Search results for 'higher-order vagueness' (try it on Scholar)

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  1. Higher-Order Vagueness (2003). Gap Principles, Penumbral Consequence, and Infinitely. In J. C. Beall (ed.), Liars and Heaps: New Essays on Paradox. Oxford University Press 195.
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  2. Susanne Bobzien (2015). I—Columnar Higher-Order Vagueness, or Vagueness is Higher-Order Vagueness. Aristotelian Society Supplementary Volume 89 (1):61-87.
    Most descriptions of higher-order vagueness in terms of traditional modal logic generate so-called higher-order vagueness paradoxes. The one that doesn't is problematic otherwise. Consequently, the present trend is toward more complex, non-standard theories. However, there is no need for this. In this paper I introduce a theory of higher-order vagueness that is paradox-free and can be expressed in the first-order extension of a normal modal system that is complete with respect to single-domain Kripke-frame semantics. (...)
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  3. Susanne Bobzien (2013). Higher-Order Vagueness and Borderline Nestings: A Persistent Confusion. Analytic Philosophy 54 (1):1-43.
    ABSTRACT: This paper argues that the so-called paradoxes of higher-order vagueness are the result of a confusion between higher-order vagueness and the distribution of the objects of a Sorites series into extensionally non-overlapping non-empty classes.
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  4.  13
    Susanne Bobzien (2016). Reply to Rosanna Keefe’s ‘Modelling Higher-Order Vagueness: Columns, Borderlines and Boundaries’.
    This paper is an expanded written version of my reply to Rosanna Keefe’s paper ‘Modelling higher-order vagueness: columns, borderlines and boundaries’ (Keefe 2015), which in turn is a reply to my paper ‘Columnar higher-order vagueness, or Vagueness is higher-order vagueness’ (Bobzien 2015). Both papers were presented at the Joint Session of the the Aristotelian Society and the Mind Association in July, 2015. At the Joint Session meeting, there was insufficient time to present all (...)
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  5. Susanne Bobzien (2012). If It's Clear, Then It's Clear That It's Clear, or is It? Higher-Order Vagueness and the S4 Axiom. In B. Morison K. Ierodiakonou (ed.), Episteme, etc. OUP UK
    The purpose of this paper is to challenge some widespread assumptions about the role of the modal axiom 4 in a theory of vagueness. In the context of vagueness, axiom 4 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 axiom 4 two different notions of clarity are (...)
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  6. Pablo Cobreros (2011). Supervaluationism and Fara's Argument Concerning Higher-Order Vagueness. In Paul Egré & Klinedinst Nathan (eds.), Vagueness and Language Use, Palgrave Studies in Pragmatics, Language and Cognition. Palgrave Macmillan
    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.
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  7.  18
    Nasim Mahoozi & Thomas Mormann, Not Much Higher-Order Vagueness in Williamson’s ’Logic of Clarity’.
    This paper deals with higher-order vagueness in Williamson's 'logic of clarity'. Its aim is to prove that for 'fixed margin models' (W,d,α ,[ ]) the notion of higher-order vagueness collapses to second-order vagueness. First, it is shown that fixed margin models can be reformulated in terms of similarity structures (W,~). The relation ~ is assumed to be reflexive and symmetric, but not necessarily transitive. Then, it is shown that the structures (W,~) come along with naturally (...)
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  8. Susanne Bobzien (2010). Higher-Order Vagueness, Radical Unclarity, and Absolute Agnosticism. Philosophers' Imprint 10 (10):1-30.
    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 (...)
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  9. Susanne Bobzien (2011). In Defense of True Higher-Order Vagueness. Synthese 180 (3):317-335.
    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; (...)
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  10. Crispin Wright (2009). The Illusion of Higher-Order Vagueness. In Richard Dietz & Sebastiano Moruzzi (eds.), Cuts and Clouds. Vaguenesss, its Nature and its Logic. Oxford University Press
    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 (...)
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  11.  35
    Susanna Rinard (forthcoming). Imprecise Probability and Higher Order Vagueness. Res Philosophica.
    There is a trade-off between specificity and accuracy in existing models of belief. Descriptions of agents in the tripartite model, which recognizes only three doxastic attitudes—belief, disbelief, and suspension of judgment—are typically accurate, but not sufficiently specific. The orthodox Bayesian model, which requires real-valued credences, is perfectly specific, but often inaccurate: we often lack precise credences. I argue, first, that a popular attempt to fix the Bayesian model by using sets of functions is also inaccurate, since it requires us to (...)
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  12.  69
