Vagueness provides the first comprehensive examination of a topic of increasing importance in metaphysics and the philosophy of logic and language. Timothy Williamson traces the history of this philosophical problem from discussions of the heap paradox in classical Greece to modern formal approaches such as fuzzy logic. He illustrates the problems with views which have taken the position that standard logic and formal semantics do not apply to vague language, and defends the controversial realistic view that vagueness is a kind (...) of ignorance--that there really is a grain of sand whose removal turns a heap into a non-heap, but we cannot know which one it is. (shrink)

This paper examines the question of how so-called indeterminate phrases in Japanese (Kuroda 1965) associate with relevant particles higher in the structure. In the universal construction in Japanese, the restrictor (provided by an indeterminate phrase) sometimes appears to be separate from the universal particle mo. It is proposed that quantification at a distance is only apparent, and that the restriction is in fact provided locally by the sister constituent of mo as a whole. The proposal leads us to a straightforward (...) uniform picture of the syntax-semantics mapping of the universal construction and wh-questions, building upon Hamblin’s (1973) semantics for wh-phrases as sets of alternatives. It allows for a switch of perspective on a long-standing puzzle regarding locality effects in the indeterminate–particle association by deriving the locality pattern from the way indeterminate phrases are interpreted and associated with particles, without any stipulations. (shrink)

This paper studies a distinction that was proposed in previous works between total and partial adjectives. In pairs of adjectives such as safe–dangerous, clean–dirty and healthy–sick, the first (“total”) adjective describes lack of danger, dirt, malady, etc., while the second (“partial”) adjective describes the existence of such properties. It is shown that the semantics of adjective phrases with modifiers such as almost, slightly, and completely is sensitive to whether the adjective is total or partial. The interpretation of such modified constructions (...) is accounted for using a novel scale structure for total and partial adjectives. It is proposed that the standard value of a total adjective is always fixed as the lower bound of the corresponding partial adjective. By contrast, the standard value of partial adjectives can take any point on the partial scale. The effects of this theoretical distinction on the behavior of modified constructions are studied in detail, and their ramifications for the semantic theory of adjectives are discussed. Some other phenomena are surveyed that show evidence for total and partial adjectival constructions with various comparatives and exceptive phrases. (shrink)

According to the alternative semantics for focus, the semantic reflec of intonational focus is a second semantic value, which in the case of a sentence is a set of propositions. We examine a range of semantic and pragmatic applications of the theory, and extract a unitary principle specifying how the focus semantic value interacts with semantic and pragmatic processes. A strong version of the theory has the effect of making lexical or construction-specific stipulation of a focus-related effect in association-with-focus constructions (...) impossible. Furthermore, while focus has a uniform import, the sources of meaning differences in association with focus are various. (shrink)

We review Potts’ influential book on the semantics of conventional implicature (CI), offering an explication of his technical apparatus and drawing out the proposal’s implications, focusing on the class of CIs he calls supplements. While we applaud many facets of this work, we argue that careful considerations of the pragmatics of CIs will be required in order to yield an empirically and explanatorily adequate account.

Degree readings of size adjectives, as in big stamp-collector, cannot be explained away as merely the consequence of some extragrammatical phenomenon. Rather, this paper proposes that they actually reflect the grammatical architecture of nominal gradability. Such readings are available only for size adjectives in attributive positions, and systematically only for adjectives that predicate bigness. These restrictions can be understood as part of a broader picture of gradable NPs in which adnominal degree morphemes—often overt—play a key role, analogous to their role (...) in the extended AP. Size adjectives acquire degree readings through a degree morpheme similar to the one that licenses AP-modifying measure phrases. Its syntax gives rise to positional restrictions on the availability of these readings, and the semantics of degree measurement interacts with the scale structure of size adjectives to give rise to restrictions on the adjective itself. (shrink)

It is a truism that people speak ‘loosely’——that is, that they often say things that we can recognize not to be true, but which come close enough to the truth for practical purposes. Certain expressions. such as those including ‘exactly’, ‘all’ and ‘perfectly’, appear to serve as signals of the intended degree of approximation to the truth. This article presents a novel formalism for representing the notion of approximation to the truth, and analyzes the meanings of these expressions in terms (...) of this formalism. Pragmatic loosencss of this kind should be distinguished from authentic truth-conditional vagueness. (shrink)

Argues for an assimilation of sentential and predicate conjunction to collective conjunction, based on modification of predicates by adverbs such as 'alternately'.

