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  1. W. R. Abbott (1983). A Note on Grim's Sorites Argument. Analysis 43 (4):161 - 164.
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  2. Mark Addis (1995). Surveyability and the Sorites Paradox. Philosophia Mathematica 3 (2):157-165.
    Some issues raised by the notion of surveyability and how it is represented mathematically are explored. Wright considers the sense in which the positive integers are surveyable and suggests that their structure will be a weakly finite, but weakly infinite, totality. One way to expose the incoherence of this account is by applying Wittgenstein's distinction between intensional and extensional to it. Criticism of the idea of a surveyable proof shows the notion's lack of clarity. It is suggested that this concept (...)
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  3. J. C. Beall (ed.) (2003). Liars and Heaps: New Essays on Paradox. Oxford University Press.
    Semantic and soritical paradoxes challenge entrenched, fundamental principles about language - principles about truth, denotation, quantification, and, among others, 'tolerance'. Study of the paradoxes helps us determine which logical principles are correct. So it is that they serve not only as a topic of philosophical inquiry but also as a constraint on such inquiry: they often dictate the semantic and logical limits of discourse in general. Sixteen specially written essays by leading figures in the field offer new thoughts and arguments (...)
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  4. JC Beall & Mark Colyvan (2001). Heaps of Gluts and Hyde-Ing the Sorites. Mind 110 (438):401--408.
    JSTOR is a not-for-profit organization founded in 1995 to build trusted digital archives for scholarship. We work with the scholarly community to preserve their work and the materials they rely upon, and to build a common research platform that promotes the discovery and use of these resources. For more information about JSTOR, please contact support@jstor.org.
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  5. Hanoch Ben-Yami (2010). A Wittgensteinian Solution to the Sorites. Philosophical Investigations 33 (3):229-244.
    I develop a solution to the Sorites Paradox, according to which a concatenation of valid arguments need not itself be valid. I specify which chains of valid arguments are those that do not preserve validity: those that pass the vague boundary between cases where the relevant concept applies and cases where that concept does not apply. I also develop various criticisms of this solution and show why they fail; basically, they all involve a petitio at some stage. I criticise the (...)
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  6. Francesco Berto, Edwin Mares, Koji Tanaka & Francesco Paoli (eds.) (2013). Paraconsistency: Logic and Applications. Springer.
    A logic is called 'paraconsistent' if it rejects the rule called 'ex contradictione quodlibet', according to which any conclusion follows from inconsistent premises. While logicians have proposed many technically developed paraconsistent logical systems and contemporary philosophers like Graham Priest have advanced the view that some contradictions can be true, and advocated a paraconsistent logic to deal with them, until recent times these systems have been little understood by philosophers. This book presents a comprehensive overview on paraconsistent logical systems to change (...)
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  7. George Boolos (1991). Zooming Down the Slippery Slope. Noûs 25 (5):695-706.
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  8. 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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  9. John A. Burgess (1990). Phenomenal Qualities and the Nontransitivity of Matching. Australasian Journal of Philosophy 68 (2):206-220.
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  10. Richmond Campbell (1974). The Sorites Paradox. Philosophical Studies 26 (3-4):175 - 191.
    The premises that a four foot man is short and that a man one tenth of an inch taller than a short man is also short entail by universal instantiation and "modus ponens" that a seven foot man is short. The negation of the second premise seems to entail there are virtually no borderline cases of short men, While to deny the second premise and its negation conflicts with the principle of bivalence, If not excluded middle. But the paradox can (...)
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  11. James Cargile (1993). Vagueness. An Investigation Into Natural Languages and the Sorites Paradox. Philosophical Books 34 (1):22-24.
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  12. James Cargile (1969). The Sorites Paradox. British Journal for the Philosophy of Science 20 (3):193-202.
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  13. Michael Clark (1987). The Truth About Heaps. Analysis 47 (4):177 - 179.
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  14. Pablo Cobreros, Paul Egré, David Ripley & Robert Rooij (2012). Tolerance and Mixed Consequence in the S'valuationist Setting. Studia Logica 100 (4):855-877.
    In a previous paper (see ‘Tolerant, Classical, Strict’, henceforth TCS) we investigated a semantic framework to deal with the idea that vague predicates are tolerant, namely that small changes do not affect the applicability of a vague predicate even if large changes do. Our approach there rests on two main ideas. First, given a classical extension of a predicate, we can define a strict and a tolerant extension depending on an indifference relation associated to that predicate. Second, we can use (...)
