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  1. Jiri Benovsky (2014). Vague Objects with Sharp Boundaries. Ratio 27 (1).
    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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  2. Max Black (1970). Margins of Precision. Ithaca [N.Y.]Cornell University Press.
  3. Max Black (1962). Models and Metaphors. Ithaca, N.Y.,Cornell University Press.
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  4. Max Black (1949/1981). Language and Philosophy: Studies in Method. Greenwood Press.
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  5. Max Black (1937). Vagueness. An Exercise in Logical Analysis. Philosophy of Science 4 (4):427-455.
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  6. John Collins (2010). Vagueness and Degrees of Truth – Nicholas J.J. Smith. Philosophical Quarterly 60 (239):422-424.
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  7. Roy T. Cook (2010). Vagueness and Degrees of Truth – By Nicholas J. J. Smith. Theoria 76 (4):380-384.
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  8. Roy T. Cook (2002). Vagueness and Mathematical Precision. 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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  9. B. Jack Copeland (1997). Vague Identity and Fuzzy Logic. Journal of Philosophy 94 (10):514-534.
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  10. William A. Dembski, Random Predicate Logic I: A Probabilistic Approach to Vagueness.
    Predicates are supposed to slice reality neatly in two halves, one for which the predicate holds, the other for which it fails. Yet far from being razors, predicates tend to be dull knives that mangle reality. If reality is a tomato and predicates are knives, then when these knives divide the tomato, plenty of mush remains unaccounted for. Of course some knives are sharper than others, just as some predicates are less vague than others. “x is water” is certainly sharper (...)
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  11. Dennis Earl (2010). Vague Analysis. 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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  12. Dorothy Edgington (1997). Vagueness by Degrees. In Rosanna Keefe & Peter Smith (eds.), Vagueness: A Reader. MIT Press.
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  13. Dorothy Edgington (1995). The Logic of Uncertainty. Critica 27 (81):27 - 54.
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  14. Dorothy Edgington (1992). Validity, Uncertainty and Vagueness. Analysis 52 (4):193 - 204.
  15. Paul Egré (2011). Vagueness and Degrees of Truth. 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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  16. Rayme E. Engel (1989). On Degrees. Journal of Philosophy 86 (1):23-37.
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  17. Christian Fermüller (2010). Review: Vagueness and Degrees of Truth. [REVIEW] 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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  18. Hartry Field (2000). Indeterminacy, Degree of Belief, and Excluded Middle. Noûs 34 (1):1–30.
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  19. Josep Maria Font (2009). Taking Degrees of Truth Seriously. 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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  20. Graeme Forbes (1983). Thisness and Vagueness. Synthese 54 (2):235-259.
    This paper is about two puzzles, or two versions of a single puzzle, which deserve to be called paradoxes, and develops some apparatus in terms of which the apparently conflicting principles which generate the puzzles can be rendered consistent. However, the apparatus itself is somewhat controversial: the puzzles are modal ones, and the resolution to be advocated requires the adoption of a counterpart theoretic semantics of essentially the kind proposed by David Lewis, which in turn requires qualified rejection of certain (...)
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  21. Gy Fuhrmann (1991). Note on the Integration of Prototype Theory and Fuzzy-Set Theory. Synthese 86 (1):1 - 27.
    Many criticisms of prototype theory and/or fuzzy-set theory are based on the assumption that category representativeness (or typicality) is identical with fuzzy membership. These criticisms also assume that conceptual combination and logical rules (all in the Aristotelian sense) are the appropriate criteria for the adequacy of the above “fuzzy typicality”. The present paper discusses these assumptions following the line of their most explicit and most influential expression by Osheron and Smith (1981). Several arguments are made against the above identification, the (...)
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  22. Gy Fuhrmann (1988). Fuzziness of Concepts and Concepts of Fuzziness. Synthese 75 (3):349 - 372.
