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.

If you’ve read the first five hundred pages of this book, you’ve read most of it (we assume that ‘most’ requires more than ‘more than half’). The set of natural numbers n such that the first n pages are most of this book is nonempty. Therefore, by the least number principle, it has a least member k. What is k? We do not know. We have no idea how to find out. The obstacle is something about the term ‘most’. It (...) is recognisably the same feature as the feature of ‘heap’ that prevents us from finding an answer to the question ‘How many grains make a heap?’ and the feature of many other expressions that prevents us from finding answers to similar questions involving them. Call this feature, whatever its underlying nature, vagueness. (shrink)

Scientific knowledge grows at a phenomenal pace--but few books have had as lasting an impact or played as important a role in our modern world as The Mathematical Theory of Communication, published originally as a paper on communication theory more than fifty years ago. Republished in book form shortly thereafter, it has since gone through four hardcover and sixteen paperback printings. It is a revolutionary work, astounding in its foresight and contemporaneity. The University of Illinois Press is pleased and honored (...) to issue this commemorative reprinting of a classic. (shrink)

The term fuzzy logic is used in this paper to describe an imprecise logical system, FL, in which the truth-values are fuzzy subsets of the unit interval with linguistic labels such as true, false, not true, very true, quite true, not very true and not very false, etc. The truth-value set, , of FL is assumed to be generated by a context-free grammar, with a semantic rule providing a means of computing the meaning of each linguistic truth-value in as a (...) fuzzy subset of [0, 1].Since is not closed under the operations of negation, conjunction, disjunction and implication, the result of an operation on truth-values in requires, in general, a linguistic approximation by a truth-value in . As a consequence, the truth tables and the rules of inference in fuzzy logic are (i) inexact and (ii) dependent on the meaning associated with the primary truth-value true as well as the modifiers very, quite, more or less, etc. (shrink)

When people speak, they often insinuate their intent indirectly rather than stating it as a bald proposition. Examples include sexual come-ons, veiled threats, polite requests, and concealed bribes. We propose a three-part theory of indirect speech, based on the idea that human communication involves a mixture of cooperation and conflict. First, indirect requests allow for plausible deniability, in which a cooperative listener can accept the request, but an uncooperative one cannot react adversarially to it. This intuition is sup- ported by (...) a game-theoretic model that predicts the costs and benefits to a speaker of direct and indirect requests. Second, language has two functions: to convey information and to negotiate the type of relationship holding between speaker and hearer (in particu- lar, dominance, communality, or reciprocity). The emotional costs of a mismatch in the assumed relationship type can create a need for plausible deniability and, thereby, select for indirectness even when there are no tangible costs. Third, people perceive language as a digital medium, which allows a sentence to generate common knowledge, to propagate a message with high fidelity, and to serve as a reference point in coordination games. This feature makes an indirect request qualitatively different from a direct one even when the speaker and listener can infer each other’s intentions with high confidence. (shrink)

We present an account of semantics that is not construed as a mapping of language to the world but rather as a mapping between individual meaning spaces. The meanings of linguistic entities are established via a “meeting of minds.” The concepts in the minds of communicating individuals are modeled as convex regions in conceptual spaces. We outline a mathematical framework, based on fixpoints in continuous mappings between conceptual spaces, that can be used to model such a semantics. If concepts are (...) convex, it will in general be possible for interactors to agree on joint meaning even if they start out from different representational spaces. Language is discrete, while mental representations tend to be continuous—posing a seeming paradox. We show that the convexity assumption allows us to address this problem. Using examples, we further show that our approach helps explain the semantic processes involved in the composition of expressions. (shrink)

This paper combines a survey of existing literature in game-theoretic pragmatics with new models that fill some voids in that literature. We start with an overview of signaling games with a conflict of interest between sender and receiver, and show that the literature on such games can be classified into models with direct, costly, noisy and imprecise signals. We then argue that this same subdivision can be used to classify signaling games with common interests, where we fill some voids in (...) the literature. For each of the signaling games treated, we show how equilibrium-refinement arguments and evolutionary arguments can be interpreted in the light of pragmatic inference. (shrink)

This paper combines a survey of existing literature in game-theoretic pragmatics with new models that fill some voids in that literature. We start with an overview of signaling games with a conflict of interest between sender and receiver, and show that the literature on such games can be classified into models with direct, costly, noisy and imprecise signals. We then argue that this same subdivision can be used to classify signaling games with common interests, where we fill some voids in (...) the literature. For each of the signaling games treated, we show how equilibrium-refinement arguments and evolutionary arguments can be interpreted in the light of pragmatic inference. (shrink)

A current focus of legal debate is the proper role of the courts in the interpretation of statutes and the Constitution. Are judges to look solely to the naked language of an enactment, then logically deduce its application in simple syllogistic fashion, as legal formalists had purported to do? Or may the inquiry into meaning be informed by perhaps unbridled and unaccountable judicial notions of public policy, using legal realism to best promote the general welfare? Judge Posner considers the concepts (...) of formalism and realism to be meaningful and useful in common law reasoning but in interpretation to be useless and, worse, forbidden. He analogizes unclear "orders" from a legislature to garbled battlefield communications, and argues that the duty of the recipient of those orders (the judge) is to advance as best he can the enterprise set on foot by the superiors. Case studies elaborate this thesis. Judicial decisions interpreting fixed texts, Judge Posner concludes, can be neither logically correct or incorrect, philosophically sound or unsound, until the ultimate jurist, time, has adjudged their results. (shrink)

A utility-based approach to the understanding of vague predicates (VPs) is proposed. It is argued that assignment of truth values to propositions containing VPs entails unjustifiable assumptions of consensus; two models of VP semantics are criticized on this basis: (1) the super-truth theory of Kit Fine (1975), which requires an unlikely consensus on base points; (2) the fuzzy logic of Lotfi Zadeh (1975), on fuzzy truth values of sentences. Pragmatism is held to provide a key: successful behavior justifies a person's (...) knowledge of the content of a VP. Instead of attempting to determine a consensus underlying successful communication, the utility of individual communications is held to rest on sufficient approximation of meanings between people. 3 Figures, 17 References. Adapted from the source document. (shrink)