Galit W. Sassoon

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.

This paper provides a new account of positive versus negative antonyms. The data includes well-known linguistic generalizations regarding negative adjectives, such as their incompatibility with measure phrases (cf. two meters tall/ *short) and ratio phrases (twice as tall/ #short) as well as the impossibility of truly crosspolar comparisons (*Dan is taller than Sam is short). These generalizations admit a variety of exceptions, e.g., positive adjectives that do not license measure phrases (cf. #two degrees warm/cold) and rarely also negative adjectives that do (cf. two hours late/early). Furthermore, new corpus data is presented regarding the use of twice with positive and negative adjectives. The analysis the paper presents supposes that grammar associates gradable adjectives with measure functions—mapping of entities to a set of degrees isomorphic to the real numbers (Kennedy, Projecting the adjective: The syntax and semantics of gradability and comparison, 1999). On this analysis, negative adjectives map entities to values that are linearly reversed and linearly transformed in comparison with their values in the positive antonyms. As shown, the generalizations, as well as their exceptions, directly follow. Negative polarity is explained in terms of function reversal, and non-licensing of measure phrases is explained in terms of transformation by an unspecified value

Vagueness is an ultimate challenge. An enormous diversity of literature on the topic has accumulated over the years, with no hint of a consensus emerging. In this light, Section 1 presents the main aspects of the challenge vagueness poses, focusing on the category of adjectives, and then gives some brief illustrations of the pervasive manifestations of vagueness in grammar.Section 2 deals with theSorites paradox, which for many philosophers is the hallmark of vagueness: By assigning avague predicate step by apparently inescapable step to more and more objects one is eventually led to assign it to entities of which it plainly isn’t true.It is hard to resist the force of the paradox once one has been exposed to it. The result of this has been that many see the philosophical problem presented by vagueness as nothing other than the problem of solving the Sorites.The efforts to solve the Sorites paradox have uncovered a range of important connections between vagueness and other aspects of language and thought. But most of these seem to lead further and further away from what some consider the core issues that vagueness raises.Given the challenge posed by the Sorites, it is rather remarkable to discover that there is a lot more to vagueness beyond the paradox. In fact, linguists traditionally leave it to the philosophers to deal with the Sorites and put their own efforts into dealing with other manifestations of vagueness in natural language and their consequences for grammar. Page 2 2Section 3 reviews some of these additional phenomena, centering around three issues: (i) the controversial connections between vagueness and morphological gradability, (ii) the similarity and differences between the phenomena of vagueness and imprecision, and (iii) the ways in which vagueness infiltrates various grammatical constructions we find in language, with consequences for the architecture of grammar.The aim of this section is to highlight the main questions which any theory of vagueness will ultimately have to address.

This volume is the first to focus specifically on experimental studies of the semantics of gradability, scale structure and vagueness. It presents support for and challenges to current formal analyses of these phenomena in view of experimentally collected data, highlighting the ways semantic and pragmatic theory can benefit from experimental methodologies. The papers in the volume contribute to an explicit and detailed account of the use, representation, and online processing of gradable and vague expressions using various kinds of controlled speaker judgment tasks, eye tracking, and ERP. The aim is to strengthen the foundations of experimental semantics and promote interaction between linguists, psycholinguists, psychologists, and philosophers who are interested in the semantics of natural language. Using data representing different languages and a variety of nominal and adjectival constructions, including degree modification and comparatives, the contributions address scale-based classifications of gradable predicates, such as the absolute vs. relative distinction; the nature of the standards for applicability of gradable expressions and the ways in which standards are determined; the nature of dimensions and multidimensionality in the meaning of scalar expressions; and the role of embodiment, subjectivity, and sociolinguistic considerations in the use and understanding of gradable expressions.

This book presents a study of the connections between vagueness and gradability, and their different manifestations in adjectives (morphological gradability effects) and nouns (typicality effects). It addresses two opposing theoretical approaches from within formal semantics and cognitive psychology. These approaches rest on different, apparently contradictory pieces of data. For example, for psychologists nouns are linked with vague and gradable concepts, while for linguists they rarely are. This difference in approach has created an unfortunate gap between the semantic and psychological studies of the concepts denoted by nouns, as well as adjectives. The volume describes a wide range of relevant facts and theories. Psychological notions such as prototypes and dimensions are addressed with formal rigor and explicitness. Existing formal semantic accounts are examined against empirically established cognitive data. The result is a comprehensive unified approach. The book will be of interest to students and researchers working on the semantics and pragmatics of natural languages and their cognitive basis, the psychology of concepts, and the philosophy of language.