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  15. Pablo Cobreros, Paul Egré, David Ripley & Robert van Rooij (forthcoming). Vagueness, Truth and Permissive Consequence. In T. Achourioti, H. Galinon, K. Fujimoto & J. Martínez-Fernández (eds.), Volume on Truth. Springer.
    We say that a sentence A is a permissive consequence of a set of premises Gamma whenever, if all the premises of Gamma hold up to some standard, then A holds to some weaker stan- dard. In this paper, we focus on a three-valued version of this notion, which we call strict-to-tolerant consequence, and discuss its fruitfulness toward a uni ed treatment of the paradoxes of vagueness and self-referential truth. For vagueness, st-consequence supports the principle of tolerance; for truth, it (...)
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  16. Mark Colyvan, Vagueness and Truth.
    In philosophy of logic and elsewhere, it is generally thought that similar problems should be solved by similar means. This advice is sometimes elevated to the status of a principle: the principle of uniform solution. In this paper I will explore the question of what counts as a similar problem and consider reasons for subscribing to the principle of uniform solution.
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  17. Mark Colyvan (2010). A Topological Sorites. Journal of Philosophy 107 (6):311-325.
    This paper considers a generalisation of the sorites paradox, in which only topological notions are employed. We argue that by increasing the level of abstraction in this way, we see the sorites paradox in a new, more revealing light—a light that forces attention on cut-off points of vague predicates. The generalised sorites paradox presented here also gives rise to a new, more tractable definition of vagueness.
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  18. John R. Cook (2005). Review of Doris Olin's Paradox. [REVIEW] Philosophy in Review (6):422-424.
    Doris Olin's Paradox is a very helpful book for those who want to be introduced to the philosophical treatment of paradoxes, or for those who already have knowledge of the general area and would like to have a helpful resource book.
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  19. R. Deas (1989). Sorenson's Sorites. Analysis 49 (1):26--31.
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  20. Robert Deas (1989). Sorensen's Sorites. Analysis 49 (1):26 - 31.
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  21. Richard DeWitt (1992). Remarks on the Current Status of the Sorites Paradox. Journal of Philosophical Research 17 (1):93.
    The past twenty or so years have seen the sorites paradox receive a good deal of philosophical air-time. Yet, in what is surely a sign of a good puzzle, no consensus has emerged. It is perhaps a good time to stop and take stock of the current status of the sorites paradox. My main contention is that the proposals offered to date as ways of blocking the paradox are seriously deficient, and hence there is, at present, no acceptable solution to (...)
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  22. Ehtibar N. Dzhafarov & Damir D. Dzhafarov (2010). Sorites Without Vagueness II: Comparative Sorites. Theoria 76 (1):25-53.
    We develop a mathematical theory for comparative sorites, considered in terms of a system mapping pairs of stimuli into a binary response characteristic whose values supervene on stimulus pairs and are interpretable as the complementary relations 'are the same' and 'are not the same' (overall or in some respect). Comparative sorites is about hypothetical sequences of stimuli in which every two successive elements are mapped into the relation 'are the same', while the pair comprised of the first and the last (...)
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  23. Ehtibar N. Dzhafarov & Damir D. Dzhafarov (2010). Sorites Without Vagueness I: Classificatory Sorites. Theoria 76 (1):4-24.
    An abstract mathematical theory is presented for a common variety of soritical arguments, treated here in terms of responses of a system, say, a biological organism, a gadget, or a set of normative linguistic rules, to stimuli. Any characteristic of the system's responses which supervenes on stimuli is called a stimulus effect upon the system. Classificatory sorites is about the identity of or difference between the effects of stimuli that differ 'only microscopically'. We formulate the classificatory sorites on arguably the (...)
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  24. Theodore J. Everett (2000). A Simple Logic for Comparisons and Vagueness. Synthese 123 (2):263-278.
    I provide an intuitive, semantic account of a new logic forcomparisons (CL), in which atomic statements are assigned both aclassical truth-value and a ``how much'''' value or extension in the range [0, 1]. The truth-value of each comparison is determinedby the extensions of its component sentences; the truth-value ofeach atomic depends on whether its extension matches a separatestandard for its predicate; everything else is computed classically. CL is less radical than Casari''s comparative logics, in that it does not allow for (...)
