Research

Publications

Greer, Kristen A. 2015. The 'whole' story of partitive quantification. In Proceedings of the 41st annual Berkeley Linguistics Society, pp. 175-196.

Greer, Kristen A. 2014. Extensionality in natural language quantification: The case of many and few. Linguistics and Philosophy, 37(4): 315-351.

Bayley, Robert, Greer, Kristen, and Holland, Cory. 2013. Lexical frequency and syntactic variation: A test of a linguistic hypothesis. In U. Penn Working Papers in Linguistics 19.2: Proceedings of NWAV 41.

Awards

Allen G. Marr Distinguished Dissertation Award, 2015

Provost's Dissertation Year Fellowship, 2013-2014

Dissertation

A general theory of quantification

(.pdf of the full text)

My dissertation details a theory of quantifiers that appear in and define the structure of the DP (henceforth, DP quantifiers) that is both (a) fully general and (b) purely extensional. By general, I mean that the structure can generate all of the interpretations (proportional, reverse, focus-affected, and cardinal) of quantifiers without resorting to lexical or structural ambiguity, as is common in extant theories of quantification. And by extensional, I mean that the semantic structure of DP quantifiers can be specified without reference to intensional constructs. In this respect, the dissertation is a strong defense of the original claim of Generalized Quantifier Theory (GQT), namely, that quantity is a logical notion, and as such, an extensional one.

To achieve this structure, the dissertation makes three claims:

1. the truth-conditional effects of context on the interpretation of DP quantifiers are represented as variables at Logical Form (LF);
2. the logical structure of DP quantifiers is always partitive; and
3. DP quantifiers form a heterogeneous class on the basis of how they instantiate this partitive structure.

The first of these claims is pivotal. I discharge Barwise and Cooper's (1986) Fixed Context Assumption, suggesting that the only thing "missing" from the original formulation of GQT is a thorough understanding of the role of context. I argue that there are two such effects: one is in determining the domain, and the second is in restricting that domain to a relevant subset (existing research focuses only on the latter of these). It is from the former effect that the fundamental account of the aforementioned ambiguity takes shape: the domain may be either the nominal or the verbal predicate from the overt structure, with the former resulting in a proportional (or verbally focused) reading and the latter in a reverse (or nominally focused) reading. I outline a detailed theory of how the content of the domain is determined by the presuppositions of the discourse (with the cardinal reading resulting when nothing is presupposed). I further argue that these presuppositions can be defined in a purely extensional way, with the result that intensional construct like alternative possible worlds or normative situations are entirely unnecessary in the architecture of the account.

If these contextual effects are represented as variables at LF, the structure we have traditionally accepted for quantifiers, which treats them as determiners taking a NP complement, must be modified to incorporate them. My second claim outlines how to accomplish this. I propose that the complement of quantifiers is a partitive prepositional phrase that dominates the variable, contextually-resolved content. In this way, I retain the traditional assumption regarding the syntax-semantics mapping, wherein what is c-commanded by the quantifier represents its domain while allowing this domain to be flexible. I also show that there is independent evidence to support this partitive structure, surveying recent arguments from the literature and advancing novel empirical and theoretical arguments of my own.

The key innovation of the partitive structure is that while it allows for a variable domain, it does not require one. As claim three indicates, quantifiers are not a homogeneous class in this regard: while some are ambiguous, others are not. For such non-ambiguous quantifiers, the domain of quantification is uniformly represented by the noun phrase at surface structure. These quantifiers may therefore c-command the noun at LF as the standard GQT architecture proposes. This rigid domain can be accommodated in the proposed structure by placing the noun within the partitive PP. Quantifiers thus divide into two categories, those that c-command variable content at LF and associate with the noun as modifiers (adjectives) and those that c-command the noun (itself embedded in a partitive PP) as determiners at LF. I argue that quantifiers divide into these two categories as follows.

Unambiguous quantifying determiners (Q-Dets): every, each, both

Ambiguous quantifying adjectives (Q-Adjs): many, few, some, several, a (one), no (none), two/three/etc., all (only), most (mostly), a few

Of the ambiguous quantifiers, I show that some, several, a (one), no (none), and two/three/etc. are trivially ambiguous, bearing logically equivalent interpretations. More contentiously, I claim that all/only and most/mostly represent surface realizations of underlying quantifier meanings, ALL and MOST, that are non-trivially ambiguous, providing morphological, etymological, and distributional evidence to support this 'allolexy' analysis.

After motivating these claims, I describe the syntactico-semantic structure that emerges once we accept them. This structure is as in Figures 1 and 2 below for Q-Adjs and Q-Dets, respectively.

Beyond the claims of generality and extensionality, this analysis sheds interesting new light on familiar problems from the literature on DP quantifiers. In particular, I explore the implications it has for referential indefinites, quantifier scope, the quantificational variability effect, and the anaphora induced by negative quantifiers.