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  1. Vagueness in Language: The Case Against Fuzzy Logic Revisited.Uli Sauerland - manuscript
    Kamp and Fine presented an influential argument against the use of fuzzy logic for linguistic semantics in 1975. However, the argument assumes that contradictions of the form "A and not A" have semantic value zero. The argument has been recently criticized because sentences of this form are actually not perceived as contradictory by naive speakers. I present new experimental evidence arguing that fuzzy logic still isn't useful for linguistic semantics even if we take such naive speaker judgements at face value. (...)
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  2. Vague Disagreements and the Sorites Paradox.Ted Everett - forthcoming - In Otavio Bueno & Ali Abasnezhad (eds.), Logic, Epistemology, and the Unity of Science 33: On the Sorites Paradox. New York: Springer.
    When you and I seriously argue over whether a man of seventy is old enough to count as an "old man", it seems that we are appealing neither to our own separate standards of oldness nor to a common standard that is already fixed in the language. Instead, it seems that both of us implicitly invoke an ideal, shared standard that has yet to be agreed upon: the place where we ought to draw the line. As with other normative standards, (...)
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  3. Consonance and Dissonance in Solutions to the Sorites.Nicholas J. J. Smith - forthcoming - In Otavio Bueno & Ali Abasnezhad (eds.), On the Sorites Paradox. Springer.
    A requirement on any theory of vagueness is that it solve the sorites paradox. It is generally agreed that there are two aspects to such a solution: one task is to locate the error in the sorites argument; the second task is to explain why the sorites reasoning is a paradox rather than a simple mistake. I argue for a further constraint on approaches to the second task: they should conform to the standard modus operandi in formal semantics, in which (...)
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  4. Prefaces, Sorites and Guides to Reasoning.Rosanna Keefe - 2021 - In Conditionals, Paradox and Probability: Themes from the Philosophy of Dorothy Edgington. Oxford, UK: pp. 212-226.
    Is there an interesting relation between the Preface paradox and the Sorites paradox that might be used to illuminate either or both of those paradoxes and the phenomena of rationality and vagueness with which they, respectively, are bound up? In particular, if we consider the analogy alongside a familiar response to the Preface Paradox that employs degrees of belief, does this give any support to the thought that we should adopt some kind of degree-theoretic treatment of vagueness and the sorites? (...)
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  5. Vagueness as Arbitrariness: Outline of a Theory of Vagueness.Sagid Salles - 2021 - Springer.
    This book proposes a new solution to the problem of vagueness. There are several different ways of addressing this problem and no clear agreement on which one is correct. The author proposes that it should be understood as the problem of explaining vague predicates in a way that systematizes six intuitions about the phenomenon and satisfies three criteria of adequacy for an ideal theory of vagueness. The third criterion, which is called the “criterion of precisification”, is the most controversial one. (...)
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  6. Conditionals, Paradox, and Probability: Themes From the Philosophy of Dorothy Edgington.Lee Walters & John Hawthorne (eds.) - 2021 - Oxford, England: Oxford University press.
    A festschrift for Dorothy Edgington, containing contributions from Cleo Condoravdi, Dorothy Edgington, Kit Fine, Alan Hájek, John Hawthorne, Sabine Iatridou, Nick Jones, Rosanna Keefe, Angelika Kratzer, David Over, Daniel Rothschild, Robert Stalnaker, Scott Sturgeon, and Timothy Williamson.
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  7. Vagueness and the Logic of the World.Zack Garrett - 2020 - Dissertation, University of Nebraska, Lincoln
    In this dissertation, I argue that vagueness is a metaphysical phenomenon---that properties and objects can be vague---and propose a trivalent theory of vagueness meant to account for the vagueness in the world. In the first half, I argue against the theories that preserve classical logic. These theories include epistemicism, contextualism, and semantic nihilism. My objections to these theories are independent of considerations of the possibility that vagueness is a metaphysical phenomenon. However, I also argue that these theories are not capable (...)
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  8. Note on Sorites Series.Friedrich Wilhelm Grafe - 2020 - Archive.Org.
