x→P(y)]]

(A predicateP is divisive if and only if whenever it holds of something, it also holds of each of its proper parts.)

The assumption that divisive reference holds of mass denotations runs into a well-known problem with very small parts of mass substances. This problem is analogous to the one that arises in connection with the subinterval property, and concerns the atomic nature of matter: arguably hydrogen atoms do not qualify as water, so if we consider hydrogen atoms to be part of water, then not every part of water is water (Quine 1960). A different form in which this problem occurs comes from heterogeneous mass predicates likefruit cake,pea soup, orsuccotash (e.g. Taylor 1977): for example, a portion of fruit cake may contain sultanas, but these sultanas do not themselves qualify as fruit cake. This type of argument is arguably stronger than Quine’s argument, because in this case, the minimal parts that do not qualify are directly accessible to the senses. While it might be possible to save the assumption that mass nouns have divisive reference by assuming that we conceptualize even predicates likefruit cakeas having divisive reference, this assumption is even more difficult to justify in the case of fake mass nouns likefurniture. Psycholinguistic experiments suggest that the cognitive structures underlying fake mass nouns are more similar to those of count nouns than to those of other mass nouns (see Section 2.4.1). It would be implausible both in light of the factual reality and in light of our cognitive modeling of it to assume that fake mass nouns have having divisive reference (Barner and Snedeker 2005; Chierchia 2010).

The conclusion that mass nouns do not always have divisive reference appears to be generally accepted. Gillon (1992) notes that “[w]hile some semanticists retain the divisivity of reference as a criterion to distinguish mass nouns from count

nouns . . . only Bunt (1979, 1985) has attempted to justify the retention.” (p. 598). Gillon gives counterarguments to Bunt’s reasons and argues that the grammar is mute on whether or not mass terms have divisive reference. This is also the position I adopt here.