    Susanne Bobzien (2014). Higher-Order Vagueness and Numbers of Distinct Modalities. Disputatio (39):131-137.
    This paper shows that the following common assumption is false: that in modal-logical representations of higher-order vagueness, for there to be borderline cases to borderline cases ad infinitum, the number of possible distinct modalities in a modal system must be infinite. (Open access journal).
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  13.  37
    Peter Pagin (forthcoming). Tolerance and Higher-Order Vagueness. Synthese:1-34.
    The idea of higher-order vagueness is usually associated with conceptions of vagueness that focus on the existence of borderline cases. What sense can be made of it within a conception of vagueness that focuses on tolerance instead? A proposal is offered here. It involves understanding ‘definitely’ not as a sentence operator but as a predicate modifier, and more precisely as an intensifier, that is, an operator that shifts the predicate extension along a scale. This idea is (...)
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  14. Delia Graff Fara (2003). Gap Principles, Penumbral Consequence, and Infinitely Higher-Order Vagueness. In J. C. Beall (ed.), New Essays on the Semantics of Paradox. Oxford University Press
    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 (...)
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  15. Susanne Bobzien, A Model-Theoretic Account of Columnar Higher-Order Vagueness.
    ABSTRACT: Paper currently being revised.
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  16. Richard Heck (1993). A Note on the Logic of (Higher-Order) Vagueness. Analysis 53 (4):201-208.
    A discussion of Crispin Wright's 'paradox of higher-order vagueness', I suggest that the paradox may be resolved by careful attention to the logical principles used in its formulation. In particular, I focus attention on the rule of inference that allows for the inference from A to 'Definitely A', and argue that this rule, though valid, may not be used in subordinate deductions, e.g., in the course of a conditional proof. Wright's paradox uses the rule (or its equivalent) in (...)
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  17. Gerald Hull, The Eliminability of Higher Order Vagueness.
    It is generally supposed that borderline cases account for the tolerance of vague terms, yet cannot themselves be sharply bounded, leading to infinite levels of higher order vagueness. This higher order vagueness subverts any formal effort to make language precise. However, it is possible to show that tolerance must diminish at higher orders. The attempt to derive it from indiscriminability founders on a simple empirical test, and we learn instead that there is no limit to how small higher (...)
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  18. Timothy Williamson (1999). On the Structure of Higher-Order Vagueness. Mind 108 (429):127-143.
    Discussions of higher-order vagueness rarely define what it is for a term to have nth-order vagueness for n>2. This paper provides a rigorous definition in a framework analogous to possible worlds semantics; it is neutral between epistemic and supervaluationist accounts of vagueness. The definition is shown to have various desirable properties. But under natural assumptions it is also shown that 2nd-order vagueness implies vagueness of all orders, and that a conjunction can have 2nd-order (...) even if its conjuncts do not. Relations between the definition and other proposals are explored; reasons are given for preferring the present proposal. (shrink)
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  19. Dominic Hyde (1994). Why Higher-Order Vagueness is a Pseudo-Problem. Mind 103 (409):35-41.
    Difficulties in arriving at an adequate conception of vagueness have led many writers to describe a phenomenon that has come to be known as "higher-order vagueness". Almost as many have found it to be a problem that needs to be addressed. In what follows I shall argue that, whilst we must acknowledge its presence, it is a pseudo-problem. The crucial point is the vagueness of "vague", which shows the phenomenon to be unproblematic though real enough.
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  20.  96
    Patrick Greenough (2005). Contextualism About Vagueness and Higher-Order Vagueness. Aristotelian Society Supplementary Volume 79 (1):167–190.
    To get to grips with what Shapiro does and can say about higher-order vagueness, it is first necessary to thoroughly review and evaluate his conception of (first-order) vagueness, a conception which is both rich and suggestive but, as it turns out, not so easy to stabilise. In Sections I–IV, his basic position on vagueness (see Shapiro [2003]) is outlined and assessed. As we go along, I offer some suggestions for improvement. In Sections V–VI, I review two (...)
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  21. Scott Soames (2003). Higher-Order Vagueness for Partially Defined Predicates. In JC Beall (ed.), Liars and Heaps: New Essays on Paradox. Oxford University Press