    Vagueness does not necessarily come in with vague predicates, nor need it be expressed by them , but undoubtedly 'vague predicates' are traditionally in the focus of main stream discussions of vagueness. In her current modal logic presentation and discussion of the Sorites paradox Susanne Bobzien[1] lists among the properties of a Sorites series a rather weak modal tolerance principle governing the 'grey zone' containing the borderline cases of the Sorites series, which later proves crucial for her solution of the (...)
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  9. Problems of Precision in Fuzzy Theories of Vagueness and Bayesian Epistemology.Nicholas J. J. Smith - 2019 - In Richard Dietz (ed.), Vagueness and Rationality in Language Use and Cognition. Springer Verlag. pp. 31-48.
    A common objection to theories of vagueness based on fuzzy logics centres on the idea that assigning a single numerical degree of truth -- a real number between 0 and 1 -- to each vague statement is excessively precise. A common objection to Bayesian epistemology centres on the idea that assigning a single numerical degree of belief -- a real number between 0 and 1 -- to each proposition is excessively precise. In this paper I explore possible parallels between these (...)
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  10. On the Borders of Vagueness and the Vagueness of Borders.Rory Collins - 2018 - Vassar College Journal of Philosophy 5:30-44.
    This article argues that resolutions to the sorites paradox offered by epistemic and supervaluation theories fail to adequately account for vagueness. After explaining the paradox, I examine the epistemic theory defended by Timothy Williamson and discuss objections to his semantic argument for vague terms having precise boundaries. I then consider Rosanna Keefe's supervaluationist approach and explain why it fails to accommodate the problem of higher-order vagueness. I conclude by discussing how fuzzy logic may hold the key to resolving the sorites (...)
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  11. What Verities May Be.Igor Douven & Lieven Decock - 2017 - Mind 126 (502):386-428.
    Edgington has proposed a solution to the sorites paradox in terms of ‘verities’, which she defines as degrees of closeness to clear truth. Central to her solution is the assumption that verities are formally probabilities. She is silent on what verities might derive from and on why they should be probabilities. This paper places Edgington’s solution in the framework of a spatial approach to conceptualization, arguing that verities may be conceived of as deriving from how our concepts relate to each (...)
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  12. Degrees of Belief, Expected and Actual.Rosanna Keefe - 2017 - Synthese 194 (10):3789-3800.
    A framework of degrees of belief, or credences, is often advocated to model our uncertainty about how things are or will turn out. It has also been employed in relation to the kind of uncertainty or indefiniteness that arises due to vagueness, such as when we consider “a is F” in a case where a is borderline F. How should we understand degrees of belief when we take into account both these phenomena? Can the right kind of theory of the (...)
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  13. Undead Argument: The Truth-Functionality Objection to Fuzzy Theories of Vagueness.Nicholas Smith - 2017 - Synthese 194 (10):1-27.
    From Fine and Kamp in the 70’s—through Osherson and Smith in the 80’s, Williamson, Kamp and Partee in the 90’s and Keefe in the 00’s—up to Sauerland in the present decade, the objection continues to be run that fuzzy logic based theories of vagueness are incompatible with ordinary usage of compound propositions in the presence of borderline cases. These arguments against fuzzy theories have been rebutted several times but evidently not put to rest. I attempt to do so in this (...)
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  14. Fuzzy Logics in Theories of Vagueness.Nicholas J. J. Smith - 2015 - In Petr Cintula, Christian Fermüller & Carles Noguera (eds.), Handbook of Mathematical Fuzzy Logic - Volume 3. College Publications.
  15. Vague Objects with Sharp Boundaries.Jiri Benovsky - 2014 - Ratio 27 (1):29-39.
    In this article I shall consider two seemingly contradictory claims: first, the claim that everybody who thinks that there are ordinary objects has to accept that they are vague, and second, the claim that everybody has to accept the existence of sharp boundaries to ordinary objects. The purpose of this article is of course not to defend a contradiction. Indeed, there is no contradiction because the two claims do not concern the same ‘everybody’. The first claim, that all ordinary objects (...)
