This paper discusses Fara's so-called 'Paradox of Higher-Order Vagueness' concerning supervaluationism. In the paper I argue that supervaluationism is not committed to global validity, as it is largely assumed in the literature, but to a weaker notion of logical consequence I call 'regional validity'. Then I show that the supervaluationist might solve Fara's paradox making use of this weaker notion of logical consequence. The paper is discussed by Delia Fara in the same volume.
In this paper we focus mainly on a kind of contextualism theory of vagueness according to which the context dependence has its source in the variation of our practical interests. We largely focus on Fara's version of the theory but our observations work at different levels of generality, some relevant only to the specifics of Fara's theory others relevant to all contextualist theories of a certain type.
I consider two possible sources of vagueness. The first is indeterminacy about which intension is expressed by a word. The second is indeterminacy about which referent (extension) is determined by an intension. Focusing on a Fregean account of intensions, I argue that whichever account is right will matter to whether vagueness turns out to be a representational phenomenon (as opposed to being “in the world”). In addition, it will also matter to whether supervaluationism is a viable semantic framework. (...) Based on these considerations, I end by developing an argument against supervaluational semantics that depends, instead, on anti-Fregean (Millian) assumptions. (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)
The purpose of this paper is to challenge some widespread assumptions about the role of the modal axiom S4 in a theory of vagueness. In the context of vagueness, S4 usually appears as the principle ‘If it is clear (determinate, definite) that A, then it is clear (determinate, definite) that it is clear (determinate, definite) that A’, or, more formally, CA → CCA. We show how in the debate over S4 two different notions of clarity are in play (...) (Williamson-style "luminosity" or self-revealing clarity and concealeable clarity) and what their respective functions are in accounts of higher-order vagueness. On this basis, we argue first that, contrary to common opinion, higher-order vagueness and S4 are perfectly compatible. This is in response to claims like that by Williamson that, if vagueness is defined with the help of a clarity operator that obeys S4, higher-order vagueness disappears. Second, we argue that, contrary to common opinion, (i) bivalence-preservers (e.g. epistemicists) can without contradiction condone S4 (by adopting what elsewhere we call columnar higher-order vagueness), and (ii) bivalence-discarders (e.g. open-texture theorists, supervaluationists) can without contradiction reject S4. Third, we rebut a number of arguments that have been produced by opponents of S4, in particular those by Williamson. (The paper is pitched towards graduate students with basic knowledge of modal logic.). (shrink)
This dissertation explores several illuminating points of intersection between the philosophy of perception and the philosophy of vagueness. Among other things, I argue: (i) that it is entirely unhelpful to theorize about perception or consciousness using Nagelian "what it's like" talk; (ii) that a popular recent account of perceptual phenomenology (representationalism) conflicts with our best theory of vagueness (supervaluationism); (iii) that there are no vague properties, for Evans-esque reasons; (iv) that it is impossible to insert "determinacy" operators into (...) representationalism in a truth-preserving manner; and (v) that strong versions of dualism are unable to accommodate the possibility of borderline consciousness. (shrink)
ABSTRACT: Stewart Shapiro recently argued that there is no higher-order vagueness. More specifically, his thesis is: (ST) ‘So-called second-order vagueness in ‘F’ is nothing but first-order vagueness in the phrase ‘competent speaker of English’ or ‘competent user of “F”’. Shapiro bases (ST) on a description of the phenomenon of higher-order vagueness and two accounts of ‘borderline case’ and provides several arguments in its support. We present the phenomenon (as Shapiro describes it) and the accounts; then discuss (...) Shapiro’s arguments, arguing that none is compelling. Lastly, we introduce the account of vagueness Shapiro would have obtained had he retained compositionality and show that it entails true higher-order vagueness. (shrink)
It is common among philosophers who take an interest in the phenomenon of vagueness in natural language not merely to acknowledge higher-order vagueness but to take its existence as a basic datum— so that views that lack the resources to account for it, or that put obstacles in the way, are regarded as deficient just on that score. My main purpose in what follows is to loosen the hold of this deeply misconceived idea. Higher-order vagueness is no (...) basic datum but an illusion, fostered by misunderstandings of the nature of (ordinary, if you will ‘first-order’) vagueness itself. To see through the illusion is to take a step that is prerequisite for a correct understanding of vagueness, and for any satisfying dissolution of its attendant paradoxes. (shrink)
