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  1. K. Akiba (1999). On Super- and Subvaluationism: A Classicist's Reply to Hyde. Mind 108 (432):727-732.
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  2. Nicholas Asher, Josh Dever & Chris Pappas (2009). Supervaluations Debugged. Mind 118 (472):901-933.
    Supervaluational accounts of vagueness have come under assault from Timothy Williamson for failing to provide either a sufficiently classical logic or a disquotational notion of truth, and from Crispin Wright and others for incorporating a notion of higher-order vagueness, via the determinacy operator, which leads to contradiction when combined with intuitively appealing ‘gap principles’. We argue that these criticisms of supervaluation theory depend on giving supertruth an unnecessarily central role in that theory as the sole notion of truth, rather than (...)
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  3. Joachim Ballweg (1983). Vagueness of Context-Dependance? Supervaluation Revisited in a Semantics Based on Scales. In Thomas T. Ballmer & Manfred Pinkal (eds.), Approaching Vagueness. North-Holland
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  4. JC Beall (ed.) (2004). Liars and Heaps: New Essays on the Semantics of Paradox. Oxford University Press.
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  5. Nuel Belnap (2009). Truth Values, Neither-True-nor-False, and Supervaluations. Studia Logica 91 (3):305 - 334.
    The first section (§1) of this essay defends reliance on truth values against those who, on nominalistic grounds, would uniformly substitute a truth predicate. I rehearse some practical, Carnapian advantages of working with truth values in logic. In the second section (§2), after introducing the key idea of auxiliary parameters (§2.1), I look at several cases in which logics involve, as part of their semantics, an extra auxiliary parameter to which truth is relativized, a parameter that caters to special kinds (...)
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  6. Jiri Benovsky (2014). Vague Objects with Sharp Boundaries. 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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  7. Andrea Borghini & Achille C. Varzi (2006). Event Location and Vagueness. Philosophical Studies 128 (2):313-336.
    Most event-referring expressions are vague; it is utterly difficult, if not impossible, to specify the exact spatiotemporal location of an event from the words that we use to refer to it. We argue that in spite of certain prima facie obstacles, such vagueness can be given a purely semantic (broadly supervaluational) account.
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  8. Joshua D. K. Brown & James W. Garson (forthcoming). A New Semantics for Vagueness. Erkenntnis:1-21.
    Intuitively, vagueness involves some sort of indeterminacy: if Plato is a borderline case of baldness, then there is no fact of the matter about whether or not he’s bald—he’s neither bald nor not bald. The leading formal treatments of such indeterminacy—three valued logic, supervaluationism, etc.—either fail to validate the classical theorems, or require that various classically valid inference rules be restricted. Here we show how a fully classical, yet indeterminist account of vagueness can be given within natural semantics, an alternative (...)
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  9. Andrea Cantini (1990). A Theory of Formal Truth Arithmetically Equivalent to ID. Journal of Symbolic Logic 55 (1):244 - 259.
    We present a theory VF of partial truth over Peano arithmetic and we prove that VF and ID 1 have the same arithmetical content. The semantics of VF is inspired by van Fraassen's notion of supervaluation.
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  10. Pablo Cobreros (2013). Vagueness: Subvaluationism. Philosophy Compass 8 (5):472-485.
    Supervaluationism is a well known theory of vagueness. Subvaluationism is a less well known theory of vagueness. But these theories cannot be taken apart, for they are in a relation of duality that can be made precise. This paper provides an introduction to the subvaluationist theory of vagueness in connection to its dual, supervaluationism. A survey on the supervaluationist theory can be found in the Compass paper of Keefe (2008); our presentation of the theory in this paper will be short (...)