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  16. What Is Graded Membership?Lieven Decock & Igor Douven - 2014 - Noûs 48 (4):653-682.
    It has seemed natural to model phenomena related to vagueness in terms of graded membership. However, so far no satisfactory answer has been given to the question of what graded membership is nor has any attempt been made to describe in detail a procedure for determining degrees of membership. We seek to remedy these lacunae by building on recent work on typicality and graded membership in cognitive science and combining some of the results obtained there with a version of the (...)
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  17. The Problem of Artificial Precision in Theories of Vagueness: A Note on the Rôle of Maximal Consistency.Vincenzo Marra - 2014 - Erkenntnis 79 (5):1015-1026.
    The problem of artificial precision is a major objection to any theory of vagueness based on real numbers as degrees of truth. Suppose you are willing to admit that, under sufficiently specified circumstances, a predication of “is red” receives a unique, exact number from the real unit interval [0, 1]. You should then be committed to explain what is it that determines that value, settling for instance that my coat is red to degree 0.322 rather than 0.321. In this note (...)
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  18. Logic: The Laws of Truth by Nicholas J. J. Smith. [REVIEW]Greg O’Hair - 2013 - Australasian Journal of Philosophy 91 (3):629.
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  19. Vagueness and Degrees of Truth, de Nicholas J. Smith.Carlos Ortiz de Landázuri - 2012 - Teorema: International Journal of Philosophy 31 (1):154-162.
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  20. Modelling Vagueness: What Can We Ignore?Rosanna Keefe - 2012 - Philosophical Studies 161 (3):453-470.
    A theory of vagueness gives a model of vague language and of reasoning within the language. Among the models that have been offered are Degree Theorists’ numerical models that assign values between 0 and 1 to sentences, rather than simply modelling sentences as true or false. In this paper, I ask whether we can benefit from employing a rich, well-understood numerical framework, while ignoring those aspects of it that impute a level of mathematical precision that is not present in the (...)
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  21. Measuring and Modelling Truth.Nicholas J. J. Smith - 2012 - American Philosophical Quarterly 49 (4):345-356.
    Philosophers, linguists and others interested in problems concerning natural language frequently employ tools from logic and model theory. The question arises as to the proper interpretation of the formal methods employed—of the relationship between, on the one hand, the formal languages and their set-theoretic models and, on the other hand, the objects of ultimate interest: natural language and the meanings and truth conditions of its constituent words, phrases and sentences. Two familiar answers to this question are descriptivism and instrumentalism. More (...)
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  22. Gradational Accuracy and Nonclassical Semantics.J. Robert G. Williams - 2012 - Review of Symbolic Logic 5 (4):513-537.
    Joyce (1998) gives an argument for probabilism: the doctrine that rational credences should conform to the axioms of probability. In doing so, he provides a distinctive take on how the normative force of probabilism relates to the injunction to believe what is true. But Joyce presupposes that the truth values of the propositions over which credences are defined are classical. I generalize the core of Joyce’s argument to remove this presupposition. On the same assumptions as Joyce uses, the credences of (...)
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  23. Vagueness and Degrees of Truth.Paul Egré - 2011 - Australasian Journal of Philosophy 89 (1):177-180.
    Nicholas Smith argues that an adequate account of vagueness must involve\ndegrees of truth. The basic idea of degrees of truth is that while\nsome sentences are true and some are false, others possess intermediate\ntruth values: they are truer than the false sentences, but not as\ntrue as the true ones. This idea is immediately appealing in the\ncontext of vagueness--yet it has fallen on hard times in the philosophical\nliterature, with existing degree-theoretic treatments of vagueness\nfacing apparently insuperable objections. Smith seeks to turn the\ntide in (...)
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  24. Vagueness and Degrees of Truth by Nicholas J. J. Smith. [REVIEW]Paul Egré - 2011 - Australasian Journal of Philosophy 89 (1):177-80.