Supervaluationism is a well known theory of vagueness. Subvaluationism is a less well known theory of vagueness. But these theories cannot be taken apart, for they are in a relation of duality that can be made precise. This paper provides an introduction to the subvaluationist theory of vagueness in connection to its dual, supervaluationism. A survey on the supervaluationist theory can be found in the Compass paper of Keefe (2008); our presentation of the theory in this paper (...) will be short to get rapidly into the logical issues. This paper is relatively self-contained. A modest background on propositional modal logic is, though not strictly necessary, advisable. The reader might find useful the Compass papers Kracht (2011) and Negri (2011) (though these papers cover issues of more complexity than what is demanded to follow this paper). (shrink)
ABSTRACT: Recently a bold and admirable interpretation of Chrysippus’ position on the Sorites has been presented, suggesting that Chrysippus offered a solution to the Sorites by (i) taking an epistemicist position1 which (ii) made allowances for higher-order vagueness.2 In this paper I argue (i) that Chrysippus did not take an epistemicist position, but − if any − a non-epistemic one which denies truth-values to some cases in a Sorites-series, and (ii) that it is uncertain whether and how he made (...) allowances for higher-order vagueness, but if he did, this was not grounded on an epistemicist position. (shrink)
This paper develops a novel problem for representationalism (also known as "intentionalism"), a popular contemporary account of perception. We argue that representationalism is incompatible with supervaluationism, the leading contemporary account of vagueness. The problem generalizes to naive realism and related views, which are also incompatible with supervaluationism.
In this paper, I start by showing that sorites paradoxes are inclosure paradoxes. That is, they fit the Inclosure Scheme which characterizes the paradoxes of self-reference. Given that sorites and self-referential paradoxes are of the same kind, they should have the same kind of solution. The rest of the paper investigates what a dialetheic solution to sorites paradoxes is like, connections with a dialetheic solution to the self-referential paradoxes, and related issues—especially so called "higher order" vagueness.
In this paper I offer a counterexample to the so called vagueness argument against restricted composition. This will be done in the lines of a recent suggestion by Trenton Merricks, namely by challenging the claim that there cannot be a sharp cut-off point in a composition sequence. It will be suggested that causal powers which emerge when composition occurs can serve as an indicator of such sharp cut-off points. The main example will be the case of a heap. It (...) seems that heaps might provide a very plausible counterexample to the vagueness argument if we accept the idea that four grains of sand is the least number required to compose a heap—the case has been supported by W. D. Hart. My purpose here is not to put forward a new theory of composition, I only wish to refute the vagueness argument and point out that we should be wary of arguments of its form. (shrink)
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)
ABSTRACT: This paper shows that authors who have recently argued that higher-order vagueness is incoherent, paradoxical, illusory or non-existent confound elements of higher-order vagueness with elements of a different paradigm of borderline borderline cases; and that, once the elements of that other paradigm are removed from the description of higher-order vagueness, the basis for the claims of paradoxicality, etc., disappears. The paper sets out the two paradigms (higher-order vagueness vs borderline nestings) and their logics (iterated modalities (...) vs. mixed-order non-empty predicates), illustrates how the notion of hierarchical higher-order vagueness gains its persuasiveness from a conflation of these paradigms, and shows how the alternative notion of columnar higher-order vagueness preserves coherence and relevance to the Sorites. .................................................................................................... .................................................................................................... ................................ -/- Section 1 presents the notion of hierarchical vagueness. Section 2 compares two ordinary language uses of “borderline case”: epistemic and classificatory use. Section 3 lays out the basic logical requirements for higher-order vagueness and shows that it can be columnar rather than hierarchical. Section 4 presents the paradigm of borderline nestings and its logic. Section 5 lists sources for the conflation of classificatory use plus borderline nestings with epistemic use plus higher-order vagueness. Section 6 shows how such conflation undermines the arguments against higher-order vagueness by Sainsbury, Shapiro, Raffman, Wright, Williamson. Section 7 concludes with a note on columnar higher-order vagueness and the Sorites. (shrink)
The paper presents a new theory of higher-order vagueness. This theory is an improvement on current theories of vagueness in that it (i) describes the kind of borderline cases relevant to the Sorites paradox, (ii) retains the ‘robustness’ of vague predicates, (iii) introduces a notion of higher-order vagueness that is compositional, but (iv) avoids the paradoxes of higher-order vagueness. The theory’s central building-blocks: Borderlinehood is defined as radical unclarity. Unclarity is defined by means of competent, rational, (...) informed speakers (‘CRISPs’) whose competence, etc., is indexed to the scope of the unclarity operator. The unclarity is radical since it eliminates clear cases of unclarity and, that is, clear borderline cases. This radical unclarity leads to a (bivalence-compatible, non-intuitionist) absolute agnosticism about the semantic status of all borderline cases. The corresponding modal system would be a non-normal variation on S4M. (shrink)