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  11. Pablo Cobreros (2011). Supervaluationism and Classical Logic. In Rick Nouwen, Robert van Rooij, Hans-Christian Schmitz & Uli Sauerland (eds.), Vagueness in Communication, Lecture Notes in Computer Science, Vol. 6517. Springer
    This paper is concerned with the claim that supervaluationist consequence is not classical for a language including an operator for definiteness. Although there is some sense in which this claim is uncontroversial, there is a sense in which the claim must be qualified. In particular I defend Keefe's position according to which supervaluationism is classical except when the inference from phi to Dphi is involved. The paper provides a precise content to this claim showing that we might provide complete (and (...)
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  12. 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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  13. Pablo Cobreros (2011). Varzi on Supervaluationism and Logical Consequence. Mind 120 (479):833-43.
    Though it is standardly assumed that supervaluationism applied to vagueness is committed to global validity, Achille Varzi (2007) argues that the supervaluationist should take seriously the idea of adopting local validity instead. Varzi’s motivation for the adoption of local validity is largely based on two objections against the global notion: that it brings some counterexamples to classically valid rules of inference and that it is inconsistent with unrestricted higher-order vagueness. In this discussion I review these objections and point out ways (...)
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  14. Pablo Cobreros (2008). Supervaluationism and Logical Consequence: A Third Way. Studia Logica 90 (3):291 - 312.
    It is often assumed that the supervaluationist theory of vagueness is committed to a global notion of logical consequence, in contrast with the local notion characteristic of modal logics. There are, at least, two problems related to the global notion of consequence. First, it brings some counterexamples to classically valid patterns of inference. Second, it is subject to an objection related to higher-order vagueness . This paper explores a third notion of logical consequence, and discusses its adequacy for the supervaluationist (...)
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  15. Pablo Cobreros (2008). Supervaluationism and Necessarily Borderline Sentences. Disputatio 3 (25):41-49.
    The supervaluationist theory of vagueness is committed to a particular notion of logical consequence known as global validity. According to a recent objection, this notion of consequence is more problematic than is usually thought since i) it bears a commitment to some sort of bizarre inferences, ii) this commitment threatens the internal coherence of the theory and iii) we might find counterexamples to classically valid pat- terns of inference even in the absence of a definitely-operator (or similar device). As a (...)
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  16. 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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  17. Pablo Cobreros & Luca Tranchini (2014). Supervaluationism: Truth, Value and Degree Functionality. Thought: A Journal of Philosophy 3 (2):136-144.
    This article deals with supervaluationism and the failure of truth-functionality. It draws some distinctions that may contribute to a better understanding of this semantic framework.
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  18. John Collins (2000). Unsharpenable Vagueness. Philosophical Topics 28 (1):1-10.
    A plausible thought about vagueness is that it involves a form of semantic incompleteness. To say that a predicate is vague is to say (at the very least) that its extension is incompletely specified. And where there is incomplete specification of extension there is indeterminacy—an indeterminacy between various ways that the specification of the predicate might be completed or, as some like to say, sharpened (or precisified). We shall argue that this idea is defective insofar as there are vague predicates (...)
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  19. John D. Collins & Achille C. Varzi (2000). Unsharpenable Vagueness. Philosophical Topics 28 (1):1-10.
    A plausible thought about vagueness is that it involves semantic incompleteness. To say that a predicate is vague is to say (at the very least) that its extension is incompletely specified. Where there is incomplete specification of extension there is indeterminacy, an indeterminacy between various ways in which the specification of the predicate might be completed or sharpened. In this paper we show that this idea is bound to founder by presenting an argument to the effect that there are vague (...)
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  20. 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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  21. Timothy J. Day (1992). Excluded Middle and Bivalence. Erkenntnis 37 (1):93 - 97.
    I consider two related objections to the claim that the law of excluded middle does not imply bivalence. One objection claims that the truth predicate captured by supervaluation semantics is not properly motivated. The second objection says that even if it is, LEM still implies bivalence. I show that LEM does not imply bivalence in a supervaluational language. I also argue that considering supertruth as truth can be reasonably motivated.
