Two theories of plurality and NPI

Two theories of plurality and NPI-licensing
Jan Köpping (Goethe-Universität Frankfurt)
&
[email protected]
Background
Viola Schmitt (Universtiät Wien)
[email protected]
The denotations of plural expressions such as the boys or John and Mary are intuitively
more complex than that of (non-collective) singular expressions such as John or the boy. The latter
denote atomic individuals, but the former seem to denote collections of such atomic individuals – i.e.
subsets of a non-empty set A of individuals. Proposals on plural denotations differ in how they root this
complexity in the ontology. Type 1 proposals (Bennett (1974), Van der Does (1992), Winter (2001) a.o.)
assume that semantic complexity is encoded uniformly: All first order objects, be they the denotations of
plurals or of intransitive predicates such as sleep or boy are members of the set ℘(A), which corresponds
to the functional layer Dheti . Type 2 proposals on the other hand (Link (1983) a.o.) assume that there
are two seperate domains, so to speak, for different kinds of first-order objects: The set ℘(A), Dheti ,
which hosts the extensions of intransitive predicates, and another set, call it +A, which is isomorphic to
℘(A) \ ∅. +A corresponds to De and hosts the denotations of plurals. Furthermore, the application of
the Linkean *-operator to elements of Dheti yields predicate extensions consiting of elements of +A; and
thus generates a second hierarchy of sets. So far, no empirical evidence differentiates between type 1 and
type 2. In the following, we present new data from German that could be considered weakly distinctive:
They are straightforwardly compatible with only with type 1.
Licensing of negative polarity items (NPIs) in plural DPs
In German, licensing of an NPI in a plural
definite DP depends on the predicate that the DP occurs as an argument of. With distributive predicates,
NPIs are always licensed, but with collective predicates, the distribution depends on the predicate in
question: Whereas the NPI auch nur irgend- (≈ the least/ even a single /any) may occur in the subject
of treffen (meet), (1-a), it cannot appear in the subject of ausfüllen (fill (up)), (1-b). (Guerzoni and
Sharvit (2007), based (Lahiri 1997, 1998), claim that definite plural DPs in English always license NPIs;
however, they only consider examples where such DPs occur as arguments of distributive predicates. )
(1)
a.
Die Buben, die auch nur irgendein Interesse an Fußball haben, haben sich gestern im
The boys rp prt prt any
interest in soccer have have refl yesterday in-the
Stadion getroffen. (Die anderen sind ins Wirtshaus gegangen.)
stadium met.
the others are in-the bar
gone
‘Those boys that have even the remotest interest in soccer met in the stadium yesterday. The
others went to a bar.’
b.
# Die Buben, die auch nur irgendein Interesse an Fußball haben, füllten das Stadion
The boys rp prt prt any
interest in soccer have filled the stadium
(schon) komplett aus. (Die anderen hätten
keine Chance gehabt.)
(already) completely prt. (the others would.have no chance had.)
‘# Those boys that have even the remotest interest in soccer, (already) filled the room to
capacity. (The others couldn’t even enter.)’
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Another minimal pair is given in (2): While the NPI is fine in subject of in der Unterzahl sein (be the
minority) in (2-a) it is bad in the subject of in der Überzahl sein (be the majority) in (2-b).
(2)
a.
Die Buben, die auch nur irgendeine Ahnung von Fußball haben, sind in der Unterzahl.
The boys rp prt prt any
clue
of soccer have are in the minority
‘Those boys, that have any clue about soccer, are the minority.’
b.
# Die Buben, die auch nur irgendeine Ahnung von Fußball haben, sind in der Überzahl.
The boys rp prt prt any
clue
of soccer have are in the majority
‘# Those boys, that have any clue about soccer, are the majority.’
Why is this phenomenon weakly distinctive?
This distribution is compatible with known generaliza-
tions about NPI-licensing, in particular, von Fintel’s 1999 notion of Strawson-downward-entailingness,
which relativizes Ladusaw’s 1979 original observation that NPIs are licensed only in downward-entailing
(DE) contexts w.r.t. definedness: NPIs in German DPs may occur only if the predicate P that the DP
is an argument of holds of every sub-plurality X 0 of the plurality X denoted by the DP – as long as P
is defined for X 0 . Type 1 is better suited than type 2 to deal with this outcome: If the cross-categorial
generalization of entailment (and thus of DE-ness) makes reference to the structural properties of the
sets denoted by the expressions in question (cf. Keenan and Faltz (1984)) and if NPI-licensing is thus
sensitive to such structural properties, then type 1, but not type 2, allows for a single condition on NPI
distribution. According to type 1, all complex denotations are members of the functional domains recursively derived from the set individuals A: plural predicates and quantifiers are members of the same
domain. Hence, the NPI-licensing condition could simply be assumed to be tied to all functional layers;
cases like those above and (3) are of the same kind (modulo definedness).
(3)
Every boy who has ever been to Paris is an idiot.
In type 2 on the other hand, quantifiers and plural predicates are different types of objects: While the
former are sets of members of ℘(A), the latter are sets of members of +A – a structure that is set apart
from the functional layers of the ontology. Needless to say, the condition on NPI distribution can be
made compatible with type 2 proposals. But because of the two domains, the adapted version needs to
be disjunctive.
References
Bennett, M.R. 1974. Some Extensions of a Montague fragment in English. Doctoral Dissertation, UCLA.
Van der Does, Jaap. 1992. Applied Quantifier Logics. Doctoral Dissertation, University of Amsterdam.
von Fintel, Kai. 1999. NPI-Licensing Strawson-entailment, and context dependency. Journal of Semantics 2:97–148.
Guerzoni, Elena, and Yael Sharvit. 2007. A question of strength: on NPIs in interrogative clauses. Linguistics and Philosophy
361–391.
Keenan, E. L., and L. M. Faltz. 1984. Boolean Semantics for Natural Language. Dordrecht: Reidel Publishing Company.
Ladusaw, William A. 1979. Polarity Sensitivity as Inherent Scope Relations. Doctoral Dissertation, University of Massachusetts, Amherst, Amherst, MA.
Lahiri, Utpal. 1997. Even-Incorporated NPIs in Hindi Definites. Ms. University of California at Irvine.
Lahiri, Utpal. 1998. Focus and Negative Polarity in Hindi. Natural Language Semantics 6:57–123.
Link, Godehard. 1983. The logical analysis of plurals and mass terms: A lattice-theoretical approach. In Meaning, Use and
Interpretation of Language, ed. R. Baeuerle, C. Schwarze, and Arnim von Stechow, 302–323. DeGruyter.
Winter, Yoad. 2001. Flexibility Principles in Boolean Semantics. Cambridge, Massachusetts: MIT Press.
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