    A theory of higher-order vagueness for partially-defined, context-sensitive predicates like is blue is offered. According to the theory, the predicate is determinately blue means roughly is an object o such that the claim that o is blue is a necessary consequence of the rules of the language plus the underlying non-linguistic facts in the world. Because the question of which rules count as rules of the language is itself vague, the predicate is determinately blue is both vague and (...)
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  22.  35
    Rosanna Keefe (2015). II—Modelling Higher-Order Vagueness: Columns, Borderlines and Boundaries. Aristotelian Society Supplementary Volume 89 (1):89-108.
    According to columnar higher-order vagueness, all orders of vagueness coincide: any borderline case is a borderline borderline case, and a third-order borderline case, etc. Bobzien has worked out many details of such a theory and models it with a modal logic closely related to S4. I take up a range of questions about the framework and argue that it is not suitable for modelling the structure of vagueness and higher-order vagueness.
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  23.  3
    Martin Montminy (2016). A Contextualist Approach to Higher‐Order Vagueness. Southern Journal of Philosophy 54 (3):372-392.
    According to contextualism about vagueness, the content of a vague predicate is context sensitive. On this view, when item a is in the penumbra of the vague predicate ‘F’, speakers may utter ‘Fa’, or they may utter ‘not-Fa’, without contravening the literal meaning of ‘F’. Unlike its more popular variants, the version of contextualism I defend rejects the principle of tolerance, a principle according to which small differences should not affect the applicability of a vague predicate. My goal is (...)
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  24.  55
    Achille C. Varzi (2003). Higher-Order Vagueness and the Vagueness of ‘Vague’. Mind 112 (446):295–298.
    R. Sorensen’s argument to the effect that ’vague’ is a vague predicate has been used by D. Hyde to infer that vague predicates suffer from higher-order vagueness. M. Tye has objected (convincingly) that this is too strong: all that follows from Sorensen’s result is that there are some border border cases, but not necessarily border border cases of every vague predicate. I argue that this is still too strong: Sorensen’s proof presupposes the existence of border border cases, hence (...)
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  25.  79
    Diana Raffman (2009). Demoting Higher-Order Vagueness. In Sebastiano Moruzzi & Richard Dietz (eds.), Cuts and Clouds. Vaguenesss, its Nature and its Logic. Oxford University Press 509--22.
    Higher-order vagueness is widely thought to be a feature of vague predicates that any adequate theory of vagueness must accommodate. It takes a variety of forms. Perhaps the most familiar is the supposed existence, or at least possibility, of higher-order borderline cases—borderline borderline cases, borderline borderline borderline cases, and so forth. A second form of higherorder vagueness, what I will call ‘prescriptive’ higher-order vagueness, is thought to characterize complex predicates constructed from vague predicates (...)
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  26.  86
    Stewart Shapiro & Patrick Greenough (2005). Stewart Shapiro. Context, Conversation, and so-Called 'Higher-Order Vagueness'. Aristotelian Society Supplementary Volume 79 (1):147–165.
    After a brief account of the problem of higher-order vagueness, and its seeming intractability, I explore what comes of the issue on a linguistic, contextualist account of vagueness. On the view in question, predicates like ‘borderline red’ and ‘determinately red’ are, or at least can be, vague, but they are different in kind from ‘red’. In particular, ‘borderline red’ and ‘determinately red’ are not colours. These predicates have linguistic components, and invoke notions like ‘competent user of the (...)
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  27.  18
    R. M. Sainsbury (1991). Is There Higher-Order Vagueness? Philosophical Quarterly 41 (163):167-182.
    I argue against a standard conception of classification, according to which concepts classify by drawing boundaries. This conception cannot properly account for "higher-order vagueness." I discuss in detail claims by Crispin Wright about "definitely," and its connection with higher-order vagueness. Contrary to Wright, I argue that the line between definite cases of red and borderline ones is not sharp. I suggest a new conception of classification: many concepts classify without drawing boundaries; they are boundaryless. Within this (...)
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  28. Scott Soames (2004). Higher-Order Vagueness for Partially Defined Predicates. In J. C. Beall (ed.), Liars and Heaps: New Essays on Paradox. Clarendon Press
    A theory of higher-order vagueness for partially-defined, context-sensitive predicates like is blue is offered. According to the theory, the predicate is determinately blue means roughly is an object o such that the claim that o is blue is a necessary consequence of the rules of the language plus the underlying non-linguistic facts in the world. Because the question of which rules count as rules of the language is itself vague, the predicate is determinately blue is both vague and (...)
     
