Collective quantification and the homogeneity constraint

Journal of Logic, Language and Information, 2008

We consider collective quantification in natural language. For many years the common strategy in formalizing collective quantification has been to define the meanings of collective determiners, quantifying over collections, using certain type-shifting operations. These type-shifting operations, i.e., lifts, define the collective interpretations of determiners systematically from the standard meanings of quantifiers. All the lifts considered in the literature turn out to be definable in second-order logic. We argue that second-order definable quantifiers are probably not expressive enough to formalize all collective quantification in natural language.

2013

It is currently assumed that most can quantify over mass domains [12][14]. The crosslinguistic data (English, Romanian, Hungarian and German) examined in the paper indicates that this is true of entity (type e)-restrictor most but not of set (type <e,t>)-restrictor most, which strongly supports the view that mass quantifiers denote relations between entities rather than relations between sets [26] [21] [14]. Nevertheless my proposal differs from previous proposals in assuming a more constrained view of the syntax-semantics mapping.

The Review of Symbolic Logic, 2008

This note explains the circumstances under which a type 〈1〉 quantifier can be decomposed into a type 〈1, 1〉 quantifier and a set, by fixing the first argument of the former to the latter. The motivation comes from the semantics of Noun Phrases (also called Determiner Phrases) in natural languages, but in this article, I focus on the logical facts. However, my examples are taken among quantifiers appearing in natural languages, and at the end, I sketch two more principled linguistic applications.

2016

The current literature on pluralities is mainly concerned with definite plurals in existential contexts and the implicit assumption is that indefinite plurals are to be analyzed in the same way, as sums of individuals (Link 1983, Landman 2000) in the general case or as groups in more specific cases (see in particular collective readings). We will argue that although plural indefinites can be modeled as sums of individuals in those contexts in which they are either bound by existential closure or indirectly bound by an operator that quantifies over events, they cannot do so when they are directly bound by an adverbial quantifier; in the latter context, plural indefinites can only be represented as groups: binary quantifiers cannot denote a relation between two sets of sums, but only a relation between two sets of groups. This generalization will be shown to follow from an individuability constraint on quantification. Quantification requires individuability and, as argued by Landman (...

Recherches linguistiques de Vincennes, 2012

2019

This paper focuses on two questions in the semantics of plural predication: (i) What is the source of variation between non-distributive predicates with respect to Homogeneity? (ii) What is the nature of the distributive/collective distinction in plural predication, i.e., do we have two different meanings corresponding to collective and distributive situations or one weak underspecified meaning compatible with both? Examining question (ii), I strengthen arguments that predicates differ in whether they give rise to one weak meaning or to stronger ones. I further claim that there is a correlation between the behavior of predicates in this regard and their behavior with respect to Homogeneity, which calls for a unified perspective on questions (i)-(ii). I propose to capture this correlation by a modest modification of a standard view of Homogeneity which relies on a trivalent semantics for the pluralization operator together with a relativization of that operator to ‘covers’.

Nous

Plural logic is widely assumed to have two important virtues: ontological innocence and determinacy. It is claimed to be innocent in the sense that it incurs no ontological commitments beyond those already incurred by the first-order quantifiers. It is claimed to be determinate in the sense that it is immune to the threat of non-standard (Henkin) interpretations that confronts higher-order logics on their more traditional, set-based semantics. We challenge both claims. Our challenge is based on a Henkin-style semantics for plural logic that does not resort to sets or set-like objects to interpret plural variables, but adopts the view that a plural variable has many objects as its values. Using this semantics, we also articulate a generalized notion of ontological commitment which enables us to develop some ideas of earlier critics of the alleged ontological innocence of plural logic.

2007

The current literature on pluralities is mainly concerned with definite plurals in existential contexts and the implicit assumption is that indefinite plurals are to be analyzed in the same way, as sums of individuals (Link 1983, Landman 2000) in the general case or as groups in more specific cases (see in particular collective readings). We will argue that although plural indefinites can be modeled as sums of individuals in those contexts in which they are either bound by existential closure or indirectly bound by an operator that quantifies over events, they cannot do so when they are directly bound by an adverbial quantifier; in the latter context, plural indefinites can only be represented as groups: binary quantifiers cannot denote a relation between two sets of sums, but only a relation between two sets of groups. This generalization will be shown to follow from an individuability constraint on quantification. Quantification requires individuability and, as argued by Landman (...

A distinction is introduced between itemized and non-itemized plural predication. It is argued that a full-fledged system of plural logic is not necessary in order to account for the validity of inferences concerning itemized collective predication. Instead, it is shown how this type of inferences can be adequately dealt with in a first-order logic system, after small modifications on the standard treatment. The proposed system, unlike plural logic, has the advantage of preserving completeness. And as a result, inferences such as 'Dick and Tony emptied the bottle, hence Tony and Dick emptied the bottle' are shown to be first-order.