On Reverse Readings of 'Many'
Partee (1989) and a long tradition thereafter distinguish two readings of many: the cardinal reading (1a) and the proportional reading (1b), with n and r as context-dependent parameters. Additionally, sentence (2) has been argued to give rise to a third reading - known in the literature as the 'reverse' proportional reading-, paraphrased in (3) and in virtue of which the sentence is judged true in scenario (4) (Westerståhl 1985, Herburger 1997, cf. Cohen 2001, a.o.). This intuitive paraphrase is formalized in (1c). However, this formalization renders manyrev.prop non-conservative, thus defying the conservativy universal in (5)-(6):
(1) Many Ps are Q.
a. Cardinal reading: |PÇQ| > n, where n is a large natural number.
b. Proportional reading: |PÇQ| : |P| > r, where r is a large proportion.
c. Reverse proportional reading: |PÇQ| : |Q| > r, where r is a large proportion.
(2) Many Scandinavians have won the Nobel Prize in literature.
(3) Intuitive paraphrase of (2): 'Many of the Nobel Prize winners are Scandinavians'.
(4) Scenario: Of the 81 Nobel Prize winners in literature, 14 come from Scandinavia.
(5) A determiner denotation f is conservative iff, for any sets of individuals P and Q:
f (P)(Q)=1 iff f (P)(PÇQ)=1
(6) Conservativity Universal: (Barwise & Cooper 1981)
All Natural Language Determiners denote conservative functions.
To circumvent this problem, Romero (2015) decomposes many into the determiner stem many plus the degree operator pos (cf. Hackl 2000) and derives the reverse proportional reading from independently motivated association patterns of pos while preserving conservativity. However, a particularly hard case remains, namely, Herburger's (1997) reading in (7)-(8):
(7) Scenario: The fellowship committee is sorting through the applications for travel funding to Paris. Without knowing how many applications there are, at an early point during the review process they observe that on average only every twentieth application was sent by a cook, which is a much lower percentage than they had anticipated.
(8) Few cooks applied.
The present talk extends Romero's analysis to derive Herburger's reading. Two ingredients will be essential. First, Romero's analysis of reverse and non-reverse proportional readings is shown to apply to cardinal readings as well. Second, pos is allowed to associate not just with overt elements in the sentence but also with a world variable. With these tools, Herburger's reading will be derived as a non-reverse cardinal reading.
Partee (1989) and a long tradition thereafter distinguish two readings of many: the cardinal reading (1a) and the proportional reading (1b), with n and r as context-dependent parameters. Additionally, sentence (2) has been argued to give rise to a third reading - known in the literature as the 'reverse' proportional reading-, paraphrased in (3) and in virtue of which the sentence is judged true in scenario (4) (Westerståhl 1985, Herburger 1997, cf. Cohen 2001, a.o.). This intuitive paraphrase is formalized in (1c). However, this formalization renders manyrev.prop non-conservative, thus defying the conservativy universal in (5)-(6):
(1) Many Ps are Q.
a. Cardinal reading: |PÇQ| > n, where n is a large natural number.
b. Proportional reading: |PÇQ| : |P| > r, where r is a large proportion.
c. Reverse proportional reading: |PÇQ| : |Q| > r, where r is a large proportion.
(2) Many Scandinavians have won the Nobel Prize in literature.
(3) Intuitive paraphrase of (2): 'Many of the Nobel Prize winners are Scandinavians'.
(4) Scenario: Of the 81 Nobel Prize winners in literature, 14 come from Scandinavia.
(5) A determiner denotation f is conservative iff, for any sets of individuals P and Q:
f (P)(Q)=1 iff f (P)(PÇQ)=1
(6) Conservativity Universal: (Barwise & Cooper 1981)
All Natural Language Determiners denote conservative functions.
To circumvent this problem, Romero (2015) decomposes many into the determiner stem many plus the degree operator pos (cf. Hackl 2000) and derives the reverse proportional reading from independently motivated association patterns of pos while preserving conservativity. However, a particularly hard case remains, namely, Herburger's (1997) reading in (7)-(8):
(7) Scenario: The fellowship committee is sorting through the applications for travel funding to Paris. Without knowing how many applications there are, at an early point during the review process they observe that on average only every twentieth application was sent by a cook, which is a much lower percentage than they had anticipated.
(8) Few cooks applied.
The present talk extends Romero's analysis to derive Herburger's reading. Two ingredients will be essential. First, Romero's analysis of reverse and non-reverse proportional readings is shown to apply to cardinal readings as well. Second, pos is allowed to associate not just with overt elements in the sentence but also with a world variable. With these tools, Herburger's reading will be derived as a non-reverse cardinal reading.