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  25. Delia Graff Fara (2001). Phenomenal Continua and the Sorites. Mind 110 (440):905-935.
    I argue that, contrary to widespread philosophical opinion, phenomenal indiscriminability is transitive. For if it were not transitive, we would be precluded from accepting the truisms that if two things look the same then the way they look is the same and that if two things look the same then if one looks red, so does the other. Nevertheless, it has seemed obvious to many philosophers (e.g. Goodman, Armstrong and Dummett) that phenomenal indiscriminability is not transitive; and, moreover, that this (...)
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  26. Paul Franceschi, On the Circularity in the Sorites Paradox.
    I begin by highlighting the importance of the step size in the induction step of the sorites paradox. A careful analysis reveals that the step size can be characterised as a proper instance of the concept very small . After having accurately described the structure of sorites-susceptible predicates, I argue that the structure of the induction step in the Sorites Paradox is inherently circular. This circularity emerges in the structure of Wang's paradox and also of the classical variations of the (...)
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  27. B. Garrett (2012). Response to Goldstein. Analysis 72 (4):742-744.
    In ‘The Sorites is disguised nonsense’ Analysis (2012) 77: 61–5 L Goldstein attempts to show that some of the conditionals in any Sorites argument are nonsensical, and hence no Sorites argument can be sound. I give four reasons why this is not the case.
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  28. Laurence Goldstein (2000). How to Boil a Live Frog. Analysis 60 (2):170–178.
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  29. Laurence Goldstein (1988). The Sorites as a Lesson in Semantics. Mind 97 (387):447-455.
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  30. J. M. Goodenough (1996). Parfit and the Sorites Paradox. Philosophical Studies 2 (2):113-20.
    This paper aims to establish that Sorites reasoning, a fundamental part of Parfit's work, is more destructive that he intends. I establish the form that Parfit's arguments take and then substitute premises whose acceptability to Parfit I show. The new argument demonstrates an eliminativism or immaterialism concerning persons which Parfit must find repugnant.
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  31. Patrick Grim (2005). The Buried Quantifier: An Account of Vagueness and the Sorites. Analysis 65 (286):95–104.
  32. Patrick Grim (1984). Taking Sorites Arguments Seriously: Some Hidden Costs. Philosophia 14 (3-4):251-272.
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  33. Patrick Grim (1983). Is This a Swizzle Stick Which I See Before Me? Analysis 43 (4):164 - 166.
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  34. Patrick Grim (1982). What Won't Escape Sorites Arguments. Analysis 42 (1):38 - 43.
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  35. Oswald Hanfling (2001). What is Wrong with Sorites Arguments? Analysis 61 (1):29–35.
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  36. C. L. Hardin (1988). Phenomenal Colors and Sorites. Noûs 22 (June):213-34.
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  37. Benj Hellie (2005). Noise and Perceptual Indiscriminability. Mind 114 (455):481-508.
    Perception represents colours inexactly. This inexactness results from phenomenally manifest noise, and results in apparent violations of the transitivity of perceptual indiscriminability. Whether these violations are genuine depends on what is meant by 'transitivity of perceptual indiscriminability'.
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  38. Jaakko Hintikka, What the Bald Man Can Tell Us.
    By speaking of the bald man, I am of course referring to the most clear-cut of the paradoxes of vagueness, the sorites paradox. Or, strictly speaking, I am referring to one of the dramatizations of this paradox. This case is nevertheless fully representative of the general issues involved. (For the sorites paradox in general, see e.g. Keefe and Smith 1987 or Sainsbury 1995, ch.2.) The allegedly paradoxical argument is well known. It might be formulated as follows.
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  39. Terence Horgan (1994). Robust Vagueness and the Forced-March Sorites Paradox. Philosophical Perspectives 8 (Logic and Language):159-188.
    I distinguish two broad approaches to vagueness that I call "robust" and "wimpy". Wimpy construals explain vagueness as robust (i.e., does not manifest arbitrary precision); that standard approaches to vagueness, like supervaluationism or appeals to degrees of truth, wrongly treat vagueness as wimpy; that vagueness harbors an underlying logical incoherence; that vagueness in the world is therefore impossible; and that the kind of logical incoherence nascent in vague terms and concepts is benign rather than malignant. I describe some implications for (...)
