Switch to: Citations

References in:

Topological Models of Columnar Vagueness

Erkenntnis 87 (2):693 - 716 (2020)

Add references

You must login to add references.
  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 (...)
    Download  
     
    Export citation  
     
    Bookmark   4 citations  
  • Vagueness.Timothy Williamson - 1994 - British Journal for the Philosophy of Science 46 (4):589-601.
    Download  
     
    Export citation  
     
    Bookmark   617 citations  
  • 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 (...)
    Download  
     
    Export citation  
     
    Bookmark   9 citations  
  • The Boundary Stones of Thought: An Essay in the Philosophy of Logic.Ian Rumfitt - 2015 - Oxford, England: Oxford University Press.
    Classical logic has been attacked by adherents of rival, anti-realist logical systems: Ian Rumfitt comes to its defence. He considers the nature of logic, and how to arbitrate between different logics. He argues that classical logic may dispense with the principle of bivalence, and may thus be liberated from the dead hand of classical semantics.
    Download  
     
    Export citation  
     
    Bookmark   62 citations  
  • Conceptual Spaces: The Geometry of Thought.Peter Gärdenfors - 2000 - Tijdschrift Voor Filosofie 64 (1):180-181.
    Download  
     
    Export citation  
     
    Bookmark   330 citations  
  • The Geometry of Meaning: Semantics Based on Conceptual Spaces.Peter Gärdenfors - 2014 - Cambridge, Massachusetts: MIT Press.
    A novel cognitive theory of semantics that proposes that the meanings of words can be described in terms of geometric structures.
    Download  
     
    Export citation  
     
    Bookmark   71 citations  
  • 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.
    Download  
     
    Export citation  
     
    Bookmark   8 citations  
  • Heyting Mereology as a Framework for Spatial Reasoning.Thomas Mormann - 2013 - Axiomathes 23 (1):137- 164.
    In this paper it is shown that Heyting and Co-Heyting mereological systems provide a convenient conceptual framework for spatial reasoning, in which spatial concepts such as connectedness, interior parts, (exterior) contact, and boundary can be defined in a natural and intuitively appealing way. This fact refutes the wide-spread contention that mereology cannot deal with the more advanced aspects of spatial reasoning and therefore has to be enhanced by further non-mereological concepts to overcome its congenital limitations. The allegedly unmereological concept of (...)
    Download  
     
    Export citation  
     
    Bookmark   2 citations  
  • If It's Clear, Then It's Clear That It's Clear, or is It? Higher-Order Vagueness and the S4 Axiom.Susanne Bobzien - 2011 - In Ben Morison & Katerina Ierodiakonou (eds.), Episteme, etc.: Essays in honour of Jonathan Barnes. Oxford, GB: Oxford University Press.
    The purpose of this paper is to challenge some widespread assumptions about the role of the modal axiom 4 in a theory of vagueness. In the context of vagueness, axiom 4 usually appears as the principle ‘If it is clear (determinate, definite) that A, then it is clear (determinate, definite) that it is clear (determinate, definite) that A’, or, more formally, CA → CCA. We show how in the debate over axiom 4 two different notions of clarity are in play (...)
    Download  
     
    Export citation  
     
    Bookmark   17 citations  
  • On the structure of higher-order vagueness.Timothy Williamson - 1999 - Mind 108 (429):127-143.
    Discussions of higher-order vagueness rarely define what it is for a term to have nth-order vagueness for n>2. This paper provides a rigorous definition in a framework analogous to possible worlds semantics; it is neutral between epistemic and supervaluationist accounts of vagueness. The definition is shown to have various desirable properties. But under natural assumptions it is also shown that 2nd-order vagueness implies vagueness of all orders, and that a conjunction can have 2nd-order vagueness even if its conjuncts do not. (...)
    Download  
     
    Export citation  
     
    Bookmark   63 citations  
  • Applications of Conceptual Spaces : the Case for Geometric Knowledge Representation.Peter Gärdenfors & Frank Zenker (eds.) - 2015 - Cham: Springer Verlag.
    Why is a red face not really red? How do we decide that this book is a textbook or not? Conceptual spaces provide the medium on which these computations are performed, but an additional operation is needed: Contrast. By contrasting a reddish face with a prototypical face, one gets a prototypical ‘red’. By contrasting this book with a prototypical textbook, the lack of exercises may pop out. Dynamic contrasting is an essential operation for converting perceptions into predicates. The existence of (...)
    Download  
     