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  25. Fuzzy Logic and Higher-Order Vagueness.Nicholas J. J. Smith - 2011 - In Petr Cintula, Christian G. Fermüller, Lluis Godo & Petr Hájek (eds.), Understanding Vagueness: Logical, Philosophical and Linguistic Perspectives. College Publications. pp. 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 true nature (...)
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  26. Degree Supervaluational Logic.J. Robert G. Williams - 2011 - Review of Symbolic Logic 4 (1):130-149.
    Supervaluationism is often described as the most popular semantic treatment of indeterminacy. There???s little consensus, however, about how to fill out the bare-bones idea to include a characterization of logical consequence. The paper explores one methodology for choosing between the logics: pick a logic that norms belief as classical consequence is standardly thought to do. The main focus of the paper considers a variant of standard supervaluational, on which we can characterize degrees of determinacy. It applies the methodology above to (...)
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  27. Vagueness and Degrees of Truth, by Nicholas J. J. Smith. [REVIEW]Robert Williams - 2011 - Mind 120 (480):1297-1305.
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  28. Vagueness and Degrees of Truth by Nicholas J. J. Smith. [REVIEW]John Collins - 2010 - Philosophical Quarterly 60 (239):422-424.
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  29. Vagueness and Degrees of Truth by Nicholas J. J. Smith. [REVIEW]Roy T. Cook - 2010 - Theoria 76 (4):380-384.
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  30. Vague Analysis.Dennis Earl - 2010 - Metaphysica 11 (2):223-233.
    It might be thought that vagueness precludes the possibility of classical conceptual analysis and, thus, that the classical or definitional view of the nature of complex concepts is incorrect. The present paper argues that classical analysis can be had for concepts expressed by vague language since (1) all of the general theories of vagueness are compatible with the thesis that all complex concepts have classical analyses and also that (2) the meaning of vague expressions can be analyzed by having the (...)
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  31. Review: Vagueness and Degrees of Truth. [REVIEW]Christian G. Fermüller - 2010 - Australasian Journal of Logic 9:1-9.
    Vagueness is one of the most persistent and challenging topics in the intersection of philosophy and logic. At least five other noteworthy books on vagueness have been written by philosophers since 1991 [2, 6, 11, 12, 15]. A (necessarily incomplete) bibliography that has been compiled for the Arché project Vagueness: its Nature and Logic (2004-2006) of the University of St Andrews lists more than 350 articles and books on vagueness until 2005.1 Many new and interesting contributions have appeared since. The (...)
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  32. Vagueness, Tolerance and Contextual Logic.Haim Gaifman - 2010 - 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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  33. Die Wahrheit verträgt kein Mehr oder Minder.Geert Keil - 2010 - In Holm Tetens & Stefan Tolksdorf (eds.), In Sprachspiele verstrickt. Festschrift für Hans Julius Schneider. de Gruyter. pp. 81-100.
    1. Einleitung 2. Herausforderungen für das Nichtgraduierbarkeits- und das Bivalenzprinzip 3. Freges Einwand gegen graduale Wahrheit 4. Warum semantische Vagheit keine Wahrheitsgrade erfordert 5. Grenzen ziehen, wo noch keine gezogen sind.
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  34. Halbglatzen statt Halbwahrheiten. Über Vagheit, Wahrheits- und Auflösungsgrade.Geert Keil - 2010 - In Martin Grajner & Adolf Rami (eds.), Wahrheit, Bedeutung, Existenz. Ontos. pp. 57-86.
    1. Semantische Vagheit 2. Bivalenz und Wahrheitsgrade 3. Zutreffen und Wahrsein 4. Mehrwertigkeit und andere Holzwege 5. Wahrheit und Genauigkeit: Einige Beispiele 6. Die Platon-Herberger-Kontroverse 7. Der Parameter der Auflösung 8. Auflösungsgrade statt Wahrheitsgrade 9. Ein der Annahme von Wahrheitsgraden komplementärer Fehler 10. Wahrheitsrelativismus, Kontextualismus, Supervaluationismus 11. Noch einmal: Wahrheit und Vagheit -/- .