A number of arguments purport to show that vague properties determine sharp boundaries at higher orders. That is, although we may countenance vagueness concerning the location of boundaries for vague predicates, every predicate can instead be associated with precise knowable cut-off points deriving from precision in their higher order boundaries. -/- I argue that this conclusion is indeed paradoxical, and identify the assumption responsible for the paradox as the Brouwerian principle B for vagueness: that if p then it's (...) completely determinate that either it's vague whether p, or p. Other paradoxes which do not appear to turn on B turn instead on some subtle issues concerning the relation between assertion, belief and higher order vagueness. -/- In this paper a B-free picture of assertion, knowledge and logic is outlined which is completely free of higher order precision. A class of realistic models containing counterexamples to B and a number of weakenings of B are introduced and its logic is shown to support vagueness at every order. A novel framework for thinking about the semantic apparatus in the presence of metalinguistic vagueness is also developed. In this framework the vague metatheoretic vocabulary is part of the object language and can readily be applied to itself. (shrink)
ABSTRACT: Hierarchical higher-order vagueness leads to incoherence when used as a means to avoid a sharp boundary in the Sorites paradox (Sainsbury 1990, Wright 1992, Shapiro 2006). The challenge is to provide (i) a compositional notion of higher-order vagueness that (ii) allows infinite higher orders, (iii) retains the desired relevance to the Sorites, (iv) allows for a model-theoretic representation that reflects such relevance, but (v) does not run into paradox. The recently introduced alternative of columnar higher-order vagueness (...) meets this challenge. The present paper explains what columnar higher-order vagueness is; gives a formalization of its core properties in terms of an axiomatic modal system; produces a modal semantics for its simplest (bivalent & classical) form and identifies its characteristic axiom; and supplies a philosophical interpretation of the semantics that utilizes both viewpoint sensitivity and extensional context sensitivity. The paper adds an illustration of how the semantics can be used as an infrastructure for epistemicist (and non-epistemicist) bivalent theories of vagueness and touches upon possible modifications for three-valued logics. It concludes with listing the considerable advantages columnar higher-order vagueness has over other theories of higher-order vagueness. (shrink)
Most expressions in natural language are vague. But what is the best semantic treatment of terms like 'heap', 'red' and 'child'? And what is the logic of arguments involving this kind of vague expression? These questions are receiving increasing philosophical attention, and in this timely book Rosanna Keefe explores the questions of what we should want from an account of vagueness and how we should assess rival theories. Her discussion ranges widely and comprehensively over the main theories of (...) class='Hi'>vagueness and their supporting arguments, and she offers a powerful and original defence of a form of supervaluationism, a theory that requires almost no deviation from standard logic yet can accommodate the lack of sharp boundaries to vague predicates and deal with the paradoxes of vagueness in a methodologically satisfying way. Her study will be of particular interest to readers in philosophy of language and of mind, philosophical logic, epistemology and metaphysics. (shrink)
This paper considers two “mysteries” having to do with vagueness. The first pertains to existence. An argument is presented for the following conclusion: there are possible cases in which ‘There exists something that is F’ is of indeterminate truth-value and with respect to which it is not assertable that there are borderline-cases of “being F.” It is contended that we have no conception of vagueness that makes this result intelligible. The second mystery has to do with “ordinary” vague (...) predicates, such as ‘tall’. An argument is presented for the conclusion that although there are people who are “tall to degree 1”—definitely tall, tall without qualification—, no greatest lower bound can be assigned to the set of numbers n such that a man who is n centimeters tall is tall to degree 1. But, since this set is bounded from below, this result seems to contradict a well-known property of the real numbers. (shrink)
Paraconsistent approaches have received little attention in the literature on vagueness (at least compared to other proposals). The reason seems to be that many philosophers have found the idea that a contradiction might be true (or that a sentence and its negation might both be true) hard to swallow. Even advocates of paraconsistency on vagueness do not look very convinced when they consider this fact; since they seem to have spent more time arguing that paraconsistent theories are at (...) least as good as their paracomplete counterparts, than giving positive reasons to believe on a particular paraconsistent proposal. But it sometimes happens that the weakness of a theory turns out to be its mayor ally, and this is what (I claim) happens in a particular paraconsistent proposal known as subvaluationism. In order to make room for truth-value gluts subvaluationism needs to endorse a notion of logical consequence that is, in some sense, weaker than standard notions of consequence. But this weakness allows the subvaluationist theory to accommodate higher-order vagueness in a way that it is not available to other theories of vagueness (such as, for example, its paracomplete counterpart, supervaluationism). (shrink)