    Export citation  
     
    Bookmark   14 citations  
  • Higher-order Vagueness, Radical Unclarity, and Absolute Agnosticism.Susanne Bobzien - 2010 - Philosophers' Imprint 10:1-30.
    The paper presents a new theory of higher-order vagueness. This theory is an improvement on current theories of vagueness in that it (i) describes the kind of borderline cases relevant to the Sorites paradox, (ii) retains the ‘robustness’ of vague predicates, (iii) introduces a notion of higher-order vagueness that is compositional, but (iv) avoids the paradoxes of higher-order vagueness. The theory’s central building-blocks: Borderlinehood is defined as radical unclarity. Unclarity is defined by means of competent, rational, informed speakers (‘CRISPs’) whose (...)
    Download  
     
    Export citation  
     
    Bookmark   15 citations  
  • (2 other versions)Vagueness.Timothy Williamson - 1994 - New York: Routledge.
    Vagueness provides the first comprehensive examination of a topic of increasing importance in metaphysics and the philosophy of logic and language. Timothy Williamson traces the history of this philosophical problem from discussions of the heap paradox in classical Greece to modern formal approaches such as fuzzy logic. He illustrates the problems with views which have taken the position that standard logic and formal semantics do not apply to vague language, and defends the controversial realistic view that vagueness is a kind (...)
    Download  
     
    Export citation  
     
    Bookmark   588 citations  
  • Higher-Order Vagueness and Paradox: The Glory and Misery of S4 Definiteness.Elia Zardini - 2005 - The Baltic International Yearbook of Cognition, Logic and Communication 1.
    Download  
     
    Export citation  
     
    Bookmark   5 citations  
  • (1 other version)Algebraic Methods in Philosophical Logic.J. Michael Dunn & Gary M. Hardegree - 2005 - Studia Logica 79 (2):305-306.
    Download  
     
    Export citation  
     
    Bookmark   55 citations  
  • The Algebra of Topology.J. C. C. Mckinsey & Alfred Tarski - 1944 - Annals of Mathematics, Second Series 45:141-191.
    Download  
     
    Export citation  
     
    Bookmark   134 citations  
  • A Topological Approach to Full Belief.Alexandru Baltag, Nick Bezhanishvili, Aybüke Özgün & Sonja Smets - 2019 - Journal of Philosophical Logic 48 (2):205-244.
    Stalnaker, 169–199 2006) introduced a combined epistemic-doxastic logic that can formally express a strong concept of belief, a concept of belief as ‘subjective certainty’. In this paper, we provide a topological semantics for belief, in particular, for Stalnaker’s notion of belief defined as ‘epistemic possibility of knowledge’, in terms of the closure of the interior operator on extremally disconnected spaces. This semantics extends the standard topological interpretation of knowledge with a new topological semantics for belief. We prove that the belief (...)
    Download  
     
    Export citation  
     
    Bookmark   15 citations  
  • (2 other versions)Précis of Vagueness.Timothy Williamson - 1997 - Philosophy and Phenomenological Research 57 (4):921-928.
    Download  
     
    Export citation  
     
    Bookmark   414 citations  
  • (1 other version)Algebraic Methods in Philosophical Logic.J. Michael Dunn & Gary M. Hardegree - 2003 - Bulletin of Symbolic Logic 9 (2):231-234.
    Download  
     
    Export citation  
     
    Bookmark   70 citations  
  • “Wang's paradox”.Crispin Wright - manuscript
    There is now a widespread accord among philosophers that the vagueness of natural language gives rise to some particularly deep and perplexing problems and paradoxes. It was not always so. For most of the first century of analytical philosophy, vagueness was generally regarded as a marginal, slightly irritating phenomenon, —receiving some attention, to be sure, in parts of the Philosophical Investigations and in the amateur linguistics enjoyed by philosophers in Oxford in the 1950s, but best idealised away in any serious (...)
    Download  
     
    Export citation  
     
    Bookmark   5 citations  
  • A Note on the Logic of (Higher-Order) Vagueness.Richard Heck - 1993 - Analysis 53 (4):201-208.
    A discussion of Crispin Wright's 'paradox of higher-order vagueness', I suggest that the paradox may be resolved by careful attention to the logical principles used in its formulation. In particular, I focus attention on the rule of inference that allows for the inference from A to 'Definitely A', and argue that this rule, though valid, may not be used in subordinate deductions, e.g., in the course of a conditional proof. Wright's paradox uses the rule (or its equivalent) in this way.
    Download  
     
    Export citation  
     
    Bookmark   23 citations  
  • Is higher order vagueness coherent?Crispin Wright - 1992 - Analysis 52 (3):129-139.
    Download  
     
    Export citation  
     
    Bookmark   33 citations  
  • 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.
    Download  
     
    Export citation  
     
    Bookmark   2 citations