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If It's Clear, Then It's Clear That It's Clear, or is It? Higher-Order Vagueness and the S4 Axiom

In B. Morison K. Ierodiakonou (ed.), Episteme, etc.: Essays in honour of Jonathan Barnes. OUP UK (2012)

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  1. Intuitionism and the Modal Logic of Vagueness.Susanne Bobzien & Ian Rumfitt - 2020 - Journal of Philosophical Logic 49 (2):221-248.
    Intuitionistic logic provides an elegant solution to the Sorites Paradox. Its acceptance has been hampered by two factors. First, the lack of an accepted semantics for languages containing vague terms has led even philosophers sympathetic to intuitionism to complain that no explanation has been given of why intuitionistic logic is the correct logic for such languages. Second, switching from classical to intuitionistic logic, while it may help with the Sorites, does not appear to offer any advantages when dealing with the (...)
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  • In Defense of True Higher-Order Vagueness.Susanne Bobzien - 2011 - Synthese 180 (3):317-335.
    ABSTRACT: Stewart Shapiro recently argued that there is no higher-order vagueness. More specifically, his thesis is: (ST) ‘So-called second-order vagueness in ‘F’ is nothing but first-order vagueness in the phrase ‘competent speaker of English’ or ‘competent user of “F”’. Shapiro bases (ST) on a description of the phenomenon of higher-order vagueness and two accounts of ‘borderline case’ and provides several arguments in its support. We present the phenomenon (as Shapiro describes it) and the accounts; then discuss Shapiro’s arguments, arguing that (...)
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  • Prototypes, poles, and tessellations: towards a topological theory of conceptual spaces.Thomas Mormann - forthcoming - Synthese:1-36.
    The aim of this paper is to present a topological method for constructing discretizations of topological conceptual spaces. The method works for a class of topological spaces that the Russian mathematician Pavel Alexandroff defined more than 80 years ago. The aim of this paper is to show that Alexandroff spaces, as they are called today, have many interesting properties that can be used to explicate and clarify a variety of problems in philosophy, cognitive science, and related disciplines. For instance, recently, (...)
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  • Higher-Order Vagueness and Borderline Nestings: A Persistent Confusion.Susanne Bobzien - 2013 - Analytic Philosophy 54 (1):1-43.
    ABSTRACT: This paper argues that the so-called paradoxes of higher-order vagueness are the result of a confusion between higher-order vagueness and the distribution of the objects of a Sorites series into extensionally non-overlapping non-empty classes.
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  • A Defense of Indeterminate Distinctness.Ken Akiba - 2014 - Synthese 191 (15):3557-3573.
    On the one hand, philosophers have presented numerous apparent examples of indeterminate individuation, i.e., examples in which two things are neither determinately identical nor determinately distinct. On the other hand, some have argued against even the coherence of the very idea of indeterminate individuation. This paper defends the possibility of indeterminate individuation against Evans’s argument and some other arguments. The Determinacy of Identity—the thesis that identical things are determinately identical—is distinguished from the Determinacy of Distinctness—the thesis that distinct things are (...)
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  • I—Columnar Higher-Order Vagueness, or Vagueness is Higher-Order Vagueness.Susanne Bobzien - 2015 - Aristotelian Society Supplementary Volume 89 (1):61-87.
    Most descriptions of higher-order vagueness in terms of traditional modal logic generate so-called higher-order vagueness paradoxes. The one that doesn't is problematic otherwise. Consequently, the present trend is toward more complex, non-standard theories. However, there is no need for this.In this paper I introduce a theory of higher-order vagueness that is paradox-free and can be expressed in the first-order extension of a normal modal system that is complete with respect to single-domain Kripke-frame semantics. This is the system QS4M+BF+FIN. It corresponds (...)
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  • Supervaluationism and Good Reasoning.Timothy Williamson - 2018 - Theoria: Revista de Teoría, Historia y Fundamentos de la Ciencia 33 (3):521-537.
    This paper is a tribute to Delia Graff Fara. It extends her work on failures of meta-rules for validity as truth-preservation under a supervaluationist identification of truth with supertruth. She showed that such failures occur even in languages without special vagueness-related operators, for standards of deductive reasoning as materially rather than purely logically good, depending on a context-dependent background. This paper extends her argument to: quantifier meta-rules like existential elimination; ambiguity; deliberately vague standard mathematical notation. Supervaluationist attempts to qualify the (...)
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  • VIII—Vagueness at Every Order.Andrew Bacon - 2020 - Proceedings of the Aristotelian Society 120 (2):165-201.
    There are some properties, like being bald, for which it is vague where the boundary between the things that have it and the things that do not lies. A number of arguments threaten to show that such properties can still be associated with determinate and knowable boundaries: not between the things that have it and those that don’t, but between the things such that it is borderline at some order whether they have it and the things for which it is (...)
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  • The Stoic Account of Apprehension.Tamer Nawar - 2014 - Philosophers' Imprint 14:1-21.
    This paper examines the Stoic account of apprehension (κατάληψις) (a cognitive achievement similar to how we typically view knowledge). Following a seminal article by Michael Frede (1983), it is widely thought that the Stoics maintained a purely externalist causal account of apprehension wherein one may apprehend only if one stands in an appropriate causal relation to the object apprehended. An important but unanswered challenge to this view has been offered by David Sedley (2002) who offers reasons to suppose that the (...)
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  • Higher-Order Vagueness and Numbers of Distinct Modalities.Susanne Bobzien - 2014 - Disputatio (39):131-137.
    This paper shows that the following common assumption is false: that in modal-logical representations of higher-order vagueness, for there to be borderline cases to borderline cases ad infinitum, the number of possible distinct modalities in a modal system must be infinite. (Open access journal).
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  • Not Much Higher-Order Vagueness in Williamson’s ’Logic of Clarity’.Nasim Mahoozi & Thomas Mormann - manuscript
    This paper deals with higher-order vagueness in Williamson's 'logic of clarity'. Its aim is to prove that for 'fixed margin models' (W,d,α ,[ ]) the notion of higher-order vagueness collapses to second-order vagueness. First, it is shown that fixed margin models can be reformulated in terms of similarity structures (W,~). The relation ~ is assumed to be reflexive and symmetric, but not necessarily transitive. Then, it is shown that the structures (W,~) come along with naturally defined maps h and s (...)
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  • Reply to Rosanna Keefe’s ‘Modelling Higher-Order Vagueness: Columns, Borderlines and Boundaries’.Susanne Bobzien - 2016
    This paper is an expanded written version of my reply to Rosanna Keefe’s paper ‘Modelling higher-order vagueness: columns, borderlines and boundaries’ (Keefe 2015), which in turn is a reply to my paper ‘Columnar higher-order vagueness, or Vagueness is higher-order vagueness’ (Bobzien 2015). Both papers were presented at the Joint Session of the the Aristotelian Society and the Mind Association in July, 2015. At the Joint Session meeting, there was insufficient time to present all of my points in response to Keefe’s (...)
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  • II—Modelling Higher-Order Vagueness: Columns, Borderlines and Boundaries.Rosanna Keefe - 2015 - Aristotelian Society Supplementary Volume 89 (1):89-108.
    According to columnar higher-order vagueness, all orders of vagueness coincide: any borderline case is a borderline borderline case, and a third-order borderline case, etc. Bobzien has worked out many details of such a theory and models it with a modal logic closely related to S4. I take up a range of questions about the framework and argue that it is not suitable for modelling the structure of vagueness and higher-order vagueness.
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