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  29. Timothy Williamson, On the Structure of Higher-Order Vagueness.
    Discussions of higher-order vagueness rarely define what it is for a term to have nth-order vagueness for n>2. This paper provides a rigorous definition in a framework analogous to possible worlds semantics; it is neutral between epistemic and supervaluationist accounts of vagueness. The definition is shown to have various desirable properties. But under natural assumptions it is also shown that 2nd-order vagueness implies vagueness of all orders, and that a conjunction can have 2nd-order (...) even if its conjuncts do not. Relations between the definition and other proposals are explored; reasons are given for preferring the present proposal. (shrink)
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  30. Elia Zardini (2013). Higher-Order Sorites Paradox. Journal of Philosophical Logic 42 (1):25-48.
    The naive theory of vagueness holds that the vagueness of an expression consists in its failure to draw a sharp boundary between positive and negative cases. The naive theory is contrasted with the nowadays dominant approach to vagueness, holding that the vagueness of an expression consists in its presenting borderline cases of application. The two approaches are briefly compared in their respective explanations of a paramount phenomenon of vagueness: our ignorance of any sharp boundary between (...)
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  31.  94
    Nicholas J. J. Smith (2011). Fuzzy Logic and Higher-Order Vagueness. In Petr Cintula, Christian G. Fermüller, Lluis Godo & Petr Hájek (eds.), Understanding Vagueness: Logical, Philosophical and Linguistic Perspectives. College Publications 1--19.
    The major reason given in the philosophical literature for dissatisfaction with theories of vagueness based on fuzzy logic is that such theories give rise to a problem of higherorder vagueness or artificial precision. In this paper I first outline the problem and survey suggested solutions: fuzzy epistemicism; measuring truth on an ordinal scale; logic as modelling; fuzzy metalanguages; blurry sets; and fuzzy plurivaluationism. I then argue that in order to decide upon a solution, we need to understand the (...)
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  32.  63
    R. Sorensen (2010). Borderline Hermaphrodites: Higher-Order Vagueness by Example. Mind 119 (474):393-408.
    The Pyrrhonian sceptic Favorinus of Arelata personified indeterminacy, cultivating his (or her) borderline status to undermine dogmatism. Inspired by the techniques of Favorinus, I show, by example, that ‘vague’ has borderline cases. These concrete steps lead to a more abstract argument that ‘vague’ has borderline borderline cases and borderline borderline borderline cases. My specimens are intended supplement earlier non-constructive proofs of the vagueness of ‘vague’.
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  33. J. A. Burgess (1990). The Sorites Paradox and Higher-Order Vagueness. Synthese 85 (3):417-474.
    One thousand stones, suitably arranged, might form a heap. If we remove a single stone from a heap of stones we still have a heap; at no point will the removal of just one stone make sufficient difference to transform a heap into something which is not a heap. But, if this is so, we still have a heap, even when we have removed the last stone composing our original structure. So runs the Sorites paradox. Similar paradoxes can be constructed (...)
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  34. Pablo Cobreros (2010). Supervaluationism and Fara's Paradox of Higher-Order Vagueness. In Paul Egre & Nathan Klinedinst (eds.), Vagueness and Language Use. Palgrave Macmillan
     
