Vagueness and Indeterminacy

ABSTRACT: Frege, and others who followed him, stressed the role of fallibility as a means to defining ‘objectivity.’ By defining objective judgments as fallible, these philosophers contributed to the consolidation of a theory of objectivity which suggested interpreting epistemological, as well as other judgements, as being objective. An important philosophical implication of this theory lies in its disclosure of the interrelations between truth and objectivity. In light of this insight, and based on an analysis of instances of false (epistemological and (...) other) judgments, I show that truth and objectivity go hand-in-hand, while falsity and objectivity do not. This finding alone indicates the necessity to revise the theory of objectivity. (shrink)

Theories of truth and vagueness are closely connected; in this article, I draw another connection between these areas of research. Gupta and Belnap’s Revision Theory of Truth is converted into an approach to vagueness. I show how revision sequences from a general theory of definitions can be used to understand the nature of vague predicates. The revision sequences show how the meaning of vague predicates are interconnected with each other. The approach is contrasted with the similar supervaluationist approach.

This book is the one to put into the hands of those who have been over-impressed by Austin 's critics....[Warnock's] brilliant editing puts everybody who is concerned with philosophical problems in his debt.

In this thesis I investigate the behaviour of uncertainty about vague matters. It is a fairly common view that vagueness involves uncertainty of some sort. However there are many fundamental questions about this kind of uncertainty that are left open. Could you be genuinely uncertain about p when there is no matter of fact whether p? Could you remain uncertain in a vague proposition even if you knew exactly which possible world obtained? Should your degrees of belief be probabilistically coherent? (...) Should your beliefs in the vague be fixed by your beliefs in the precise? Could one in principle tell what credences a person has in the vague? (shrink)

I think it is a lapse of taste to spend a grown-up life on problems of which people in the office next door, let alone those outside the building, cannot see the point. I rather fear that the so-called semantic or logical problem of vagueness, Professor Williamson’s own showcase example of his compulsory methods, strikes me as like that.

This paper analyzes communication with a language that is vague in the sense that identical messages do not always result in identical interpretations. It is shown that strategic agents frequently add to this vagueness by being intentionally vague, i.e. they deliberately choose less precise messages than they have to among the ones available to them in equilibrium. Having to communicate with a vague language can be welfare enhancing because it mitigates conflict. In equilibria that satisfy a dynamic stability condition intentional (...) vagueness increases with the degree of conflict between sender and receiver. (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)

This paper gives a novel analysis of the logical structure underlying three classes of vague adjectival predicates (relative adjectives, i.e., tall; total adjectives, i.e., straight; and partial adjectives, i.e., wet) and the realisation of this structure in arguments formed with comparative constructions (i.e., John is taller than Mary). I analyse three classes of valid arguments that can be formed with different types of gradable predicates in comparative constructions: scalarity arguments (i.e., Mary is taller than John and John is tall Mary (...) is tall), maximality arguments (i.e., Stick A is straighter than Stick B Stick B is not straight), and evaluativity arguments (i.e., This towel is wetter than that towel this towel is wet) I show how a previously proposed multi-valued logical system (called Delineation TCS; see Burnett, 2012b; Burnett, 2013) based on the trivalent framework of (Cobreros et al., 2012) can be used to model the reasoning patterns described in the paper. In this system, we derive the scalarity, maximality and evaluativity properties of different classes of adjectives from statements about the properties of cognitive indifference relations associated with these predicates. I therefore conclude that systems such as DelTCS give us valuable insight into the relationship between cognitive judgements of indifference and reasoning patterns with scalar terms. (shrink)