Recently a fascinating debate has been rekindled over whether vagueness is metaphysical or linguistic. That is, is vagueness an objective feature of reality or is it merely an artifact of our language? Bertrand Russell's contribution to this debate is considered by many to be decisive. Russell suggested that it is a mistake to conclude that the world is vague simply because the language we use to describe it is vague. He argued that to draw such an inference is (...) to commit "the fallacy of verbalism". I argue that this is only a fallacy if we have no reason to believe that the world is as our language says. Since vagueness is apparently not eliminable from our language—a fact that Russell himself acknowledged—an indispensability argument can be launched for metaphysical vagueness. In this paper I outliine such an argument. (shrink)
A standard response to the problem of diachronic vagueness is ‘the semantic solution’, which demands an abundant ontology. Although it is known that the abundant ontology does not logically preclude endurantism, their combination is rejected because it necessitates massive coincidence between countless objects. In this paper, I establish that the semantic solution is available not only to perdurantists but also to endurantists by showing that there is no problem with such ubiquitous and principled coincidence.
Vagueness is a familiar but deeply puzzling aspect of the relation between language and the world. It is highly controversial what the nature of vagueness is -- a feature of the way we represent reality in language, or rather a feature of reality itself? May even relations like identity or parthood be affected by vagueness? Sorites arguments suggest that vague terms are either inconsistent or have a sharp boundary. The account we give of such paradoxes plays a (...) pivotal role for our understanding of natural languages. If our reasoning involves any vague concepts, is it safe from contradiction? Do vague concepts really lack any sharp boundary? If not, why are we reluctant to accept the existence of any sharp boundary for them? And what rules of inference can we validly apply, if we reason in vague terms? Cuts and Clouds presents the latest work towards a clearer understanding of these old puzzles about the nature and logic of vagueness. The collection offers a stimulating series of original essays on these and related issues by some of the world's leading experts. (shrink)
A sorites argument is a symptom of the vagueness of the predicate with which it is constructed. A vague predicate admits of at least one dimension of variation (and typically more than one) in its intended range along which we are at a loss when to say the predicate ceases to apply, though we start out confident that it does. It is this feature of them that the sorites arguments exploit. Exactly how is part of the subject of this (...) paper. The majority of philosophers writing on vagueness take it to be a kind of semantic phenomenon. If we are right, they are correct in this assumption, which is surely the default position, but they have not so far provided a satisfactory account of the implications of this or a satisfactory diagnosis of the sorites arguments. Other philosophers have urged more exotic responses, which range from the view that the fault lies not in our language, but in the world, which they propose to be populated with vague objects which our semantics precisely reflects, to the view that the world and language are both perfectly in order, but that the fault lies with our knowledge of the properties of the words we use (epistemicism). In contrast to the exotica to which some philosophers have found themselves driven in an attempt to respond to the sorites puzzles, we undertake a defense of the commonsense view that vague terms are semantically vague. Our strategy is to take fresh look at the phenomenon of vagueness. Rather than attempting to adjudicate between different extant theories, we begin with certain pre-theoretic intuitions about vague terms, and a default position on classical logic. The aim is to see whether (i) a natural story can be told which will explain the vagueness phenomenon and the puzzling nature of soritical arguments, and, in the course of this, to see whether (ii) there arises any compelling pressure to give up the natural stance. We conclude that there is a simple and natural story to be told, and we tell it, and that there is no good reason to abandon our intuitively compelling starting point. The importance of the strategy lies in its dialectical structure. Not all positions on vagueness are on a par. Some are so incredible that even their defenders think of them as positions of last resort, positions to which we must be driven by the power of philosophical argument. We aim to show that there is no pressure to adopt these incredible positions, obviating the need to respond to them directly. If we are