This paper asks why information should ever be expressed vaguely, re-assessing some previously proposed answers to this question and suggesting some new ones. Particular attention is paid to the benefits that vague expressions can have in situations where agreement over the meaning of an expression cannot be taken for granted. A distinction between two different versions of the above-mentioned question is advocated. The first asks why human languages contain vague expressions, the second question asks when and why a speaker should (...) choose a vague expression when communicating with a hearer. While the former question is purely theoretical, the latter has practical implications for the computational generation of utterances in Natural Language Generation (NLG). (shrink)

In this paper we investigate a semantics for first-order logic originally proposed by R. van Rooij to account for the idea that vague predicates are tolerant, that is, for the principle that if x is P, then y should be P whenever y is similar enough to x. The semantics, which makes use of indifference relations to model similarity, rests on the interaction of three notions of truth: the classical notion, and two dual notions simultaneously defined in terms of it, (...) which we call tolerant truth and strict truth. We characterize the space of consequence relations definable in terms of those and discuss the kind of solution this gives to the sorites paradox. We discuss some applications of the framework to the pragmatics and psycholinguistics of vague predicates, in particular regarding judgments about borderline cases. (shrink)

[688/2197] In many economic matters there arises a paradox that may be related to what in logic courses is called the “sophism of the heap of wheat”. Among the sophisms bequeathed to us by the Greeks, none is worthier to have come down through the centuries than this “sophism of the heap of wheat”; indeed this no mere puzzle, but a topical example of a frequent difficulty, as much in practical life as in pure speculation.One grain of wheat does not (...) make a heap; neither do two grains; nor do three grains; \(\ldots \) on the other hand, if a million grains are gathered, we can agree that they constitute a heap. What is the exact limit? Should we say that 2,342 grains, for instance, do not make a heap, whereas 2,343 grains do? This is obviously ridiculous. There appears no logical way out of this dead-end; it is therefore not possible to know what a heap of wheat is.The expression of the sophism can be varied in many ways; a classification of these expressions will not be unhelpful. (shrink)

We present an investigation of the ways in which speakers' subjective perspectives are likely to affect the meaning of gradable adjectives like tall or heavy. We present the results of a study showing that people tend to use themselves as a yardstick when ascribing these adjectives to human figures of varied measurements: subjects' height and weight requirements for applying tall and heavy are found to be positively correlated with their personal measurements. We draw more general lessons regarding the definition of (...) subjectivity and the ways in which a standard of comparison and a significant deviation from that standard are specified. (shrink)

Someone asked ‘What time is it?’ when her watch reads 3:08 is likely to answer ‘It is 3:10.’ We argue that a fundamental factor that explains such rounding is a psychological disposition to give an answer that, while not necessarily strictly truthful or accurate, is an optimally relevant one (in the sense of relevance theory) i.e. an answer from which hearers can derive the consequences they care about with minimal effort. A rounded answer is easier to process and may carry (...) the same consequences as one that is accurate to the minute. Hence rounding is often a way of optimising relevance. Three simple experiments give support and greater precision to the view that relevance is more important than strict truthfulness in verbal communication. (shrink)

Wright holds that the following two theses are jointly incoherent: Rules determine correct language use. These rules are discoverable via internal reflection on language use. I argue that incoherence is derivable from alone and examine two types of probabilistic accounts that model a modification of, one in terms of inexact knowledge, the other in terms of viewing semantic rules as reasons for linguistic actions. Both accommodate tolerance by breaking the link between justified assertion and truth, but incoherence threatens their conception (...) of justified assertion. I argue that the rules-as-reasons approach can relocate sharp boundaries to a place where they are not only more tolerable, but to be expected. (shrink)

Why is common priors are implicit or explicit in the vast majority of the differential information literature in economics and game theory? Why has the economic community been unwilling, in practice, to accept and actually use the idea of truly personal probabilities in much the same way that it did accept the idea of personal utility functions? After all, in, both the utilities and probabilities are derived separately for each decision maker. Why were the utilities accepted as personal, and the (...) probabilities not? (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)

This paper addresses the apparent mismatch between the normative and descriptive literatures in the cognitive science of conditional reasoning. Descriptive psychological theories still regard material implication as the normative theory of the conditional. However, over the last 20 years in the philosophy of language and logic the idea that material implication can account for everyday indicative conditionals has been subject to severe criticism. The majority view is now apparently in favour of a subjective conditional probability interpretation. A comparative model fitting (...) exercise is presented that shows that a conditional probability model can explain as much of the data on abstract indicative conditional reasoning tasks as psychological theories that supplement material implication with various rationally unjustified processing assumptions. Consequently, when people are asked to solve laboratory reasoning tasks, they can be seen as simply generalising their everyday probabilistic reasoning strategies to this novel context. (shrink)

