How vagueness could cut out at any order

Review of Symbolic Logic 8 (1):1-10 (2015)
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Abstract

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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Cian Dorr
New York University

Citations of this work

Very Improbable Knowing.Timothy Williamson - 2014 - Erkenntnis 79 (5):971-999.
Supervaluationism and good reasoning.Timothy Williamson - 2018 - Theoria: Revista de Teoría, Historia y Fundamentos de la Ciencia 33 (3):521-537.
II—Modelling Higher-Order Vagueness: Columns, Borderlines and Boundaries.Rosanna Keefe - 2015 - Aristotelian Society Supplementary Volume 89 (1):89-108.

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References found in this work

Knowledge and its Limits.Timothy Williamson - 2000 - Tijdschrift Voor Filosofie 64 (1):200-201.
Vagueness.Loretta Torrago - 1998 - Philosophical Review 107 (4):637.
Identity and Discrimination.Stephen P. Schwartz - 1992 - Philosophical Review 101 (4):888.

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