right, semantic vagueness is neither surprising, nor threatening. It provides no reason to suppose that the logic of natural languages is not classical or to give up any independently plausible principle of bivalence. Properly understood, it provides us with a satisfying diagnosis of the sorites argumentation. It would be rash to claim to have any completely novel view about a topic so well worked as vagueness. But we believe that the subject, though ancient, still retains its power to inform and challenge us. In particular, we will argue that taking seriously the central phenomenon of predicate vagueness—the “boundarylessness” of vague predicates—on the commonsense assumption that vagueness is semantic, leads ineluctably to the view that no sentences containing vague expressions (henceforth ‘vague sentences’) are truth-evaluable. This runs counter to much of the literature on vagueness, which commonly assumes that, though some applications of vague predicates to objects fail to be truth-evaluable, in clear positive and negative cases vague sentences are unproblematically true or false. It is clarity on this, and related points, that removes the puzzles associated with vagueness, and helps us to a satisfying diagnosis of why the sorites arguments both seem compelling and yet so obviously a bit of trickery. We give a proof that semantically vague predicates neither apply nor fail-to-apply to anything, and that consequently it is a mistake to diagnose sorites arguments, as is commonly done, by attempting to locate in them a false premise. Sorites arguments are not sound, but not unsound either. We offer an explanation of their appeal, and defend our position against a variety of worries that might arise about it. The plan of the paper is as follows. We first introduce an important distinction in terms of which we characterize what has gone wrong with vague predicates. We characterize what we believe to be our natural starting point in thinking about the phenomenon of vagueness, from which only a powerful argument should move us, and then trace out the consequences of accepting this starting point. We consider the charge that among the consequences of semantic vagueness are that we must give up classical logic and the principle of bivalence, which has figured prominently in arguments for epistemicism. We argue there are no such consequences of our view: neither the view that the logic of natural languages is classical, nor any plausible principle of bivalence, need be given up. Next, we offer a diagnosis of what has gone wrong in sorites arguments on the basis of our account. We then present an argument to show that our account must be accepted on pain of embracing (in one way or another) the epistemic view of “vagueness”, i.e., of denying that there are any semantically vague terms at all. Next, we discuss some worries that may arise about the intelligibility of our linguistic practices if our account is correct. We argue none of these worries should force us from our intuitive starting point. Finally, we cast a quick glance at other forms of semantic incompleteness. (shrink)
Chrisoula Andreou says procrastination qua imprudent delay is modeled by Warren Quinn’s self-torturer, who supposedly has intransitive preferences that rank each indulgence in something that delays his global goals over working toward those goals and who finds it vague where best to stop indulging. His pair-wise choices to indulge result in his failing the goals, which he then regrets. This chapter argues, contra the money-pump argument, that it is not irrational to have or choose from intransitive preferences; so the agent’s (...) delays are not imprudent, not instances of procrastination. Moreover, the self-torturer case is intelligible only if there is no vagueness and if the agent’s preferences are transitive. But then he would delay only from ordinary weakness of will. And when it is vague where best to stop indulging, rational agents would use symmetry-breaking techniques; so, again, any procrastination would be explained by standard weakness of will, not vagueness. (shrink)
In this paper we compare different models of vagueness viewed as a specific form of subjective uncertainty in situations of imperfect discrimination. Our focus is on the logic of the operator “clearly” and on the problem of higher-order vagueness. We first examine the consequences of the notion of intransitivity of indiscriminability for higher-order vagueness, and compare several accounts of vagueness as inexact or imprecise knowledge, namely Williamson’s margin for error semantics, Halpern’s two-dimensional semantics, and the system (...) we call Centered semantics. We then propose a semantics of degrees of clarity, inspired from the signal detection theory model, and outline a view of higher-order vagueness in which the notions of subjective clarity and unclarity are handled asymmetrically at higher orders, namely such that the clarity of clarity is compatible with the unclarity of unclarity. (shrink)
In their paper “Vagueness, Ignorance, and Margins for Error” Kenton Machina and Harry Deutsch criticize the epistemic theory of vagueness. This paper answers their objections. The main issues discussed are: the relation between meaning and use; the principle of bivalence; the ontology of vaguely specified classes; the proper form of margin for error principles; iterations of epistemic operators and semantic compositionality; the relation or lack of it between quantum mechanics and theories of vagueness.