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)

A Theory of Truth and Semantic Representation Hans Kamp. INTRODUCTION Two conceptions of meaning have dominated formal semantics of natural language. ...

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.

Chomsky proposes a reformulation of the theory of transformational generative grammar that takes recent developments in the descriptive analysis of particular ...

This paper is devoted to the study of bare nominal arguments (i.e., determinerless NPs occurring in canonical argumental positions) from a crosslinguistic point of view. It is proposed that languages may vary in what they let their NPs denote. In some languages (like Chinese), NPs are argumental (names of kinds) and can thus occur freely without determiner in argument position; in others they are predicates (Romance), and this prevents NPs from occurring as arguments, unless the category D(eterminer) is projected. Finally, (...) there are languages (like Germanic or Slavic) which allow both predicative and argumental NPs; these languages, being the ‘union’ of the previous two types, are expected to behave like Romance for certain aspects of their nominal system (the singular count portion) and like Chinese for others (the mass and plural portions). This hypothesis (the ‘Nominal Mapping Parameter’) is investigated not just through typological considerations, but also through a detailed contrastive analysis of bare arguments in Germanic (English) vs. Romance (Italian). Some general consequences of this view, which posits a limited variation in the mapping from syntax into semantics, for current theories of Universal Grammar and acquisition are considered. (shrink)

This book revives the study of conventional implicatures in natural language semantics. H. Paul Grice first defined the concept. Since then his definition has seen much use and many redefinitions, but it has never enjoyed a stable place in linguistic theory. Christopher Potts returns to the original and uses it as a key into two presently under-studied areas of natural language: supplements and expressives. The account of both depends on a theory in which sentence meanings can be multidimensional. The theory (...) is logically and intuitively compositional, and it minimally extends a familiar kind of intensional logic, thereby providing an adaptable, highly useful tool for semantic analysis. The result is a linguistic theory that is accessible not only to linguists of all stripes, but also philosophers of language, logicians, and computer scientists who have linguistic applications in mind. (shrink)

Semantic underspecification is an essential and pervasive property of natural language. This monograph provides a comprehensive survey of the various phenomena in the field of ambiguity and vagueness. The book discusses the major theories of semantic indefiniteness, which have been proposed in linguistics, philosophy and computer science. It argues for a view of indefiniteness as the potential for further contextual specification, and proposes a unified logical treatment of indefiniteness on this basis. The inherent inconsistency of natural language induced by irreducible (...) imprecision is investigated, and treated in terms of a dynamic extension of the proposed logic. The book is an extended edition of a German monograph and is addressed to advanced students and researchers in theoretical and computational linguistics, logic, philosophy of language, and NL- oriented AI. Although it makes extensive use of logical formalisms, it requires only some basic familiarity with standard predicate logic concepts since all technical terms are carefully explained. (shrink)

This is a collection of papers that helped shape the field of formal semantics in linguistics.

The Antisymmetry of Syntax proposes a restrictive theory of word order and phrase structure that denies this assumption.

What I hope to achieve in this paper is some rather deeper understanding of the semantic and pragmatic properties of utterances which are said to involve the phenomenon of metalinguistic negation[FN1]. According to Laurence Horn, who has been primarily responsible for drawing our attention to it, this is a special non-truthfunctional use of the negation operator, which can be glossed as 'I object to U' where U is a linguistic utterance. This is to be distinguished from descriptive truthfunctional negation which (...) operates over a proposition. (shrink)

(1) is an example of an adjectival comparative. In it, the adjective important is flanked by more and a comparative clause headed by than. This article is a survey of recent ideas about the interpretation of comparatives, including (i) the underlying semantics based on the idea of a threshold; (ii) the interpretation of comparative clauses that include quantifiers (brighter than on many other days); (iii) remarks on differentials such as much in (1) above: what they do in the comparative and (...) what they do elsewhere in the language; (iv) the relationship between comparatives and other Degree constructions (e.g. as important, too impor- tant); and (v) the types of phrases in which comparatives are found (adjective: tighter versus noun: more water). Given the nature and purpose of this essay, I have tried not to presuppose background in formal semantics and I have departed from standard practice in journal articles by, as much as possible, not interrupting the flow with footnotes and references. There are two appendices. The first provides more analytical detail and there I do rely on formal techniques of natural language semantics. The second covers the sources for the ideas surveyed here. (shrink)