This book offers a unique synthesis of past and current work on the structure, meaning, and use of negation and negative expressions, a topic that has engaged thinkers from Aristotle and the Buddha to Freud and Chomsky. Horn's masterful study melds a review of scholarship in philosophy, psychology, and linguistics with original research, providing a full picture of negation in natural language and thought; this new edition adds a comprehensive preface and bibliography, surveying research since the book's original publication.

The sentence Irving was closer to me than he was to most of the others contains a quantifier, most of the other, in the scope a comparative. The first part of this paper explains the challenges presented by such cases to existing approaches to the semantics of the comparative. The second part presents a new analysis of comparatives based on intervals rather than points on a scale. This innovation is analogized to the move from moments to intervals in tense semantics. (...) The remainder of the paper is concerned with an interval-based semantics of degree in relation to issues other than the comparative proper. The paper begins with a discussion of the role negative polarity has played in studies on the semantics of comparatives. (shrink)

Written by two of the leading figures in the field, this is a lucid and systematic introduction to semantics as applied to transformational grammars of the ...

This paper deals with the truth-Conditions and the logic for vague languages. The use of supervaluations and of classical logic is defended; and other approaches are criticized. The truth-Conditions are extended to a language that contains a definitely-Operator and that is subject to higher order vagueness.

The notion of measurement plays a central role in human cognition. We measure people’s height, the weight of physical objects, the length of stretches of time, or the size of various collections of individuals. Measurements of height, weight, and the like are commonly thought of as mappings between objects and dense scales, while measurements of collections of individuals, as implemented for instance in counting, are assumed to involve discrete scales. It is also commonly assumed that natural language makes use of (...) both types of scales and subsequently distinguishes between two types of measurements. This paper argues against the latter assumption. It argues that natural language semantics treats all measurements uniformly as mappings from objects (individuals or collections of individuals) to dense scales, hence the Universal Density of Measurement (UDM). If the arguments are successful, there are a variety of consequences for semantics and pragmatics, and more generally for the place of the linguistic system within an overall architecture of cognition. (shrink)

This paper investigates the way that linguistic expressions influence vagueness, focusing on the interpretation of the positive (unmarked) form of gradable adjectives. I begin by developing a semantic analysis of the positive form of ‘relative’ gradable adjectives, expanding on previous proposals by further motivating a semantic basis for vagueness and by precisely identifying and characterizing the division of labor between the compositional and contextual aspects of its interpretation. I then introduce a challenge to the analysis from the class of ‘absolute’ (...) gradable adjectives: adjectives that are demonstrably gradable, but which have positive forms that relate objects to maximal or minimal degrees, and do not give rise to vagueness. I argue that the truth conditional difference between relative and absolute adjectives in the positive form stems from the interaction of lexical semantic properties of gradable adjectives—the structure of the scales they use—and a general constraint on interpretive economy that requires truth conditions to be computed on the basis of conventional meaning to the extent possible, allowing for context dependent truth conditions only as a last resort. (shrink)

Comparative constructions form two classes, those that permit direct comparisons (comparisons of measurements as in Seymour is taller than he is wide) and those that only allow indirect comparisons (comparisons of relative positions on separate scales as in Esme is more beautiful than Einstein is intelligent). In contrast with other semantic theories, this paper proposes that the interpretation of the comparative morpheme remains the same whether it appears in sentences that compare individuals directly or indirectly. To develop a unified account, (...) I suggest that all comparisons (whether in terms of height, intelligence or beauty) involve a scale of universal degrees that are isomorphic to the rational (fractional) numbers between 0 and 1. Crucial to a unified treatment, the connection between the individuals being compared and universal degrees involves two steps. First individuals are mapped to a value on a primary scale that ranks individuals with respect to the gradable property (whether it be height, beauty or intelligence). Second, the value on the primary scale is mapped to a universal degree that encodes the value’s relative position on the primary scale. Direct comparison results if measurements such as seven feet participate in the primary scale (as in Seven feet is tall). Otherwise the result is an indirect comparison. (shrink)

In a recent paper, Martin Hackl and I identified a variety of circumstances where scalar implicatures, questions, definite descriptions, and sentences with the focus particle only are absent or unacceptable (Fox and Hackl 2006, henceforth F&H). We argued that the relevant effect is one of maximization failure (MF): an application of a maximization operator to a set that cannot have the required maximal member. We derived MF from our hypothesis that the set of degrees relevant for the semantics of degree (...) constructions is always dense (the Universal Density of Measurement, UDM). The goal of this paper is to present an apparent shortcoming of F&H and to argue that it is overcome once certain consequences of the proposal are shown to follow from more general properties of MF. Specifically, the apparent problem comes from evidence that the core generalizations argued for in F&H extend to areas for which an account in terms of density is unavailable. Nevertheless, I will argue that the account could still be right. Certain dense sets contain "too many alternatives" for there to be a maximal member, thus leading to MF. But, there are other sets that lead to the same predicament. My goal will be to characterize a general signature of MF in the hope that it could be used to determine the identity of alternatives in areas where their identity is not clear on independent grounds. (shrink)

This paper uses the distribution and interpretation of antonymous adjectives in comparative constructions as an empirical basis to argue that abstract representations of measurement, or ‘degrees’, must be modeled as intervals on a scale, rather than as points, as commonly assumed. I begin by demonstrating that the facts in this domain must be accounted for in terms of the interaction of the semantics of adjectival polarity and the semantics of the comparative, rather than principles governing the (overt) expression of particular (...) types of adjectives in comparatives. I then show that a principled account of the full range of data under consideration can be constructed within a model in which degrees are formalized as intervals on a scale and adjectival polarity is characterized in terms of two structurally distinct and complementary sorts of `positive' and `negative' degrees. (shrink)

This paper presents a novel semantic analysis of unit names (like pound and meter) and gradable adjectives (like tall, short and happy), inspired by measurement theory (Krantz et al. In Foundations of measurement: Additive and Polynomial Representations, 1971). Based on measurement theory’s four-way typology of measures, I claim that different adjectives are associated with different types of measures whose special characteristics, together with features of the relations denoted by unit names, explain the puzzling limited distribution of measure phrases, as well (...) as unit-based comparisons between predicates (as in the table is longer than it is wide). All considered, my analyses support the view that the grammar of natural languages is sensitive to features of measurement theory. (shrink)

Structures for Semantics offers an advanced course in logical and mathematical techniques and structures that are used in semantics, in relation to their semantic applications. The book helps students with a background in semantics to develop their skills of formalization and it makes research in semantics accessible. Workers in other disciplines will use it to discover more about the role of formal modelling in current semantic research, and about semantics itself. Following a chapter on logic and set theory there are (...) three parts of chapters: two pairs of chapters on partial order and equivalence relations in relation to semantic analyses of tense, partial information and vagueness; two chapters on methods for creating ordered structures in relation to intervals, events, and the semantics of change; two chapters on lattices and Boolean algebras in relation to types for noun phrases and verbs, and the semantics of plurals and mass nouns. For upper-level undergraduate students and graduate students in semantics: theoretical linguists, logicians, philosophers of language, computer scientists interested in natural language semantics. (shrink)

The paper concerns the expression of non-strict comparison, focusing in particular on constructions of the form [no(t) . . .-er than] in modified numerals. The main empirical finding is the observation that negated comparatives contrast with regular comparatives in that the former but not the latter can give rise to (scalar) implicatures. It is shown that such a contrast falls out of theories of exhaustive interpretation that claim alternatives to form dense scales. An important result is that the paper sharpens (...) the desiderata for theories of exhaustification. (shrink)