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Gradable adjectives not only raise (now familiar) puzzles about discourse-oriented uses of context-sensitive expressions. They also constitute a principal source of vagueness. This chapter starts by examining various uses of gradable adjectives in communicating information and adjusting contextually operative standards. It is shown how to apply the Discourse Contextualist framework to capture these discourse dynamics, utilizing a particular contextualist interpretation of a standard degree semantics. Although standards-sensitivity isn’t sufficient for vagueness, the foregoing Discourse Contextualist semantics and pragmatics motivates an attractive account of various paradigmatic vagueness phenomena. Vagueness is diagnosed as a form of contextual indecision. The proposed treatment of context in vagueness phenomena—in particular, the sorites paradox and borderline cases—sheds light on general issues concerning the logic, semantics, and dynamics of vagueness. It provides the basis for a theory combining features many have thought incompatible: a classical semantics, and a non-epistemic treatment of vagueness. Issues concerning gradability and vagueness phenomena in language generally are briefly considered.

This chapter is the first installment of a history of the treatment of evaluativity in degree semantics. It begins with a brief tutorial in degree semantics and a short discussion of the ontological status of degrees. It details the origins of degree semantics (Bartsch and Vennemann 1972; Cresswell 1976), which was also the origin of POS, a null degree modifier proposed to treat evaluativity in positive constructions. The second half of the chapter includes a review of semantic and philosophical discussions about the nature of the standard invoked by evaluativity, as well as a review of recent applications of POS outside of evaluative adjectival constructions, particularly in event semantics.

This chapter discusses Edgington’s probabilistic, degree-theoretic semantics for vagueness. After describing Edgington’s semantics, her suggestion that it and classical semantics provide non-competing descriptions of a single phenomenon is examined. It is argued that the suggestion should be rejected because classical semantics is incompatible with plausible principles about the relationship between the two frameworks. Edgington also argues that the many degrees assigned to sentences in her semantics are not new truth-values. It is argued that these arguments presuppose a certain non-semantic conception of truth. Although Edgington’s arguments do force a distinction between two theoretical roles typically associated with the notion of truth, one properly semantic and one merely expressive, they do not preclude identification of the many degrees of her probabilistic formalism with new truth-values in the semantic sense.

Since many modal expressions in English are overtly gradable, we need to understand gradability in general if we are to understand their semantics. This chapter introduces a number of core notions in the lexical and compositional semantics of gradable expressions, including the distinction between gradability and scalarity, key notions around adjective type and scale structure, and discusses some background issues such as the treatment of comparison classes and vagueness.

This chapter reviews the motivations (both conceptual and formal) for the degree-based analyses of comparatives generally, and in this way presents the basic details of the semantic framework that the book presupposes. In particular, this chapter establishes the vocabulary of measure functions, degrees, and scales, and sets up the book’s answer to the central question of which expressions introduce measure functions into the compositional semantics. By establishing the central distinction between “measurable” and “non-measurable” domains for predication, this chapter initiates the comparison between standard, lexically-based theories of degree introduction, from the book’s theory in which degrees are uniformly introduced by the comparative morphology itself.

Chapter 7 starts by examining “predicates of personal taste” (PPTs). It is argued that PPTs are an instance of a more interesting category of evaluational predicates, including PPTs, aesthetic predicates, moral predicates, and epistemic predicates, among others. What distinguishes evaluational adjectives is that their context-sensitivity persists in comparative constructions. The Discourse Contextualist degree semantics and pragmatics from Chapter 6 is extended to capture this. The two loci of context-sensitivity associated with evaluational adjectives lead to distinct kinds of vagueness phenomena. These phenomena raise challenges for the treatment of the sorites paradox from Chapter 6. It is shown how speakers’ substantive assumptions about “subjectivity/objectivity” lead to certain differences among evaluational adjectives in patterns of use. Considering the broader range of evaluational adjectives poses problems for existing characterizations of felicitous embedding under ‘find’, a common diagnostic for PPTs/“subjectivity.” The discussions in this book of the varieties of context-sensitive uses of language motivate a more adequate characterization.

This chapter proposes an explanation for the oddness of negative islands, such as *How didn’t John behave at the party? and *How many children doesn’t John have?. These examples contrast with Who didn’t John invite to the party?, which shows that a wh-word ranging over individuals can escape negation without problems. The chapter proposes that the reason for the unacceptability of the ungrammatical questions above is that they cannot have a maximally informative true answer (MIP). Fox and Hackl (2007) have argued this presupposition explains the unacceptability of negative degree islands if we assume that scales of degrees are dense (UDM). This chapter argues that the unacceptability of negative degree islands is not rooted in the UDM, but follows from degree questions ranging over intervals (cf. also Abrusán and Spector 2011). I further show that in the case of negative manner questions, the MIP can also never be met.

This chapter is the second installment of a history of the treatment of evaluativity in degree semantics. It introduces the null degree modifier EVAL proposed in Rett (2008), along with the broader empirical facts that originally motivated it. It introduces the relevance of markedness and semantic competition to the issue of evaluativity. It also discusses some problems with the EVAL account, including the absence of any overt counterparts of EVAL, the asymmetry in evaluativity between the matrix and embedded clauses of equatives, and the lack of uniformity across relative adjective antonym pairs. It ends by discussing a few proposed alternatives to POS and EVAL.

This chapter considers how the compositional theory argued for in the preceding chapters might apply to a variety of additional cases where a lexical, degree-theoretic semantics has been proposed. For example, the analysis of attitude verbs like “to want”, nouns like “idiot”, and verbs like “to cool”. The chapter suggests that, rather than diagnosing scalar structure, the kinds of data motivating lexical degree-theoretic interpretation here should be understood as diagnostic of order-theoretic properties on the relevant expression’s domain of predication. Supporting the idea of a general recipe for how such cases should be addressed, the chapter raises theoretical questions like the following: do any lexical categories natively have a degree semantics? When is a degree-theoretic treatment appropriate? Should there be morphosyntactic requirements (e.g., overt or covert “much”) for an interpretation based on degrees, or not? What alternative analyses of extant cases are available?

This chapter studies a first class of extensions of the framework developed in the first part of the book: theoretical/formal extensions. More precisely, this chapter explores to what extent the enrichment of current theories of the semantics of gradable expressions, besides Delineation semantics (DelS), with the structure of a non-classical logic such as Tolerant, Classical, Strict, can be useful to understanding the complex relationships between context sensitivity, vagueness, and scale structure that are discussed in the first part of the book. Focus is particularly on the detailed comparison of the DelTCS framework and current analyses of the absolute/relative distinction set within Degree semantics (DegS), with particular attention to the differences and similarities between DelTCS and (a parallel formalization of) the account presented in Kennedy (2007).

This chapter contains a summary of the work and a discussion of its role in the larger frameworks of degree semantics and the semantics/pragmatics interface. It summarizes the main themes of the book with particular emphasis on the core proposal: that evaluativity arises in some adjectival constructions as the result of a conversational implicature.

This chapter presents the problem of evaluativity in the semantics of adjectival constructions. It previews the traditional account of evaluativity in positive constructions, and summarizes the implicature-based approach defended in the book. It introduces the rest of the chapters in the book and outlines the main themes, including the null morphemes POS and EVAL, implicature and the interaction between evaluativity and markedness, and extensions of the account of evaluativity as implicature.