The conceptual spaces approach has recently emerged as a novel account of concepts. Its guiding idea is that concepts can be represented geometrically, by means of metrical spaces. While it is generally recognized that many of our concepts are vague, the question of how to model vagueness in the conceptual spaces approach has not been addressed so far, even though the answer is far from straightforward. The present paper aims to fill this lacuna.
Roy Sorenson offers a unique exploration of an ancient problem: vagueness. Did Buddha become a fat man in one second? Is there a tallest short giraffe? According to Sorenson's epistemicist approach, the answers are yes! Although vagueness abounds in the way the world is divided, Sorenson argues that the divisions are sharp; yet we often do not know where they are. Written in Sorenson'e usual inventive and amusing style, this book offers original insight on language and logic, the (...) way world is, and our understanding of it. (shrink)
In this paper we propose an approach to vagueness characterised by two features. The first one is philosophical: we move along a Kantian path emphasizing the knowing subject’s conceptual apparatus. The second one is formal: to face vagueness, and our philosophical view on it, we propose to use topology and formal topology. We show that the Kantian and the topological features joined together allow us an atypical, but promising, way of considering vagueness.
I argue that for those who follow Evans in finding indeterminacy of de re identity statements problematic, ontic vagueness within a three-dimensionalist metaphysics will raise some problems that are not faced by the four-dimensionalist. For the types of strategies used to avoid de re indeterminacy within the context of ontic vagueness at-at-time, that is, spatial vagueness, are problematic within a three-dimensionalist framework when put to use within the context of ontic vagueness across-time, that is temporal (...) class='Hi'>vagueness. (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.
'Epistemic' theories of vagueness notoriously claim that (despite the appearances to the contrary) all of our vague terms have sharp boundaries, it's just that we can't know what they are. Epistemic theories are typically criticized for failing to explain (1) the source of the ignorance postulated, and (2) how our terms could come to have such precise boundaries. Both of these objections will, however, be shown to rest on certain 'presentist' assumptions about the relation between use and meaning, and (...) if allows that the meaning constitutive elements of our linguistic practices can extend into the future, the possibility of a new sort of 'normative epistemicism' emerges. (shrink)
In this paper we point out some interesting structural similarities between vagueness and moral dilemmas as well as between some of the proposed solutions to both problems. Moral dilemma involves a situation with opposed obligations that cannot all be satisfied. Transvaluationism as an approach to vagueness makes three claims concerning the nature of vagueness: (1) it involves incompatibility between mutually unsatisfiable requirements, (2) the underlying requirements retain their normative power even when they happen to be overruled, and (...) (3) this incompatibility turns out to be rather benign in practice. Given that transvaluationism is inspired by moral dilemmas, these claims are assessed in respect to them. Transvaluationism provides a smooth account of the mentioned claims concerning vagueness. Following a brief discussion of Sorensen’s views on moral dilemmas and conflict vagueness, we offer a model of moral pluralism accommodating structurally similar claims about the nature of moral conflict and moral dilemmas. (shrink)
Philosophers disagree about whether vagueness requires us to admit truth-value gaps, about whether there is a gap between the objects of which a given vague predicate is true and those of which it is false on an appropriately constructed sorites series for the predicate—a series involving small increments of change in a relevant respect between adjacent elements, but a large increment of change in that respect between the endpoints. There appears, however, to be widespread agreement that there is some (...) sense in which vague predicates are gappy which may be expressed neutrally by saying that on any appropriately constructed sorites series for a given vague predicate there will be a gap between the objects of which the predicate is deﬁnitely true and those of which it is deﬁnitely false. Taking as primitive the operator ‘it is deﬁnitely the case that’, abbreviated as ‘D’, we may stipulate that a predicate F is deﬁnitely true (or deﬁnitely false) of an object just in case ‘DF (a)’, where a is a name for the object, is true (or false) simpliciter.1 This yields the following conditional formulation of a ‘gap principle’: (DΦ(x) ∧ D¬Φ(y)) → ¬R(x, y). Here ‘Φ’ is to be replaced with a vague predicate, while ‘R’ is to stand for a