Eliminating Comparison Classes (Kennedy, 2005a)

Kennedy (2005a) proposes that for-PP's are modifiers of gradable adjective phrases and compared-to phrases are modifiers of DegP's. The important thing to notice about this proposal is that there is only one DegP, headed by a POS operator –

this notion of for-PP's and compared-to phrases is in (279). I have modified it in order to include our previous conclusion that the thematic-PP is introduced above the

for-PP. (279) DegP ! DegP wo Deg' PP 3 6 Deg aP compared-to 3 PParg a' 3 a AP wo AP PP ! 5 A for-PP

For now, let's focus on the for-PP and just consider a structure that does not include modification of the DegP by a compared-to phrase. These assumptions require a change to the semantics of both the for-PP and the POS operator.

First, the for-PP is a modifier of gradable adjectives phrases, i.e., a modifier of measure functions. In essence, the for-PP restricts the domain of the gradable adjective phrase. But Kennedy has it do so in a unique way. Since the gradable adjective is a measure phrase, we cannot simply conjoin the AP and the for-PP without saying that the for-PP is a measure phrase as well (an assumption that seems impossible). Instead, Kennedy bases his analysis on the following sentences (from Kennedy (2005a)).

(280) a. Kyle's car is expensive for a Honda. b. Kyle's car is not expensive for a Honda. c. Is Kyle's car expensive for a Honda?

(281) a. #Kyle's BMW is expensive for a Honda. b. #Kyle's BMW is not expensive for a Honda. c. #Is Kyle's BMW expensive for a Honda?

Kennedy says that the reason the sentences in (281) sound odd in comparison to those in (280) is because there is a requirement on positive adjectives with for-PP's, first pointed out in Wheeler (1972). In sentences of the form x is A for a NP, we have a strong inclination to suppose that x is an NP. So, for example, in (280)a, Kyle's car is not only expensive compared to the typical Honda, it is also a Honda. Now, if this generalization is correct, then in (281)a, Kyle's BMW must be a Honda. And since BMW's cannot be Hondas, the sentence sounds odd. Therefore, we can conclude that there is some sort of a relationship between the object predicated of the gradable adjective phrase and the NP part of the for-PP.

One might think that this relationship can be represented by predicating the subject of the NP part of the for-PP. This could be accomplished by integrating the adjective and the for-PP together in a way that x is A for a NP means x is A for a NP

and x is a NP. (Platts, 1979, Siegel, 1976a, Siegel, 1976b, Wheeler, 1972) This type

Kennedy points out that this is not the case. The relationship between the subject and the for-PP persists even in negated sentences and questions, as evidenced by the oddness of (281)b and (281)c. Kennedy concludes from this that the requirement is not an assertion, but rather a presupposition. Hence, it cannot be that the adjective and the for-PP are simply conjoined, i.e., x is A for a NP and x is NP, because that would be an asserted predication relationship.42

Kennedy suggests that the presupposition arises from a modification of the domain of the AP by the for-PP. In this analysis, the for-PP does not combine as an argument of the DegP. Instead, it is a function of type <<e,d>, <e,d>>, and thus, combines with a gradable adjective returning another gradable adjective phrase. The new gradable adjective phrase presupposes that everything in its domain has the property denoted by the NP.

(282) ||[PP for a NP]|| = λGλx: ||NP||(x). G(x)

One interesting benefit of this analysis is that the for-part of the for-PP is not treated as a vacuous element. It turns the NP into a function that modifies the

presuppositional structure of measure phrases. For example, (283)a is the denotation of an unmodified gradable adjective, expensive. It is a measure function, and it takes an individual and returns the cost of that individual. (283)b is a gradable adjective modified by the phrase for a Honda. It is a function that takes an individual which is presupposed to be a Honda, and returns its cost.

(283) a. ||[AP expensive]|| = λx. EXPENSIVE (x)

b. ||[AP expensive for a Honda]|| = λx: Honda(x). EXPENSIVE (x)

This means that POS must be slightly changed so that it does not expect a comparison

class as its second argument.43

(284) POS = λGλx. G(x) ≥ NORM (G)

This new POS operator contains a NORM function that works only on adjective

denotations. This does not create a problem, however, because the comparison class information (the property denoted by the NP) is contained inside the adjective denotation. So, for instance, if (284) were applied to (283)b, we would get a predicate of individuals such as in (285).

(285) a. ||[DegPPOS [AP expensive for a Honda]]|| =

b. [λGλx. G(x) ≥ NORM (G)]( λx: Honda(x). EXPENSIVE (x)) =

c. λx: Honda(x). EXPENSIVE (x) ≥ NORM (λx: Honda(x). EXPENSIVE (x))

This predicate presupposes that its single argument x is a Honda, and it says that x's cost is greater than or equal to the typical cost of things that are presupposed to be

43 _{Kennedy (2005a) actually proposes another change to the denotation of}

POS

concerning the status of the NORM function, which is not relevant here so I will ignore

Hondas. So, the comparison class is used to determine the standard degree, but it does not have any special status in the syntax or semantics: it is simply one more thing that the NORM function takes into account when it determines the standard.