Relative measurement and scope

Haoze Li, GDUFS

Abstract

Ahn & Sauerland (2017) observe that proportional number expressions like 20% and two thirds can be used in two different structures:

(1) Huawei hired 40% of the locals.
(2) Huawei hired 40% locals.

These two sentences have different readings. (1) expresses the ratio of locals hired by Huawei relative to all locals. (2) communicates the ratio of the locals hired by Huawei relative to all Huawei’s hires. In terms of conservativity of quantifiers, they call the interpretation of (1) `conservative reading’ and the interpretation of (2) `non-conservative reading’. This is because only the quantification expressed by (1) can be construed as:

(3) [40% x: x is a local] (Huawei hired x)
  (= [40% x: x is a local hired by Huawei] [Huawei hired x] )

The meaning of (2), as represented in (4), seems to be an inverted version of (1).

(4) [40% x: x is a person hired by Huawei] (x is a local)

This paper takes up this observation and investigates the scope of relative measure phrases. Based on relative measurement constructions in Mandarin, I show that relative measure phrase exhibits distinct scope patterns when it receives different interpretations. For example, a relative measure phrase can take scope over negation if it has a conservative reading, but cannot when it has a non-conservative reading.

Based on the scope distinctions, I propose that a relative measure phrase should be decomposed into two parts — a proportional number expression, such as 30%, and a counting quantifier, which has the same denotation as many NPs. The proportional number expression scopes at different positions when the relative measure phrase hosting it is interpreted differently: on the conservative reading, the proportional number expression scopes at the edge of the relative measure phrase; whereas, on the non-conservative reading, the proportional number expression scopes beyond the relative measure phrase and is parasitic on the covert focus movement of the NP complement in the relative measure phrase.