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  35. Libor Běhounek (2011). Comments on 'Fuzzy Logic and Higher-Order Vagueness' by Nicholas J.J. Smith. In Petr Cintula, Christian G. Fermüller, Lluis Godo & Petr Hájek (eds.), Understanding Vagueness: Logical, Philosophical and Linguistic Perspectives. College Publications 21-8.
     
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  36. Francesco Paoli (2011). Comments on 'Fuzzy Logic and Higher-Order Vagueness' by Nicholas J.J. Smith. In Petr Cintula, Christian G. Fermüller, Lluis Godo & Petr Hájek (eds.), Understanding Vagueness: Logical, Philosophical and Linguistic Perspectives. College Publications 33-5.
     
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  37. Nicholas J. J. Smith (2011). Reply to Francesco Paoli’s Comments on 'Fuzzy Logic and Higher-Order Vagueness'. In Petr Cintula, Christian G. Fermüller, Lluis Godo & Petr Hájek (eds.), Understanding Vagueness: Logical, Philosophical and Linguistic Perspectives. College Publications 37-40.
     
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  38. Nicholas J. J. Smith (2011). Reply to Libor Běhounek’s Comments on 'Fuzzy Logic and Higher-Order Vagueness'. In Petr Cintula, Christian G. Fermüller, Lluis Godo & Petr Hájek (eds.), Understanding Vagueness: Logical, Philosophical and Linguistic Perspectives. College Publications 29-32.
     
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  39. Crispin Wright (1992). Is Higher Order Vagueness Coherent? Analysis 52 (3):129-139.
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  40.  52
    Mark Sainsbury (1991). Is There Higher-Order Vagueness? Philosophical Quarterly 41 (163):167-182.
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  41.  44
    Dorothy Edgington (1993). Wright and Sainsbury on Higher-Order Vagueness. Analysis 53 (4):193-200.
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  42. Andrew Bacon, Vagueness at Every Order: The Prospects of Denying B.
    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 determinate (...)
     
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  43. Elia Zardini (2005). Higher-Order Vagueness and Paradox: The Glory and Misery of S4 Definiteness. The Baltic International Yearbook of Cognition, Logic and Communication 1.
     
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  44.  3
    Patrick Greenough (2005). II—Patrick Greenough: Contextualism About Vagueness and Higher‐Order Vagueness. Aristotelian Society Supplementary Volume 79 (1):167-190.
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  45. R. Sainsbury (1991). Mark: Is There Higher-Order Vagueness. Philosophical Quarterly 167:167-182.
     
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  46.  7
    How To Set Up A. Surprise (1999). On the Structure of Higher-Order Vagueness, Timothy Williamson. Mind 82 (4).
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  47. Delia Graff (2004). Gap Principles, Penumbral Consequence, and Infinitely Higher-Order Vagueness. In J. C. Beall (ed.), Liars and Heaps: New Essays on Paradox. Clarendon Press
     
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  48. R. Jobanputra & P. R. Bhat (2001). On Why We Cannot Escape Higher Order Vagueness. Indian Philosophical Quarterly 28 (1):57-68.
     
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  49. Scott Soames (2009). Essay Thirteen. Higher-Order Vagueness for Partially Defined Predicates. In Philosophical Essays, Volume 2: The Philosophical Significance of Language. Princeton University Press 340-361.
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  50. Haim Gaifman (2010). Vagueness, Tolerance and Contextual Logic. Synthese 174 (1):5 - 46.
    The goal of this paper is a comprehensive analysis of basic reasoning patterns that are characteristic of vague predicates. The analysis leads to rigorous reconstructions of the phenomena within formal systems. Two basic features are dealt with. One is tolerance: the insensitivity of predicates to small changes in the objects of predication (a one-increment of a walking distance is a walking distance). The other is the existence of borderline cases. The paper shows why these should be treated as different, though (...)
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