Preliminary: degree and scale

kan DQ XP 'watch' | ge

From the overall discussion of the syntactic perspective, ge is concluded to be a DQ, head selecting phrases composed of [+N] categories.

4.4. The semantic interpretation of ge

4.4.1 Preliminary: degree and scale

Previously, in the syntactic aspect, ge was analyzed as a DQ denoting an uncertain quantity that is minimal; and ge can saturate a q-position of nouns and a g-position of adjectives. The next question that arises is how to interpret ge from the semantic point of view. A good place to start is to examine the g-position because adjectives inherently acquire degrees and scales.

The approach I assume here is based on Kennedy & McNally (1999 and 2005). Kennedy and McNally (2005) provide a brief definition of degree and scale:

Gradable adjectives map their arguments onto abstract representations of

measurement, or DEGREES, which are formalized as points or intervals partially ordered along some DIMENSION (e.g., height, cost, weigh,...). The set of ordered degrees corresponds to a SCALE....

(Kennedy and McNally 2005:349)

Given that definition, gradable adjectives are assumed to contain a set of degrees on a scale, illustrated in (120), where the mark '+' represents different ordered degrees which can be low or high on the scale.

(120) Gradable adjectives

+ + + + + +

However, the above configuration is too rough since the scale may or may not have maximal and minimal elements for adjectives to encode different scalar information. Given that, Kennedy and McNally (2005) further propose four types of scale structures as in (121), where R and ∆ represent the ordering relation and dimension for the scale respectively, and D signifies degree.

(121) A typology of scale structures (Kennedy and McNally 2005, ) a. 〈D^(0,1), R, ∆ 〉 (Totally) OPEN SCALE

b. 〈D^[0,1), R, ∆ 〉 LOWER CLOSED SCALE c. 〈D^(0,1], R, ∆ 〉 UPPER CLOSED SCALE d. 〈D^[0,1], R, ∆ 〉 (Totally) CLOSED SCALE

In Kennedy and McNally (2005:354), scales that are closed on the lower end include such a

minimal value, equal to 0. Scales that are open on the upper end include all degrees that are near the limit 1. Those closed on the upper end have a maximal degree whose value is 1.

Given this definition, scales of different types of APs can be defined as follows.

(122) Adjectives, such as guoyin 'satisfied' and tongkuai 'joyful,' are of a lower closed scale.

(123) Idiom chunks, such as yi-qing-er-chu 'perfectly clear,' are of a closed scale.

Thus, a gradable adjective guoyin 'satisfied' contains a set of degrees on a scale that can be illustrated as (124). The mark '+' represents different ordered degrees which can be low or high on the scale of adjectives, such as 'a little bit satisfied' or 'very satisfied.'

(124) guoyin 'satisfied'

+ + + + + +

On the other hand, idiom chunks have inherent maximal standards. The scale is totally closed.

(125) Yi-gan-er-ging 'thoroughly clean'

(the scale of cleanness)

Kennedy and McNally (2005) further distinguish the relative standard and context-free standard. For the latter, adjectives inherently contain maximal or minimal standards regardless of context, illustrated in (126) and (127).

(126) Adjectives with inherent minimal standard:

open, bent, awake

(127) Adjectives with inherent maximal standard:

full, closed, straight

The idea of the maximal/minimal context-free standard can also refer to Rothstien and Winter's (2004) 'total' vs. 'partial' predicate distinction on the scale structure. Roughly speaking, a total predicate is one such as straight, which is true if the object has a maximal degree of straightness. While a partial predicate is one such as bent, which is true if the object has some degree of bentness.

Similar to the total predicate straight, adjectives in V ge AP have context-free maximum standards. Take the idiom chunk yi-gan-er-jing 'thoroughly clean' for example. The state has to be completely clean thus can be called yi-gan-er-jing 'thoroughly clean.' The observation proves that the property of high degree in a V ge AP construction is not derived from ge but from APs themselves. In other words, the lexical meaning of these adjectives inherently denote high degree. Obvious examples are from idiom chunks as mentioned above. For other adjectives such as guoyin 'satisfied,' tongkuai 'joyful' and lanzui 'dead drunk,' they denote high degree reading compared with other adjectives. Therefore, it is obvious that ge does not denotes high degree by itself, though ge may involve degree modification.¹⁰

By contrast, nouns are unlike g-position which has inherent degree and scale. Doetjes (1997:43) argues that the scalar property of the q-position of nouns is derived based on her assumption that a plural formation can make the q scalar. The plural account of which can be referenced in Chierchia (1998).

Though Chinese bare NPs such as shu 'book' and shui 'water' are considered to be mass nouns (cf. Chierchia 1998 and Doetjes 1997), they may also have q-position since, under

10 Zhu (1982) considers that ge denotes high degree in the adjectives. Others such as Wu (2002), Biq (2002) and Shu (2007) hold the same assumption. On the other hand, Shi (2006) argues the high degree expression is contributed to the adjectives. However, it is undeniable that, in V ge AP construction, high degree expressions such as idiom chunks frequently occur with ge. For the reason, it is worth further studies.

Doetjes' definition, only singular NPs contain the r(eference)-position, or non-scalar q-position.

Given the above assumption, Chinese bare NPs also have scalar q-positions. In other words, nouns have a scale of quantity by definition. Therefore, I propose that the scale of nouns can be considered quite similar to that of adjectives, illustrated in (128). The mark '+' represents different quantities which can be small or big on the scale of shui 'water.' The scale is closed at the lower end since the bottom end for the quantity is the zero point, which means no existence of such quantity of nouns. Its upper end is open since there is no upper limit for the quantity.

(128) shui 'water', shu 'book'

0 + + + + + +

In a similar way, for the case of NumPs, numerals are assumed to have a scale with a set of ordered numbers, which is closed at the lower bound as well, as in (129).

(129) [Number]-wan (fan) CL-bowl (rice)

0 1 2 3 4 5... 10...15...

Therefore, it is concluded that each phrase in V ge XP, such as AP, NP, or NumP, contains a scale corresponding to either degree or quantity and such a scale is closed at the lower end (regardless of whether the upper end is closed or not). The basic configuration for XP assumed is as (130).

(130) XP

+ + + + + +