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  22. Dan López De Sa (2010). How to Respond to Borderline Cases. In Richard Dietz & Sebastiano Moruzzi (eds.), Cuts and Clouds: Vaguenesss, its Nature and its Logic. OUP Oxford
    Some philosophers seem to think that borderline cases provide further cases of apparent faultless disagreement. This chapter argues against such a suggestion. It contends that with respect to borderline cases, people typically do not respond by taking a view, in contrast to what is the case in genuine cases of apparent faultless disagreement. It shows that the claim of the chapter is indeed respected, and is accounted for by paradigm cases of semantic and epistemic views on the nature of vagueness. (...)
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  23. Lieven Decock & Igor Douven (2014). What Is Graded Membership? 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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  24. Richard Dietz & Sebastiano Moruzzi (eds.) (2010). (2010) ‘Scope Confusions and Unsatisfiable Disjuncts: Two Problems for Supervaluation- Ism’, in Eds., Cuts and Clouds: Vaguenesss, Its Nature, and Its Logic,. Oxford University Press.
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  25. Cian Dorr (2003). Vagueness Without Ignorance. Philosophical Perspectives 17 (1):83–113.
    I motivate and briefly sketch a linguistic theory of vagueness, on which the notion of indeterminacy is understood in terms of the conventions of language: a sentence is indeterminate iff the conventions of language either forbid asserting it and forbid asserting its negation, under the circumstances, or permit asserting either. I then consider an objection that purports to show that if this theory (or, as far as I can see, any other theory of vagueness that deserved the label "linguistic" were (...)
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  26. Michael Dummett (1975). Wang's Paradox. Synthese 30 (3-4):201--32.
  27. Paul Egre & Nathan Klinedinst (eds.) (2010). Vagueness and Language Use. Palgrave Macmillan.
    This volume brings together twelve papers by linguists and philosophers contributing novel empirical and formal considerations to theorizing about vagueness. Three main issues are addressed: gradable expressions and comparison, the semantics of degree adverbs and intensifiers (such as 'clearly'), and ways of evading the sorites paradox.
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  28. Matti Eklund (2001). Supervaluationism, Vagueifiers, and Semantic Overdetermination. Dialectica 55 (4):363–378.
    Supervaluationism, traditionally conceived, is the conjunction of three theses: Vagueness in a language gives rise to there being a multitude of acceptable assignments of semantic values to some expressions of the language, These assignments correspond to possible completions of the meanings of vague expressions, Truth is truth under all acceptable assignments, and falsity is falsity under all acceptable assignments. Supervaluationism has three chief virtues. It preserves classical logic. It provides an account of what vagueness is . And it extends nicely (...)
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  29. Delia Graff Fara (2011). Truth in a Region. In Paul Egre & Nathan Klinedinst (eds.), Vagueness and Language Use. Palgrave Macmillan
    In this paper I criticize a version of supervaluation semantics. This version is called "Region-Valuation" semantics. It's developed by Pablo Cobreros. I argue that all supervaluationists, regionalists in particular, and truth-value gap theorists of vagueness more generally, are commited to the validity of D-intro, the principle that every sentence entails its definitization (the truth of "Paul is tall" guarantees the truth of "Paul is definitely tall"). The principle embroils one in a paradox that's distinct from, but related to, the sorites (...)
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  30. Delia Graff Fara (2010). Scope Confusions and Unsatisfiable Disjuncts: Two Problems for Supervaluationism. In Richard Dietz & Sebastiano Moruzzi (eds.), (2010) ‘Scope Confusions and Unsatisfiable Disjuncts: Two Problems for Supervaluation- ism’, in eds., Cuts and Clouds: Vaguenesss, Its Nature, and Its Logic,. Oxford University Press
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  31. Kit Fine (1975). Vagueness, Truth and Logic. Synthese 30 (3-4):265-300.
    This paper deals with the truth-Conditions and the logic for vague languages. The use of supervaluations and of classical logic is defended; and other approaches are criticized. The truth-Conditions are extended to a language that contains a definitely-Operator and that is subject to higher order vagueness.