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  35. Fuzzy Epistemicism.John MacFarlane - 2010 - In Richard Dietz & Sebastiano Moruzzi (eds.), Cuts and Clouds. Vaguenesss, its Nature and its Logic. Oxford University Press.
    It is taken for granted in much of the literature on vagueness that semantic and epistemic approaches to vagueness are fundamentally at odds. If we can analyze borderline cases and the sorites paradox in terms of degrees of truth, then we don’t need an epistemic explanation. Conversely, if an epistemic explanation suffices, then there is no reason to depart from the familiar simplicity of classical bivalent semantics. I question this assumption, showing that there is an intelligible motivation for adopting a (...)
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  36. Review of Vagueness and Degrees of Truth, by Nicholas J. Smith. [REVIEW]David Ripley - 2010 - Analysis 70 (1):188-190.
    (No abstract is available for this citation).
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  37. Taking Degrees of Truth Seriously.Josep Maria Font - 2009 - Studia Logica 91 (3):383-406.
    This is a contribution to the discussion on the role of truth degrees in manyvalued logics from the perspective of abstract algebraic logic. It starts with some thoughts on the so-called Suszko’s Thesis (that every logic is two-valued) and on the conception of semantics that underlies it, which includes the truth-preserving notion of consequence. The alternative usage of truth values in order to define logics that preserve degrees of truth is presented and discussed. Some recent works studying these in the (...)
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  38. On Vagueness, Truth Values and Fuzzy Logics.Petr Hájek - 2009 - Studia Logica 91 (3):367-382.
    Some aspects of vagueness as presented in Shapiro’s book Vagueness in Context [23] are analyzed from the point of fuzzy logic. Presented are some generalizations of Shapiro’s formal apparatus.
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  39. Degree of Belief is Expected Truth Value.Nicholas J. J. Smith - 2009 - In Sebastiano Moruzzi & Richard Dietz (eds.), Cuts and Clouds. Vaguenesss, its Nature and its Logic. Oxford University Press. pp. 491--506.
    A number of authors have noted that vagueness engenders degrees of belief, but that these degrees of belief do not behave like subjective probabilities. So should we countenance two different kinds of degree of belief: the kind arising from vagueness, and the familiar kind arising from uncertainty, which obey the laws of probability? I argue that we cannot coherently countenance two different kinds of degree of belief. Instead, I present a framework in which there is a single notion of degree (...)
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  40. Vagueness and Degrees of Truth.Nicholas J. J. Smith - 2008 - Oxford, England: Oxford University Press.
    In VAGUENESS AND DEGREES OF TRUTH, Nicholas Smith develops a new theory of vagueness: fuzzy plurivaluationism. -/- A predicate is said to be VAGUE if there is no sharply defined boundary between the things to which it applies and the things to which it does not apply. For example, 'heavy' is vague in a way that 'weighs over 20 kilograms' is not. A great many predicates -- both in everyday talk, and in a wide array of theoretical vocabularies, from law (...)
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  41. The Things We (Sorta Kinda) Believe. [REVIEW]John Macfarlane - 2006 - Philosophy and Phenomenological Research 73 (1):218–224.
    On Schiffer’s new view, propositions are easy to come by. Any that-clause can be counted on to express one. Thus, trivially, there are vague propositions, conditional propositions, moral and aesthetic propositions. And where propositions go, truth and falsity follow: barring paradoxical cases, Schiffer accepts instances of the schemata “the proposition that p is true iff p” and “the proposition that p is false iff not-p.” What isn’t easy to find, Schiffer thinks, is determinate truth. By the end of the book, (...)
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  42. Fuzziness and the Sorites Paradox.Marcelo Vasconez - 2006 - Dissertation, Catholic University of Louvain
    The dissertation has two parts, each dealing with a problem, namely: 1) What is the most adequate account of fuzziness -the so-called phenomenon of vagueness?, and 2) what is the most plausible solution to the sorites, or heap paradox? I will try to show that fuzzy properties are those which are gradual, amenable to be possessed in a greater or smaller extent. Acknowledgement of degrees in the instantiation of a property allows for a gradual transition from one opposite to the (...)