sorites relation for that predicate: a relation that can be used to construct a sorites series for the predicate—such as the relation of being just one millimetre shorter than for the predicate ‘is tall’. Disagreements about the sense in which it is correct to say that vague predicates are gappy can then be recast as disagreements about how to understand the deﬁnitely operator. One might give it, for example, a pragmatic construal such as ‘it would not be misleading to assert that’; or an epistemic construal such as ‘it is known that’ or ‘it is knowable that’; or a semantic construal such as ‘it is true that’. (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 paper is concerned with a quality space model as an account of the intelligibility of explanation. I argue that descriptions of causal or functional roles (Chalmers Levine, 2001) are not the only basis for intelligible explanations. If we accept that phenomenal concepts refer directly, not via descriptions of causal or functional roles, then it is difficult to find role fillers for the described causal roles. This constitutes a vagueness constraint on the intelligibility of explanation. Thus, I propose to (...) use quality space models to develop a systematic way of studying different modalities of perception and feelings, e.g., visual and auditory perception, pain, and emotion, that can reveal some structural relations among these modalities. It might turn out that topological explanation can be more intelligible than causal explanation in this case. I discuss two accounts of a quality space for color vision (Clark, 2000; Rosenthal, 2010) and propose how to construct a quality space for pain. Daniel Kostic is Associated Researcher at Berlin School of Mind and Brain. (shrink)
We argue that the epistemic theory of vagueness cannot adequately justify its key tenet-that vague predicates have precisely bounded extensions, of which we are necessarily ignorant. Nor can the theory adequately account for our ignorance of the truth values of borderline cases. Furthermore, we argue that Williamson’s promising attempt to explicate our understanding of vague language on the model of a certain sort of “inexact knowledge” is at best incomplete, since certain forms of vagueness do not fit Williamson’s (...) model, and in fact fit an alternative model. Finally, we point out that a certain kind of irremediable inexactitude postulated by physics need not be-and is not commonly-interpreted as epistemic. Thus, there are aspects of contemporary science that do not accord well with the epistemicist outlook. (shrink)
Vagueness demands many boundaries. Each is permissible, in that a thinker may without error use it to distinguish objects, though none is mandatory. This is revealed by a thought experiment—scrambled sorites—in which objects from a sorites series are presented in a random order, and subjects are required to make their judgments without access to any previous objects or their judgments concerning them.
Contemporary discussions do not always clearly distinguish two different forms of vagueness. Sometimes focus is on the imprecision of predicates, and sometimes the indefiniteness of statements. The two are intimately related, of course. A predicate is imprecise if there are instances to which it neither definitely applies nor definitely does not apply, instances of which it is neither definitely true nor definitely false. However, indefinite statements will occur in everyday discourse only if speakers in fact apply imprecise predicates to (...) such indefinite instances. (What makes an instance indefinite is, it should be clear, predicate-relative.) The basic issue in the present inquiry is whether this indefiniteness ever really occurs; the basic question is, Why should it ever occur? (shrink)
Recently, Terry Horgan and Matjaž Potrč have defended the thesis of ‘existence monism’, according to which the whole cosmos is the only concrete object. Their arguments appeal largely to considerations concerning vagueness. Crucially, they claim that ontological vagueness is impossible, and one key assumption in their defence of this claim is that vagueness always involves ‘sorites-susceptibility’. I aim to challenge both the claim and this assumption. As a consequence, I seek to undermine their defence of existence monism (...) and support a common-sense pluralist ontology of ‘ordinary objects’ as being fully consistent with a thoroughgoing metaphysical realism. (shrink)
Four-dimensionalism, the stage theory version in particular, has been defended as the best solution for avoiding vagueness in regards to composition, persistence and identity. Stage theory is highly problematic by itself, and the two views usually packed with it, unrestricted composition and counterpart theory, are a heavy burden. However, dispensing with these two views, four-dimensionalism could avoid vague persistence by issuing a criterion that would establish sharp temporal boundaries for the existence of genuine entities (simples, molecules and living organisms). (...) This would avoid vague existence and vague identity, but in a way that is still compatible with endurantism. Nevertheless, a minimal (substantialist) four-dimensionalism, a worm perdurantist ontology, would fit better with the unique way in which organisms persist: by retaining both identity and intrinsic change. (shrink)
