This chapter offers a logical, linguistic, and philosophical account of modern quantification theory. Contrasting the standard approach to quantifiers (according to which logical quantifiers are defined by enumeration) with the generalized approach (according to which quantifiers are defined systematically), the chapter begins with a brief history of standard quantifier theory and identifies some of its logical, linguistic, and philosophical strengths and weaknesses. It then proceeds to a brief history of generalized quantifier theory and explains how it overcomes the weaknesses of (...) the standard theory. One of the main philosophical advantages of the generalized theory is its philosophically informative criterion of logicality. The chapter describes the work done so far in this theory, highlights some of its central logical results, offers an overview of its main linguistic contributions, and discusses its philosophical significance. (shrink)

With this paper I aim to demonstrate that a look beyond the Aristotelian square of opposition, and a related non-conservative view on logical determiners, contributes to both the understanding of Aristotelian syllogistics as well as to the study of quantificational structures in natural language.

This paper presents an extensional account of manyand few that explains data that have previously motivated intensional analyses of these quantifiers :599–620, 2000). The key insight is that their semantic arguments are themselves set intersections: the restrictor is the intersection of the predicates denoted by the N’ or the V’ and the restricted universe, U, and the scope is the intersection of the N’ and V’. Following Cohen, I assume that the universe consists of the union of alternatives to the (...) nominal and verbal predicates, where an alternative to a property ψ is one that shares a pragmatic presupposition with ψ, and a pragmatic presupposition is one that is selected by context from a set of potential presuppositions associated with the sentence. A many/few-quantified sentence is then true iff the proportion of the scope to the restrictor is greater/less than some threshold, n. In addition to explaining various problematic cases from the literature, the analysis shows how the readings of a many/few-quantified sentence can be derived from the same syntactico-semantic structure, it being unnecessary to claim lexical or structural ambiguity. The analysis also provides strong support for the idea that natural language quantification is always purely extensional. (shrink)

The Bounds of Logic presents a new philosophical theory of the scope and nature of logic based on critical analysis of the principles underlying modern Tarskian logic and inspired by mathematical and linguistic development. Extracting central philosophical ideas from Tarski’s early work in semantics, Sher questions whether these are fully realized by the standard first-order system. The answer lays the foundation for a new, broader conception of logic. By generally characterizing logical terms, Sher establishes a fundamental result in semantics. Her (...) development of the notion of logicality for quantifiers and her work on branching are of great importance for linguistics. Sher outlines the boundaries of the new logic and points out some of the philosophical ramifications of the new view of logic for such issues as the logicist thesis, ontological commitment, the role of mathematics in logic, and the metaphysical underpinning of logic. She proposes a constructive definition of logical terms, reexamines and extends the notion of branching quantification, and discusses various linguistic issues and applications. (shrink)

In this paper, a theory T H based on combining type freeness with logic is introduced and is then used to build a theory of properties which is applied to determiners and quantifiers.

Reporting on the 7th International Congress of Logic, Methodology, and Philosophy of Science, first the main topics and some organisational aspects of the congress are presented; the main part of the report focuses on recent developments in Philosophical Logic , in particular the theory of so-called generalized quantifiers as presented at the congress. In addition, some background information on logical language analysis, its possible applications and consequences is provided.

This work adopts the perspective of plural logic and measurement theory in order first to focus on the microstructure of comparative determiners; and second, to derive the properties of comparative determiners as these are studied in Generalized Quantifier Theory, locus of the most sophisticated semantic analysis of natural language determiners. The work here appears to be the first to examine comparatives within plural logic, a step which appears necessary, but which also harbors specific analytical problems examined here.Since nominal comparatives involve (...) plural and mass reference, we begin with a domain of discourse upon which a lattice structure (Link's) is imposed, and which maps (via abstract dimensions such asweight in kilograms) to concrete measures (in N,R+). The mapping must be homomorphic and Archimedean. Comparisons begin as simple predicates on dimensions or measures; from these we derive classes of predicates on the domain, i.e., generalized determiners (quantifiers), and show, e.g., how monotonicity properties follow in the derivation. This results in a proposal for a logical language which includes derived determiners, and which is an attractive target for semantics interpretation; it also turns out that some interesting comparative determiners are first order, at least when restricted to nonparametric and noncollective predications. (shrink)

We generalize an observation made by Goldblatt in "Diodorean modality in Minkowski spacetime" by proving that each -dimensional integral spacetime frame equipped with Robb's irreflexive `after' relation determines a unique temporal logic. Our main result is that, unlike -dimensional spacetime where, as Goldblatt has shown, the Diodorean modal logic is the same for each frame , in the case of -dimensional integral spacetime, the frame determines a unique Diodorean modal logic.

The semantics of noun phrases (NPs) is of crucial importance for both philosophy and linguistics. Throughout much of the history of the debate about the semantics of noun phrases there has been an implicit assumption about how they are to be understood. Basically, it is the assumption that NPs come only in two kinds. In this paper we would like to make that assumption explicit and discuss it and its status in the semantics of natural language. We will have a (...) look at how the assumption is to be understood more precisely, what its methodological status should be, whether it has been abandoned in recent work in semantics, and whether it should be abandoned in future work. To do all this, it’s best to start with some historical context. (shrink)