Reverse quantification with proportional quantifiers
Dorothy Ahn (Harvard University) · Uli Sauerland (ZAS)
1. Novelties
3. Proposal: Two Structures
2. Korean Q-Float and Q-Reversal
First study of proportional quantifiers like “30 percent” and “two thirds”
Discovery A: Evidence against existing accounts of measurement
Discovery B: Non-conservative quantification (at least on the surface)
Conservative and Reverse Quantification
Q-float with proportional quantifiers isn’t meaning preserving
Discovery A: Reversed readings are only possible with Q-float
Discovery B: Association with focus rather than only reversal
Reverse
(genitive)
(appositive)
DP
Korean Quantifier Float with Proportions
Conservativity Universal: All generalized quantifiers that are expressed by
a determiner in any language are conservative. (Barwise & Cooper 1981,
Keenan & Stavi 1986)
Conservative
n
percent
In Korean, the reverse reading is only possible when the quantifier
occurs after the Nominative marker -ka (i.e. is floated) (cf. Park 2007).
They hired 30% of the women.
They hired 30% women.
KYOSWUF -ka 20-phulo wassta.
professor-NOM 20-percent came
‘20 percent of those who came were professors.’ (reverse)
DP
D/NP
n
(the) [substance]
[Kyoswu 20-phulo]-ka wassta.
professor 20-percent-NOM came
‘20 percent of the professors came.’ (conservative)
Conservative
Reverse
DP
[percent]
NP
percent (C)
= λx ∈ De λn ∈ Dd λy ∈ De .
[substance]-F
µ(xu⊕y )
µ(x)
=
n
100
LF-Adjustment with Reverse structure
They hired 30% women.
?
Proportional Measures
‘Percent’ and fractions are relational, but existing accounts of measures are
only good for non-relational ones like ‘ounces’ (e.g. Krifka 1989, Schwarzschild
2006, Scontras 2014):
30% λx they hired [thex women]
[thirty percent max(C )] ∼C λx they hired [the = x [women]F]
P’07: Only discusses reverse readings with taypwupwun (‘most’) and
argues that the floating quantifier is an adverbial.
→ (a) denominal, (b) not all floating quantifiers
Focus Sensitivity
a. C = {λx . they hired the = x women, λx . they hired the = x men}
L
b. max(C ) = {x | they hired x}
x is 5 ounces of gold
K’89:
S’06:
Narrow focus interpretation is possible.
ounces(x) = 5 & gold(x)
∃ Dim: gold(x) & 5-ounces(Dim(x)) & MON(Dim,gold)
Our Lexical Entry for ‘Percent’
[percent] = λx ∈ De λn ∈ Dd λy ∈ Det .
µ(xu⊕y )
µ(x)
=
n
100
German: Case decides (Sauerland 2014)
Quantitative Genitive (conservative) vs. Quantitative Appositive (reversed):
Ein gut-es Prozent (des) westflischen Bieres trinken die Berliner.
one good-ACC percent the.GEN Westphalian-GEN beer-GEN drink the Berliners
‘Berliners drink over one percent of (the) Westphalian beer.’
Ein gut-es Prozent westflisches Bier trinken die Berliner.
one good-sg percent-ACC Westphalian-ACC beer-ACC drink the Berliners
‘Over one percent of what Berliners drink is Westphalian beer.’
Analysis of Korean
[YECAF kyoswu]-ka 20-phulo wassta.
professor-NOM 20-percent came
‘20 percent of the profs who came were female profs.’
Conservative (not floated)
Reverse (floated)
CaseP
DP
CaseP
NP
Crosslinguistic View
DP
Case
kyoswu Case n
kyoswui
Reverse readings of proportions in many other languages: French
(Benjamin Spector, p.c.)
n
Ce film a été vu par deux tiers de journalistes
This movie has been seen by two thirds of journalists
‘Two thirds of the people who have seen this movie are journalists’
ti percent
NOM
DP
percent (C)
NOM
(identical to Watanabe 2006)
German LF-adjustment ⇔ overt movement in Korean
Ambiguity in Mandarin (Hongyuan Sun, p.c.):
?
[x professor] -nom 20% λx [professor x] came
Tmen lyng le 5% de bnd-rn
3pl. hire perf. 5% DE local-person
‘They hired 5% of the locals.’ / ‘5% of the persons they hired are locals.’
6
Conclusion
Proportional quantifiers
I Widely overlooked class of reverse quantification
I Structural ambiguity of quantitatives
I Cross-linguistic variation on overtness of adjustment
I
References
Krifka, M. 1989. Nominal reference, temporal constitution and quantification in event semantics. Semantics and contextual expressions. Park, Y. G. 2007. A study on the semantic
characteristics of the proportional quantifers in Korean. MA Thesis, Seoul National University. Sauerland, U. 2014. Surface non-conservativity in German. Empirical Issues in Syntax and
Semantics. (in print) Schwarzschild, R. 2006. The role of dimensions in the syntax of noun phrases. Syntax, 9(1), 67-110. Scontras, G. 2014. The Semantics of Measurement. Ph.D
Thesis, Harvard University. Shin, K. Y. 2007. Partitive structures. Ph.D Thesis, University of Illinois at Urbana-Champaign. Watanabe, A. 2006. Functional Projections of Nominals
in Japanese: Syntax of Classifiers. Natural Language & Linguistic Theory, 24(1), 241-306.
NELS 45, October 31–November 2, 2014
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