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  32. Jerry A. Fodor & Ernest Lepore (1996). What Cannot Be Evaluated Cannot Be Evaluated and It Cannot Be Supervalued Either. Journal of Philosophy 93 (10):516-535.
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  33. Bryan Frances (forthcoming). Why the Vagueness Paradox is Amazing. Think.
    One of the hardest problems in philosophy, one that has been around for over two thousand years without generating any significant consensus on its solution, involves the concept of vagueness: a word or concept that doesn’t have a perfectly precise meaning. There is an argument that seems to show that the word or concept simply must have a perfectly precise meaning, as violently counterintuitive as that is. Unfortunately, the argument is usually so compressed that it is difficult to see why (...)
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  34. Manuel García-Carpintero (2010). Supervaluationism and the Report of Vague Contents. In Richard Dietz & Sebastiano Moruzzi (eds.), Cuts and Clouds: Vaguenesss, its Nature and its Logic. OUP Oxford
    Schiffer has given an argument against supervaluationist accounts of vagueness, based on reports of vague contents. Suppose that Al tells Bob ‘Ben was there’, pointing to a certain place, and later Bob says, ‘Al said that Ben was there’, pointing in the same direction. According to supervaluationist semantics, Schiffer contends, both Al’s and Bob’s utterances of ‘there’ indeterminately refer to myriad precise regions of space; Al’s utterance is true just in case Ben was in any of those precisely bounded regions (...)
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  35. Manuel García-Carpintero (2000). Vagueness and Indirect Discourse. Philosophical Issues 10 (1):258-270.
    This commentary is devoted to offer a rejoinder to an argument by Schiffer against semantic accounts of vagueness (typically relying on supervaluationist techniques) based on indirect discourse. A short sketch of the argument can be found on pp. 246-48 of ‘Vagueness and Partial Belief’ ; a more elaborated presentation occurs in “TWOIs sues of Vagueness”.
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  36. John Gardner, Supervaluationism and its Logics.
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  37. John Hawthorne (2005). Vagueness and the Mind of God. Philosophical Studies 122 (1):1 - 25.
    This paper examines the mind and language of an omniscient being from a supervaluationist perspective. Two questions hall receive special attention. How ought the supervaluationist explicate the concept of omniscience? And what ought the supervaluationist expect an omniscient speaker to say about a Sorites series?
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  38. Richard Heck (2003). Semantic Accounts of Vagueness. In J. C. Beall (ed.), Liars and Heaps. OUP 106-27.
    Read as a comment on Crispin Wright's \"Vagueness: A Fifth Column Approach\", this paper defends a form of supervaluationism against Wright's criticisms. Along the way, however, it takes up the question what is really wrong with Epistemicism, how the appeal of the Sorities ought properly to be understood, and why Contextualist accounts of vagueness won't do.
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  39. Hans G. Herzberger (1980). Supervaluations Without Truth-Value Gaps. Canadian Journal of Philosophy, Supplementary Volume 6:15.
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  40. Andrea Iacona (2014). Ockhamism Without Thin Red Lines. Synthese 191 (12):2633-2652.
    This paper investigates the logic of Ockhamism, a view according to which future contingents are either true or false. Several attempts have been made to give rigorous shape to this view by defining a suitable formal semantics, but arguably none of them is fully satisfactory. The paper draws attention to some problems that beset such attempts, and suggests that these problems are different symptoms of the same initial confusion, in that they stem from the unjustified assumption that the actual course (...)
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  41. Andrea Iacona (2010). Saying More (or Less) Than One Thing. In Richard Dietz & Sebastiano Moruzzi (eds.), Cuts and Clouds. Oxford University Press
    In a paper called 'Definiteness and Knowability', Tim Williamson addresses the question whether one must accept that vagueness is an epistemic phenomenon if one adopts classical logic and a disquotational principle for truth. Some have suggested that one must not, hence that classical logic and the disquotational principle may be preserved without endorsing epistemicism. Williamson’s paper, however, finds ‘no plausible way of substantiating that possibility’. Its moral is that ‘either classical logic fails, or the disquotational principle does, or vagueness is (...)
