The Weekly Newsletter of MIT Linguistics

MIT Colloquium 12/02 - Maribel Romero (Universität Konstanz)

Speaker: Maribel Romero (Universität Konstanz)
Title: On the many readings of ‘many’
Time/date: Friday, December 2, 3:30-5pm
Location: 32-155

Partee (1989) and a long tradition thereafter distinguish two readings of many and its antonym few: the cardinal reading (1a) and the proportional reading (1b), with n and ρ as context- dependent parameters. These readings are exemplified against scenario (2). Sentence (3) is judged true in virtue of its cardinal reading and sentence (4) in virtue of its proportional reading:

(1) Many Ps are Q.
a. CARDINAL reading: |P∩Q| > n, where n is a large natural number.
b. PROPORTIONAL reading: |P∩Q| : |P| > ρ, where ρ is a large proportion.

(2) Scenario: All the faculty children were at the 1980 picnic, but there were few faculty children back then. Almost all faculty children had a good time.
(3) There were few faculty children at the 1980 picnic.
a. Cardinal: true in (2)
b. Proportional: false in (2)

(4) Many (of the) faculty children had a good time.
a. Cardinal: false in (2)
b. Proportional: true in (2)

Additionally, Westerståhl (1985) famously noted a third interpretation of many, known in the literature as the ‘reverse’ proportional reading (see also Herburger 1997, Cohen 2001). This is exemplified in (5)-(6). Sentence (6) is judged true in scenario (5) in virtue not of its cardinal or proportional reading, but in virtue of its reverse proportional reading paraphrased in (6a) and formulated in (7):

(5) Scenario: Of a total of 81 Nobel Prize winners in literature, 14 come from Scandinavia.
(6) Many Scandinavians have won the Nobel Prize in literature.
a. Intuitive paraphrase of the reverse proportional: ‘Many of the Nobel Prize winners are Scandinavians ’

(7) Many Ps are Q.
REVERSE PROPORTIONAL reading: |P∩Q| : |Q| > ρ, where ρ is a large proportion.

This third reading is problematic for semantic theory no matter whether many is treated as a determiner or as adjectival in nature. If treated as a (parametrized) determiner (cf. Hackl 2000), the lexical entries corresponding to the three readings above will be as in (8). While the cardinal and proportional lexical entries (8a)-(8b) obey Conservativity, defined in (9), the reverse proportional reading (8c) does not, thus challenging the Conservativity Universal (Keenan & Stavi 1986, cf. Barwise & Cooper 1981:U3):

(8) Many as a parametrized determiner:
a. Cardinal:
b. Proportional:
c. Reverse proportional:

λdd. λP. λQ. |P∩Q| ≥ d
λdd. λP. λQ. |P∩Q| : |P| ≥ d λdd. λP. λQ. |P∩Q| : |Q| ≥ d

(9) A determiner denotation f is conservative iff, for any sets of individuals P and Q: f (P)(Q)=1 iff f (P)(P∩Q)=1

If treated as adjectival (cf. Hackl 2009), the lexical entries corresponding to the cardinal and proportional reading can be formulated as in (10a)-(10b). But a serious compositionality problem arises for the reverse proportional reading, since a proportion over |Q| has to be computed while having no λQ-argument in the adjectival entry (10c):

(10) Many as adjective:
a. Cardinal:
b. Proportional:
c. Reverse proportional:

λdd. λP. λxe. P(x) ∧ |x|≥d
λdd. λP. λxe. P(x) ∧ |x|:|P| ≥ d λdd. λP. λxe. P(x) ∧ |x|:|Q| ≥ d ???

Treating many as a determiner, Romero (2015) decomposes many into the determiner stem MANY plus the degree operator POS, and derives the reverse proportional reading from the conservative proportional entry (8b) and independently motivated association patterns of POS. The present talk extends Romero’s analysis in two new directions. First, POS is allowed to associate not just with overt elements in the sentence but also with a world variable. This move, necessary to account for examples like (11), allows us to derive certain difficult cases of apparent reverse proportional readings remaining in the literature. Second, Romero’s (2015) analysis is extended to attributive uses like (12). Using the adjectival entries in (10a)- (10b) and allowing the same association possibilities for POS as in non-attributive uses, different readings are predicted and shown to arise.

(11) For what I had wished for, few students came.

(12) The many demonstrators protested loudly.