    It has been a vexing question in recent years whether concepts are fuzzy. In this paper several views on the fuzziness of concepts are pointed out to have stemmed from dubious concepts of fuzziness. The underlying notions of the roles feasibly played byprototype, set, andprobability in modeling concepts strongly suggest that the controversy originates from a vague relation between intuitive and mathematical ideas in the cognitive sciences. It is argued that the application of fuzzy sets cannot resolve this vagueness since (...)
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  23. Gy Fuhrmann (1988). “Prototypes” and “Fuzziness” in the Logic of Concepts. Synthese 75 (3):317 - 347.
    Prototypes and fuzziness are regarded in this paper as fundamental phenomena in the inherent logic of concepts whose relationship, however, has not been sufficiently clarified. Therefore, modifications are proposed in the definition of both. Prototypes are defined as the elements possessing maximal degree of membership in the given category such thatthis membership has maximal cognitive efficiency in representing theelement. A modified fuzzy set (m-fuzzy set) is defined on aclass (possibly self-contradictory collection) such that its core (the collection of elements with (...)
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  24. 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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  25. J. A. Goguen (1969). The Logic of Inexact Concepts. Synthese 19 (3-4):325-373.
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  26. Patrick Grim, A Fuzzy Fairly Happy Face.
    happy face, in my view, is this. It starts with two simple claims about our language that I think just have to be right. On the basis of essentially those two claims alone it offers what I think is a very plausible account of both (1) what really is wrong with the argument and (2) why there doesn't seem to be anything wrong with the argument.
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  27. Susan Haack (1996). Deviant Logic, Fuzzy Logic: Beyond the Formalism. University of Chicago Press.
    Initially proposed as rivals of classical logic, alternative logics have become increasingly important in areas such as computer science and artificial intelligence. Fuzzy logic, in particular, has motivated major technological developments in recent years. Susan Haack's Deviant Logic provided the first extended examination of the philosophical consequences of alternative logics. In this new volume, Haack includes the complete text of Deviant Logic , as well as five additional papers that expand and update it. Two of these essays critique fuzzy logic, (...)
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  28. Susan Haack (1974). Deviant Logic: Some Philosophical Issues. Cambridge University Press.
    PART ONE I 'Alternative' in 'Alternative logic There are many systems of logic — many-valued systems and modal systems for instance - which are non-standard ...
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  29. Petr Hájek (2009). On Vagueness, Truth Values and Fuzzy Logics. 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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  30. Rosanna Keefe (2012). Modelling Vagueness: What Can We Ignore? 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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  31. Rosanna Keefe (2003). Unsolved Problems with Numbers: Reply to Smith. Mind 112 (446):291-293.
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  32. Rosanna Keefe (1998). Vagueness by Numbers. Mind 107 (427):565-579.
    Degree theories of vagueness build on the observation that vague predicates such as 'tall' and 'red' come in degrees. They employ an infinite-valued logic, where the truth values correspond to degrees of truth and are typically represented by the real numbers in the interval [0,1]. In this paper, the success with which the numerical assignments of such theories can capture the phenomenon of vagueness is assessed by drawing an analogy with the measurement of various physical quantities using real numbers. I (...)
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  33. George Lakoff (1973). Hedges: A Study in Meaning Criteria and the Logic of Fuzzy Concepts. [REVIEW] Journal of Philosophical Logic 2 (4):458 - 508.
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  34. John MacFarlane (2010). Fuzzy Epistemicism. 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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  35. Kenton F. Machina (1976). Truth, Belief, and Vagueness. Journal of Philosophical Logic 5 (1):47-78.
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  36. Kenton F. Machina (1972). Vague Predicates. American Philosophical Quarterly 9 (3):225 - 233.
  37. Charles Grady Morgan & Francis Jeffry Pelletier (1977). Some Notes Concerning Fuzzy Logics. Linguistics and Philosophy 1 (1):79 - 97.
    Fuzzy logics are systems of logic with infinitely many truth values. Such logics have been claimed to have an extremely wide range of applications in linguistics, computer technology, psychology, etc. In this note, we canvass the known results concerning infinitely many valued logics; make some suggestions for alterations of the known systems in order to accommodate what modern devotees of fuzzy logic claim to desire; and we prove some theorems to the effect that there can be no fuzzy logic which (...)