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  43. 4. Contradictorial Gradualism Vs. Discontinuism: Two Views On Fuzziness And The Transition Problem.Marcelo VÁsconez - 2006 - Logique Et Analyse 49 (195).
    The dissertation has two parts, each dealing with a problem, namely: 1) What is the most adequate account of fuzziness -the so-called phenomenon of vagueness?, and 2) what is the most plausible solution to the sorites, or heap paradox? I will try to show that fuzzy properties are those which are gradual, amenable to be possessed in a greater or smaller extent. Acknowledgement of degrees in the instantiation of a property allows for a gradual transition from one opposite to the (...)
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  44. Vagueness as Closeness.Nicholas J. J. Smith - 2005 - Australasian Journal of Philosophy 83 (2):157 – 183.
    This paper presents and defends a definition of vagueness, compares it favourably with alternative definitions, and draws out some consequences of accepting this definition for the project of offering a substantive theory of vagueness. The definition is roughly this: a predicate 'F' is vague just in case for any objects a and b, if a and b are very close in respects relevant to the possession of F, then 'Fa' and 'Fb' are very close in respect of truth. The definition (...)
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  45. True, Truer, Truest.Brian Weatherson - 2005 - Philosophical Studies 123 (1-2):47-70.
    What the world needs now is another theory of vagueness. Not because the old theories are useless. Quite the contrary, the old theories provide many of the materials we need to construct the truest theory of vagueness ever seen. The theory shall be similar in motivation to supervaluationism, but more akin to many-valued theories in conceptualisation. What I take from the many-valued theories is the idea that some sentences can be truer than others. But I say very different things to (...)
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  46. Vagueness and Blurry Sets.Nicholas J. J. Smith - 2004 - Journal of Philosophical Logic 33 (2):165-235.
    This paper presents a new theory of vagueness, which is designed to retain the virtues of the fuzzy theory, while avoiding the problem of higher-order vagueness. The theory presented here accommodates the idea that for any statement S₁ to the effect that 'Bob is bald' is x true, for x in [0, 1], there should be a further statement S₂ which tells us how true S₁ is, and so on - that is, it accommodates higher-order vagueness without resorting to the (...)
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  47. Unsolved Problems with Numbers: Reply to Smith.Rosanna Keefe - 2003 - Mind 112 (446):291-293.
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  48. Vagueness by Numbers? No Worries.Nicholas J. J. Smith - 2003 - Mind 112 (446):283-290.
    Rosanna Keefe (`Vagueness by Numbers' MIND 107 1998 565--79) argues that theories of vagueness based upon fuzzy logic and set theory rest on a confusion: once we have assigned a number to an object to represent (for example) its *height*, there is no distinct purpose left to be served by assigning a number to the object to represent its *degree of tallness*; she claims that ``any numbers assigned in an attempt to capture the vagueness of `tall' do no more than (...)
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  49. Cut-Offs and Their Neighbors.Achille C. Varzi - 2003 - In Jc Beall (ed.), Liars and Heaps: New Essays on Paradox. Clarendon Press. pp. 24–38.
    In ‘Towards a Solution to the Sorites Paradox’, Graham Priest gives us a new account of the sorites based on fuzzy logic. The novelty lies in the suggestion that truth-value assignments should themselves be treated as fuzzy objects, i.e., objects about which we can make fuzzy identity statements. I argue that Priest’s solution does not have the explanatory force that Priest advocates. That is, it does not explain why we find the existence of a cut-off point counter-intuitive. I also argue (...)
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  50. Vagueness and Mathematical Precision.Roy T. Cook - 2002 - Mind 111 (442):225-247.
    One of the main reasons for providing formal semantics for languages is that the mathematical precision afforded by such semantics allows us to study and manipulate the formalization much more easily than if we were to study the relevant natural languages directly. Michael Tye and R. M. Sainsbury have argued that traditional set-theoretic semantics for vague languages are all but useless, however, since this mathematical precision eliminates the very phenomenon (vagueness) that we are trying to capture. Here we meet this (...)
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