As is rather generally admitted today, the terms of our language in scientific as well as in everyday use, are not completely precise, but exhibit a more or less high degree of vagueness. It is the purpose of this paper to examine the consequences of this circumstance for a series of questions which belong to the field of logic. First of all, the meaning and the logical status of the concept of vagueness will be analyzed; then we will try to (...) find out whether logical terms are free from vagueness, and whether vagueness has an influence upon the validity of the customary principles of logic; finally, the possibilities of diminishing the vagueness of scientific concepts by suitable logical devices will be briefly dealt with. As starting point for the subsequent considerations we choose the clear and stimulating analysis of the concept of vagueness which has recently been carried out by Max Black ([1]) and which has suggested the considerations of this paper. (shrink)

Confusion in terms inspires confusion in concepts. When a relevant distinction is not clearly marked or not marked at all, it is apt to be blurred or even missed altogether in our thinking. This is true in any area of inquiry, pragmatics in particular. No one disputes that there are various ways in which what is communicated in an utterance can go beyond sentence meaning. The problem is to catalog the ways. It is generally recognized that linguistic meaning underdetermines speaker (...) meaning because of the need for disambiguation and reference assignment and because people can speak figuratively or indirectly. But philosophers and linguists are coming to recognize that these are not the only ways. The situation may be described in Gricean terms: the distinction between what is said and what is implicated is not exhaustive. Charting the middle ground between the two will require attending to specific examples, noting their distinctive features, and articulating the relevant concepts. That is what I aim to do here. The basic idea will be to distinguish not only the implied from the explicit but the implicit from the implied. (shrink)

It is natural to think that law ought not to be vague. After all, law is supposed to guide conduct, and vague law seems poorly suited to do that. Contrary to this common impression, however, a number of authors have argued that vagueness in the law is sometimes a good thing, because it is a means to achieving certain valuable legislative ends. In this article, I argue that many authors—including Timothy Endicott and Jeremy Waldron—wrongly associate vagueness with instrumental roles that (...) are really played by a closely related semantic phenomenon. (shrink)

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)

It is a paradox, whose importance familiarity fails to diminish, that the most highly developed and useful scientific theories are ostensibly expressed in terms of objects never encountered in experience. The line traced by a draughtsman, no matter how accurate, is seen beneath the microscope as a kind of corrugated trench, far removed from the ideal line of pure geometry. And the “point-planet” of astronomy, the “perfect gas” of thermodynamics, or the “pure species” of genetics are equally remote from exact (...) realization. Indeed the unintelligibility at the atomic or sub-atomic level of the notion of a rigidly demarcated boundary shows that such objects not merely are not but could not be encountered. While the mathematician constructs a theory in terms of “perfect” objects, the experimental scientist observes objects of which the properties demanded by theory are and can, in the very nature of measurement, be only approximately true. As Duhem remarks, mathematical deduction is not useful to the physicist if interpreted rigorously. It is necessary to know that its validity is unaltered when the premise and conclusion are only “approximately true.” But the indeterminacy thus introduced, it is necessary to add in criticism, will invalidate the deduction unless the permissible limits of variation are specified. To do so, however, replaces the original mathematical deduction by a more complicated mathematical theory in respect of whose interpretation the same problem arises, and whose exact nature is in any case unknown. (shrink)

Most of our knowledge is inexact, and known by us to be so. An example of such known inexactness will be described in some detail. The description seems to entail a contradiction. However, the paradoxical reasoning rests on an assumption. It will be suggested that the description is correct and this assumption false. Its failure will be explained by means of a picture of inexact knowledge in which the notion of a margin for error is central. This picture suggests diagnoses (...) of other paradoxical arguments: Surprise Examinations, backwards inductions about Iterated Prisoner's Dilemma, and the Heap. (shrink)

Much of everyday language is vague, even in situations where vagueness could have been avoided. Yet the benefits of vagueness for hearers and readers are proving to be elusive. We discuss a range of earlier controlled experiments with human participants, and we report on a new series of experiments that we ourselves have conducted in recent years. These experiments, which focus on vague expressions that are part of referential noun phrases, aim to separate the utility of vagueness from the utility (...) of other factors that tend to co-occur with vagueness. After presenting the evidence, we argue that it supports a view where the benefits that vague terms exert are due to other influences, and not to vagueness itself. (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.

Islamic building codes require mosques to face Mecca. The further Islam spreads, the more apt are believers to fall into a quandary. X faces Y only when the front of X is closer to Y than any other side of X. So the front of the mosque should be oriented along a shortest path to Mecca. Which way is that? Does the path to Mecca tunnel through the earth? Or does the path follow the surface of the earth?

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)

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)

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)

A vexing puzzle about vagueness, rationality, and evolution runs, in crude abbreviation, as follows: vague language use is demonstrably suboptimal if the goal is efficient, precise and cooperative information transmission; hence rational deliberation or evolutionary selection should, under this assumed goal, eradicate vagueness from language use. Since vagueness is pervasive and entrenched in all human languages, something has to give. In this paper, we focus on this problem in the context of signaling games. We provide an overview of a number (...) of proposed ways in which vagueness may come into the picture in formal models of rational and evolutionary signaling. Most argue that vague signal use is simply the best we can get, given certain factors. Despite the plausibility of the proposals, we argue that a deeper understanding of the benefits of vagueness needs a more ecological perspective, namely one that goes beyond the local optimization of signaling strategies in a homogeneous population. As an example of one possible way to expand upon our current models, we propose two variants of a novel multi-population dynamic of imprecise imitation where, under certain conditions, populations with vague language use dominate over populations with precise language use. (shrink)

THERE IS OFTEN UNCERTAINTY ABOUT WHETHER SOME PREDICATE APPLIES TO SOME PHYSICAL OBJECT OR STATE. THIS UNCERTAINTY MAY HAVE ANY OF THREE SOURCES - VAGUENESS OF A TERM, INEXACTNESS OF A CONCEPT, OR PRACTICAL DIFFICULTY IN DETERMINING ITS APPLICABILITY. VARIOUS WAYS IN WHICH CONCEPTUAL INEXACTNESS OR PRACTICAL DIFFICULTY MAY PRODUCE UNCERTAINTY ARE DISTINGUISHED. NEITHER TERMINOLOGICAL VAGUENESS, NOR PRACTICAL DIFFICULTY IN DETERMINING THE APPLICABILITY OF A CONCEPT ARE NECESSARY FEATURES OF EVERY LANGUAGE IN EVERY PHYSICAL WORLD, BUT CONCEPTUAL INEXACTNESS IS A (...) NECESSARY FEATURE OF EMPIRICAL CONCEPTS. THESE RESULTS ARE UTILIZED TO DETERMINE THE SOURCES AND NECESSITY OF IMPRECISION IN MEASUREMENT. (shrink)