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  40. Terry Horgan (2000). Facing Up to the Sorites Paradox. The Proceedings of the Twentieth World Congress of Philosophy 6:99-111.
    The ancient sorites paradox has important implications for metaphysics, for logic, and for semantics. Metaphysically, the paradox can be harnessed to produce a powerful argument for the claim that there cannot be vague objects or vague properties. With respect to logic, the paradox forces a choice between the highly counterintuitive ‘epistemic’ account of vagueness and the rejection of classical two-valued logic. Regarding semantics, nonclassical approaches to the logic of vagueness lead naturally to the idea that truth, for vague discourse, is (...)
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  41. Colin Howson (2009). Sorites is No Threat to Modus Ponens: A Reply to Kochan. International Studies in the Philosophy of Science 23 (2):209-212.
    A recent article by Jeff Kochan contains a discussion of modus ponens that among other thing alleges that the paradox of the heap is a counterexample to it. In this note I show that it is the conditional major premise of a modus ponens inference, rather than the rule itself, that is impugned. This premise is the contrapositive of the inductive step in the principle of mathematical induction, confirming the widely accepted view that it is the vagueness of natural language (...)
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  42. Gerald Hull, Vagueness Without Indefiniteness.
    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 (...)
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  43. Dominic Hyde, Sorites Paradox. Stanford Encyclopedia of Philosophy.
    The sorites paradox is the name given to a class of paradoxical arguments, also known as little by little arguments, which arise as a result of the indeterminacy surrounding limits of application of the predicates involved. For example, the concept of a heap appears to lack sharp boundaries and, as a consequence of the subsequent indeterminacy surrounding the extension of the predicate ‘is a heap’, no one grain of wheat can be identified as making the difference between being a heap (...)
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  44. Rosanna Keefe (2011). Phenomenal Sorites Paradoxes and Looking the Same. Dialectica 65 (3):327-344.
    Taking a series of colour patches, starting with one that clearly looks red, and making each so similar in colour to the previous one that it looks the same as it, we appear to be able to show that a yellow patch looks red. I ask whether phenomenal sorites paradoxes, such as this, are subject to a unique kind of solution that is unavailable in relation to other sorites paradoxes. I argue that they do not need such a solution, nor (...)
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  45. Lee F. Kerckhove & Sara Waller (1998). Fetal Personhood and the Sorites Paradox. Journal of Value Inquiry 32 (2):175-189.
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  46. John L. King (1979). Bivalence and the Sorites Paradox. American Philosophical Quarterly 16 (1):17 - 25.
    Putative resolutions of the sorites paradox in which the major premise is declared false or illegitimate, Including max black's treatment in terms of the alleged illegitimacy of vague attributions to borderline cases, Are rejected on semantical grounds. The resort to a non-Bivalent logic of representational "accuracy" with a continuum of accuracy values is shown to resolve the paradox, And the identification of accuracy values as truth values is defended as compatible with the central insight of the correspondence theory of truth (...)
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  47. Jeff Kochan (2009). The Exception Makes the Rule: Reply to Howson. International Studies in the Philosophy of Science 23 (2):213-216.
    Colin Howson argues that (1) my sociologistic reliabilism sheds no light on the objectivity of epistemic content, and that (2) sorites does not threaten the reliability of modus ponens . I reply that argument (1) misrepresents my position, and that argument (2) is beside the point.
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  48. R. C. Koons (1994). A New Solution to the Sorites Problem. Mind 103 (412):439-450.
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  49. Leib Litman & Mark Zelcer (2013). A Cognitive Neuroscience, Dual-Systems Approach to the Sorites Paradox. Journal of Experimental and Theoretical Artificial Intelligence 25 (3):355-366.
    Typical approaches to resolving the sorites paradox attempt to show, in one way or another, that the sorites argument is not paradoxical after all. However, if one can show that the sorites is not really paradoxical, the task remains of explaining why it appears to be a paradox. Our approach begins by addressing the appearance of paradox and then explores what this means for the paradox itself. We examine the sorites from the perspective of the various brain systems that are (...)
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  50. Kirk Ludwig (2002). Vagueness And The Sorites Paradox. Noûs 36 (s16):419-461.
    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. (...)
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