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  42. Nicholas K. Jones (2011). Williams on Supervaluationism and Logical Revisionism. Journal of Philosophy 108 (11):633-641.
    Central to discussion of supervaluationist accounts of vagueness is the extent to which they require revisions of classical logic and if so, whether those revisions are objectionable. In an important recent Journal of Philosophy article, J.R.G. Williams presents a powerful challenge to the orthodox view that supervaluationism is objectionably revisionary. Williams argues both that supervaluationism is non-revisionary and that even if it were, those revisions would be unobjectionable. This note shows that his arguments for both claims fail.
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  43. Rosanna Keefe (2010). Teaching & Learning Guide For: Vagueness: Supervaluationism. Philosophy Compass 5 (2):213-215.
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  44. Rosanna Keefe (2008). Vagueness: Supervaluationism. Philosophy Compass 3 (2):315–324.
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  45. Rosanna Keefe (2000). Supervaluationism and Validity. Philosophical Topics 28 (1):93-105.
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  46. Rosanna Keefe (2000). Theories of Vagueness. Cambridge University Press.
    Most expressions in natural language are vague. But what is the best semantic treatment of terms like 'heap', 'red' and 'child'? And what is the logic of arguments involving this kind of vague expression? These questions are receiving increasing philosophical attention, and in this timely book Rosanna Keefe explores the questions of what we should want from an account of vagueness and how we should assess rival theories. Her discussion ranges widely and comprehensively over the main theories of vagueness and (...)
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  47. Philip Kremer (2008). Supervaluation Fixed-Point Logics of Truth. Journal of Philosophical Logic 37 (5):407 - 440.
    Michael Kremer defines fixed-point logics of truth based on Saul Kripke’s fixed point semantics for languages expressing their own truth concepts. Kremer axiomatizes the strong Kleene fixed-point logic of truth and the weak Kleene fixed-point logic of truth, but leaves the axiomatizability question open for the supervaluation fixed-point logic of truth and its variants. We show that the principal supervaluation fixed point logic of truth, when thought of as consequence relation, is highly complex: it is not even analytic. We also (...)
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  48. Dan López de Sa (2009). Can One Get Bivalence From (Tarskian) Truth and Falsity? Canadian Journal of Philosophy 39 (2):273-282.
    Timothy Williamson famously offered an argument from these Tarskian principles in favor of bivalence. I show, dwelling on (Andjelkovic & Williamson, 2000), that the argument depends on a contentious formulation of the Tarskian principles about truth (and falsity), which the supervaluationist can reject without jeopardizing the Tarskian insight. In the mentioned paper, Adjelkovic and Williamson argue that, even if the appropriate formulation seems to make room for failure of bivalence in borderline cases, this appearance is illusory, once one grants an (...)
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  49. Dan López de Sa (2007). On the Semantic Indecision of Vague Singular Terms. Sorites 19:88-91.
    Donald Smith (2006) argues that if ‘I’ is indeed vague, and the view of vagueness as semantic indecision correct after all, then ‘I’ cannot refer to a composite material object. But his considerations would, if sound, also establish that ‘Tibbles,’ ‘Everest,’ or ‘Toronto,’ do not refer to composite material objects either—nor hence, presumably, to cats, mountains, or cities. And they can be resisted, anyway. Or so I argue.
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  50. Neil McKinnon, Persistence and a New Problem of the Many.
    One winter’s Saturday Clarence wakes up. He realises he has left his umbrella at work. The office is locked, and he can’t get in. Being one of those people who punish themselves for their mistakes, he can’t bring himself to buy a replacement. He has an engagement six kilometres down the road and starts wondering whether it will rain. Normally, this would not be a problem, but his motor vehicle has broken down because he forgot to have it serviced. And (...)
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