This work is a multidisciplinary project that explores the “borderline” concept as it is adopted in psychological, psychiatric and psychoanalytic theory in notions of “borderline phenomena”, “borderline personality organization” and “borderline personality disorder”. I argue that usage of the borderline concept has become overburdened by ethical ambiguity and a lack of conceptual clarity because prevailing theories focus upon approaches that are excessively individualistic, categorical, intrapsychic, and atemporal. I argue that the borderline concept has become a problematic limit concept that requires (...) an interpretative framework of elucidation to understand how it is applied in developmental theories and clinical work. I choose to see the borderline concept as arising in a culturally and historically determined context that has constituted borderline experience as something that is problematic for suffering individuals and clinicians alike. My methodology firstly involves the philosophical elaboration of a hermeneutic ontological approach to understanding this developmental and clinical field. In the first “philosophical” section of the project, I describe the philosophy of Martin Heidegger, and explore and elaborate how his philosophical approach was developed or advanced by a group of philosophers who followed him within a certain philosophical tradition. I develop this hermeneutic ontological orientation as an open framework developed in terms of four themes, those of relationality, temporality, embodied affectivity and technicity. In the second “developmental” section of the project, I advance this orientation by considering development in terms of those four hermeneutic ontological themes, engaging with a group of psychoanalytic theorists, before I critically analyse what several prevalent contemporary theories uphold as the developmental determinants of borderline personality disturbance. And in the third and final “clinical” section, this orientation is further advanced in terms of those four hermeneutic ontological themes by elucidating clinical approaches to borderline disturbance where many of the ambiguities which pervade this clinical field, often related to the use of broad and ambiguous concepts such as dissociation, self, trauma and abuse, are arguably overcome. The central methodology of this project is to elaborate an interpretative framework originating from Heideggerian philosophy and referred to as a hermeneutic ontological orientation. Not only do I attempt to historicise and critically appraise the borderline concept and other implicated concepts, but I also attempt to contextualize them within a more open and complex field of understanding that favours approaches to interpretation that focus upon the fundamentally relational, temporal, embodied, affective and technical aspects of our existence. Throughout my study I aim to enhance the developmental and clinical understanding of individuals presenting within the context of borderline experience whilst avoiding the various forms of closed, reductionistic or objectivist forms of understanding I have critically engaged. (shrink)

John Broome has argued that incomparability and vagueness cannot coexist in a given betterness order. His argument essentially hinges on an assumption he calls the ‘collapsing principle’. In an earlier article I criticized this principle, but Broome has recently expressed doubts about the cogency of my criticism. Moreover, Cristian Constantinescu has defended Broome’s view from my objection. In this paper, I present further arguments against the collapsing principle, and try to show that Constantinescu’s defence of Broome’s position fails.

I discuss the interest-relative account of vagueness and argue for a distinction between relational vague predicates and non-relational vague predicates depending on the kind of properties expressed by them. The strategy rests on three arguments arising from the existence of clear cases of a vague predicate, from contexts in which a different answer is required for questions about whether a vague predicate applies to an item, and whether such an item satisfies the interest of an agent, and from cases where (...) an object changes up to the point of becoming P, where P is a vague predicate. In the second part of the paper, I distinguish between relational properties and non-relational properties, and I argue for the view that some vague predicates can express non-relational properties, comparative relational properties and interest-relative properties. On the basis of these arguments, I conclude that vagueness cannot be reduced to interest-relativity. (shrink)

The book from which these sections are excerpted is concerned with the prospects for assimilating the study of human intelligence and its products to the natural sciences through the investigation of cognitive structures, understood as systems of rules and representations that can be regarded as These mental structui′es serve as the vehicles for the exercise of various capacities. They develop in the mind on the basis of an innate endowment that permits the growth of rich and highly articulated structures along (...) an intrinsically determined course under the triggering and partially shaping effect of experience, which fixes parameters in an intricate system of predetermined form. It is argued that the mind is modular in character, with a diversity of cognitive structures, each with its specific properties arid principles. Knowledge of language, of the behavior of objects, and much else crucially involves these mental structures, and is thus not characterizable in terms of capacities, dispositions, or practical abilities, nor is it necessarily grounded in experience in the standard sense of this term. (shrink)

Recent experiments have shown that naive speakers find borderline contradictions involving vague predicates acceptable. In Cobreros et al. we proposed a pragmatic explanation of the acceptability of borderline contradictions, building on a three-valued semantics. In a reply, Alxatib et al. show, however, that the pragmatic account predicts the wrong interpretations for some examples involving disjunction, and propose as a remedy a semantic analysis instead, based on fuzzy logic. In this paper we provide an explicit global pragmatic interpretation rule, based on (...) a somewhat richer semantics, and show that with its help the problem can be overcome in pragmatics after all. Furthermore, we use this pragmatic interpretation rule to define a new consequence-relation and discuss some of its properties. (shrink)

Abstract The paper is concerned with the status of vague predicates. It is argued that they are for the most part ?classifiers?, which are covertly comparatives and name not monadic properties but relations. The Sorites Paradox, it is claimed, is thus defused and a verdict theory of vague predicates is presented. Our practice in using vague words is described and it is contended that in our use of these predicates we always have a permanent possibility of independent demarcation. Wittgenstein's picture (...) of the wall and the swamp is deployed to avoid the Transition Problem and it is argued against Fregeans that we need vague language for the advancement of knowledge and understanding. (shrink)