This paper addresses the apparent mismatch between the normative and descriptive literatures in the cognitive science of conditional reasoning. Descriptive psychological theories still regard material implication as the normative theory of the conditional. However, over the last 20 years in the philosophy of language and logic the idea that material implication can account for everyday indicative conditionals has been subject to severe criticism. The majority view is now apparently in favour of a subjective conditional probability interpretation. A comparative model fitting (...) exercise is presented that shows that a conditional probability model can explain as much of the data on abstract indicative conditional reasoning tasks as psychological theories that supplement material implication with various rationally unjustified processing assumptions. Consequently, when people are asked to solve laboratory reasoning tasks, they can be seen as simply generalising their everyday probabilistic reasoning strategies to this novel context. (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)

We derive a probabilistic account of the vagueness and context-sensitivity of scalar adjectives from a Bayesian approach to communication and interpretation. We describe an iterated-reasoning architecture for pragmatic interpretation and illustrate it with a simple scalar implicature example. We then show how to enrich the apparatus to handle pragmatic reasoning about the values of free variables, explore its predictions about the interpretation of scalar adjectives, and show how this model implements Edgington’s Vagueness: a reader, 1997) account of the sorites paradox, (...) with variations. The Bayesian approach has a number of explanatory virtues: in particular, it does not require any special-purpose machinery for handling vagueness, and it is integrated with a promising new approach to pragmatics and other areas of cognitive science. (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)

In 1907 Borel published a remarkable essay on the paradox of the Heap (“Un paradoxe économique: le sophisme du tas de blé et les vérités statistiques”), in which Borel proposes what is likely the first statistical account of vagueness ever written, and where he discusses the practical implications of the sorites paradox, including in economics. Borel’s paper was integrated in his book Le Hasard, published 1914, but has gone mostly unnoticed since its publication. One of the originalities of Borel’s essay (...) is that it puts forward a model of vagueness as imprecision, making particular use of the Gaussian law of measurement errors to model categorization. The aim of our paper is to give a presentation of the historical context of Borel’s essay, to spell out the mathematical details of his model, and to provide a critical assessment of his theory. Three aspects of Borel’s account are particularly discussed: the first concerns the comparison between Borel’s statistical account and posterior degree-theoretic accounts of vagueness. The second concerns the anti-epistemicist flavor of Borel’s approach, whereby the idea of statistical fluctuation is used to undermine the notion of sharp boundary for vague predicates. The third concerns the problematic link between Borel’s model of vagueness as imprecision and the notion of semantic indeterminacy. An English translation of Borel’s original essay is appended to this paper (Erkenntnis, this issue). (shrink)

Is language understanding a special case of social cognition? To help evaluate this view, we can formalize it as the rational speech-act theory: Listeners assume that speakers choose their utterances approximately optimally, and listeners interpret an utterance by using Bayesian inference to “invert” this model of the speaker. We apply this framework to model scalar implicature (“some” implies “not all,” and “N” implies “not more than N”). This model predicts an interaction between the speaker's knowledge state and the listener's interpretation. (...) We test these predictions in two experiments and find good fit between model predictions and human judgments. (shrink)

Signalling games are popular models for studying the evolution of meaning, but typical approaches do not incorporate vagueness as a feature of successful signalling. Complementing recent like-minded models, we describe an aggregate population-level dynamic that describes a process of imitation of successful behaviour under imprecise perception and realization of similar stimuli. Applying this new dynamic to a generalization of Lewis’s signalling games, we show that stochastic imprecision leads to vague, yet by-and-large efficient signal use, and, moreover, that it unifies evolutionary (...) outcomes and helps avoid sub-optimal categorization. The upshot of this is that we see ‘as-if’-generalization at an aggregate level, without agents actually generalizing. _1_ Introduction _2_ Background _2.1_ Sim-max games and conceptual spaces _2.2_ Vagueness in sim-max games and conceptual spaces _2.3_ Vagueness, functional pressure, and transmission biases _3_ Imprecise Imitation _3.1_ Replicator dynamic in behavioural strategies _3.2_ Noise-perturbed conditional imitation _4_ Exploring Imprecise Imitation _4.1_ Setting the stage _4.2_ Simulation set-up _4.3_ Measures of interest _4.4_ Results _5_ Discussion _5.1_ Levels of vagueness _5.2_ Evolutionary benefits of imprecision _5.3_ Related work _6_ Conclusion Appendix. (shrink)

Vagueness is often regarded as a kind of defect of our language or of our thinking. This paper portrays vagueness as the natural outcome of applying a number of rationality principles to the cognitive domain. Given our physical and cognitive makeup, and given the way the world is, applying those principles to conceptualization predicts not only the concepts that are actually in use, but also their vagueness, and how and when their vagueness manifests itself.

Voorzover het maken van kopieën uit deze uitgave is toegestaan op grond van artikel 16B Auteurswet 1912 j0 het Besluit van 20 juni 1974, St.b. 351, zoals gewijzigd bij het Besluit van 23 augustus 1985, St.b. 471 en artikel 17 Auteurswet 1912, dient men de daarvoor wettelijk verschuldigde vergoedingen te voldoen aan de Stichting Reprorecht (Postbus 882, 1180 AW Amstelveen). Voor het overnemen van gedeelte(n) uit deze uitgave in bloemlezingen, readers en andere compilatiewerken (artikel 16 Auteurswet 1912) dient men zich (...) tot de uitgever te wenden. (shrink)