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  38. Daniel N. Osherson & Edward E. Smith (1981). On the Adequacy of Prototype Theory as a Theory of Concepts. Cognition 9 (1):35-58.
  39. Josh Parsons, Fuzzy Mereology.
    This paper began life as a short section of a more general paper about non-classical mereologies. In that paper I had a mereological theory that I wanted to show could be applied to all sorts of different metaphysical positions — notably, to those positions that believe in mereological vagueness in re — in “vague individuals”. To do that I felt I first had to dispatch the leading rival theory of vague individuals, which is due to Peter van Inwa-gen, and holds (...)
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  40. Christopher Peacocke (1981). Are Vague Predicates Incoherent? Synthese 46 (1):121-141.
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  41. George Rea (1989). Degrees of Truth Versus Intuitionism. Analysis 49 (1):31 - 32.
    The purpose of this article is to compare the theory that there are degrees of truth with putnam's intuitionist theory as rival solutions to the sorites paradox. I argue that intuitionist logic lacks explanatory support and is self-Defeating. The degree theory on the other hand offers an illuminating explanation of the sorites fallacy.
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  42. David Ripley (2010). Review of Vagueness and Degrees of Truth, by Nicholas J. Smith. [REVIEW] Analysis 70 (1):188-190.
    (No abstract is available for this citation).
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  43. M. Sainsbury & T. Williamson (1995). Sorites. In B. Hale & C. Wright (eds.), Blackwell Companion to the Philosophy of Language. Blackwell.
  44. R. M. Sainsbury (1988). Tolerating Vagueness. Proceedings of the Aristotelian Society 89:33 - 48.
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  45. David H. Sanford (2002). Vague Numbers. Acta Analytica 17 (1):63-73.
    If there are vague numbers, it would be easier to use numbers as semantic values in a treatment of vagueness while avoiding precise cut-off points. When we assign a particular statement a range of values (less than 1 and greater than 0) there is no precise sharp cut-off point that locates the greatest lower bound or the least upper bound of the interval, I should like to say. Is this possible? “Vague Numbers” stands for awareness of the problem. I do (...)
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  46. David H. Sanford (1975). Borderline Logic. American Philosophical Quarterly 12 (1):29-39.
    To accommodate vague statements and predicates, I propose an infinite-valued, non-truth-functional interpretation of logic on which the tautologies are exactly the tautologies of classical two-valued logic. iI introduce a determinacy operator, analogous to the necessity operator in alethic modal logic, to allow the definition of first-order and higher-order borderline cases. On the interpretation proposed for determinacy, every statement corresponding to a theorem of modal system T is a logical truth, and I conjecture that every logical truth on the interpretation corresponds (...)
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  47. Uli Sauerland, Vagueness in Language: The Case Against Fuzzy Logic Revisited.
    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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  48. Stephen P. Schwartz (1990). Intuitionism Versus Degrees of Truth. Analysis 50 (1):43 - 47.
    Putnam's intuitionist proposal for a logic of vague terms is defended. It is argued that both classical logic and the degrees of truth approach are committed to treating vague terms as having hidden precise borderlines. This is a crucial failing in a logic of vagueness. Intuitionism, because of the nature of intuitionist negation, avoids this failing.
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  49. La Verne Shelton (1983). On the Ramification of Inexactness. Philosophy Research Archives 9:347-367.
    I argue that though a satisfactory semantics for the logic of inexact reference may assign no truth value to some statements, it should not assign truth (or falsity) of various degrees. Well-formed assertions are simply true or not. Inexactness does not “ramify.” I distinguish inexactness from other sorts of vagueness, including nonspecificity. I show that arguments from (i) use of quantifiers, (ii) the existence of properties which can be construed as a series of properties (as, e. g., red can be (...)
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  50. Peter Simons (1995). Multivalence and Vagueness: A Reply to Copeland. Proceedings of the Aristotelian Society 95:201 - 209.
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