Stewart Shapiro's ambition in Vagueness in Context is to develop a comprehensive account of the meaning, function, and logic of vague terms in an idealized version of a natural language like English. It is a commonplace that the extensions of vague terms vary according to their context: a person can be tall with respect to male accountants and not tall (even short) with respect to professional basketball players. The key feature of Shapiro's account is that the extensions of vague (...) terms also vary in the course of conversations and that, in some cases, a competent speaker can go either way without sinning against the meaning of the words or the non-linguistic facts. As Shapiro sees it, vagueness is a linguistic phenomenon, due to the kinds of languages that humans speak; but vagueness is also due to the world we find ourselves in, as we try to communicate features of it to each other. (shrink)
There are three main traditional accounts of vagueness : one takes it as a genuinely metaphysical phenomenon, one takes it as a phenomenon of ignorance, and one takes it as a linguistic or conceptual phenomenon. In this paper I first very briefly present these views, especially the epistemicist and supervaluationist strategies, and shortly point to some well-known problems that the views carry. I then examine a 'statistical epistemicist' account of vagueness that is designed to avoid precisely these problems (...) – it will be a view that provides an account of the phenomenon of vagueness as coming from our linguistic practices, while insisting that meaning supervenes on use, and that our use of vague terms does yield sharp and precise meanings, which we ignore, thus allowing bivalence to hold. (shrink)
The topic of this paper is whether there is metaphysical vagueness. It is shown that it is important to distinguish between the general phenomenon of indeterminacy and the more narrow phenomenon of vagueness (the phenomenon that paradigmatically rears its head in sorites reasoning). Relatedly, it is important to distinguish between metaphysical indeterminacy and metaphysical vagueness. One can wish to allow metaphysical indeterminacy but rule out metaphysical vagueness. As is discussed in the paper, central argument against metaphysical (...)vagueness, like those of Gareth Evans and Mark Sainsbury, would if successful rule out metaphysical indeterminacy. One way to argue specifically against the possibility of metaphysical vagueness might be thought to be to argue for a specific theory of the nature of vagueness according to which vagueness is a semantic phenomenon. But it is shown that there are complications also pertaining to arguments with that structure. Toward the end of the paper, I discuss Trenton Merricks’ well-known argument against a semantic view on vagueness and for a metaphysical view. (shrink)
In the past few years, deflationary positions in the debate on the nature of composite material objects have become prominent. According to Ted Sider these include the thesis of quantifier variance, against which he has defended ontological realism. Recently, Sider has considered the possibility of rejecting his arguments against the vagueness of the unrestricted quantifiers in terms of translation functions. Against this strategy, he has presented an intuitive complaint and has argued that it can only be resisted if quantifier (...) variance is accepted. But this is false. In this paper I argue, against Sider, that there is a coherent way to combine the rejection of quantifier variance with the vagueness of the unrestricted quantifiers. I sketch a model to show this, and then I consider, on the basis of it, several versions of the indeterminacy argument against the vagueness of the unrestricted quantifiers that Sider has formulated over the years. (shrink)
Abstract In Causing Actions, Pietroski defends a distinctive view of the relationship between mind and body which he calls Personal Dualism. Central to his defence is the Argument from Differential Vagueness. It moves from the claim that mental events have different vagueness of spatiotemporal boundaries from neural events to the claim that mental events are not identical to neural events. In response, I argue that this presupposes an ontological account of vagueness that there is no reason to (...) believe in this context. I further argue that Pietroski's reasons for rejecting the possibility that mental events are vaguely constituted from neural events are inadequate. I go on to show how Pietroski's Personal Dualism is ill-equipped to deal with the problem of mental causation because of its apparently necessary appeal to ceteris paribus laws. (shrink)