How vagueness could cut out at any order

Review of Symbolic Logic 8 (1):1-10 (2015)
Timothy Williamson has shown that the B axiom for 'definitely' (α → Δ¬Δ¬α) guarantees that if a sentence is second-order vague in a Kripke model, it is nth order vague for every n. More recently, Anna Mahtani has argued that Williamson's epistemicist theory of vagueness does not support the B axiom, and conjectured that if we consider models in which the “radius of accessibility” varies between different points, we will be able to find sentences that are nth-order vague but (n+1)th-order precise, for any n. This paper bolsters Mahtani's argument, shows her conjecture to be true, and shows that imposing certain further natural constraints on "variable radius" models does not change the situation.
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DOI 10.1017/S175502031400032X
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References found in this work BETA
Epistemicism About Vagueness and Meta-Linguistic Safety.Stephen Kearns & Ofra Magidor - 2008 - Philosophical Perspectives 22 (1):277-304.
An Anti-Epistemicist Consequence of Margin for Error Semantics for Knowledge.Delia Graff Fara - 2002 - Philosophy and Phenomenological Research 64 (1):127-142.
Can Vagueness Cut Out at Any Order?Anna Mahtani - 2008 - Australasian Journal of Philosophy 86 (3):499 – 508.
Vagueness and Semantic Indiscriminability.Michael Caie - 2012 - Philosophical Studies 160 (3):365-377.

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Citations of this work BETA
Very Improbable Knowing.Timothy Williamson - 2014 - Erkenntnis 79 (5):971-999.
II—Modelling Higher-Order Vagueness: Columns, Borderlines and Boundaries.Rosanna Keefe - 2015 - Aristotelian Society Supplementary Volume 89 (1):89-108.

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