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

Susanne Bobzien
Oxford University
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 (Williamson-style "luminosity" or self-revealing clarity and concealeable clarity) and what their respective functions are in accounts of higher-order vagueness. On this basis, we argue first that, contrary to common opinion, higher-order vagueness and S4 are perfectly compatible. This is in response to claims like that by Williamson that, if vagueness is defined with the help of a clarity operator that obeys axiom 4, higher-order vagueness disappears. Second, we argue that, contrary to common opinion, (i) bivalence-preservers (e.g. epistemicists) can without contradiction condone axiom 4 (by adopting what elsewhere we call columnar higher-order vagueness), and (ii) bivalence-discarders (e.g. open-texture theorists, supervaluationists) can without contradiction reject axiom 4. Third, we rebut a number of arguments that have been produced by opponents of axiom 4, in particular those by Williamson. (The paper is pitched towards graduate students with basic knowledge of modal logic.)
Keywords columnar higher-order vagueness  higher-order vagueness  modal logic  modal system S4  kk principle  epistemicism  clarity  definiteness  williamson  luminosity
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References found in this work BETA

Scorekeeping in a Language Game.David Lewis - 1979 - Journal of Philosophical Logic 8 (1):339--359.
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Scorekeeping in a Language Game.David Lewis - 1979 - Journal of Philosophical Logic 8 (3):339.
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Citations of this work BETA

The Stoic Account of Apprehension.Tamer Nawar - 2014 - Philosophers' Imprint 14:1-21.
I—Columnar Higher-Order Vagueness, or Vagueness is Higher-Order Vagueness.Susanne Bobzien - 2015 - Aristotelian Society Supplementary Volume 89 (1):61-87.
Supervaluationism and Good Reasoning.Timothy Williamson - 2018 - Theoria: Revista de Teoría, Historia y Fundamentos de la Ciencia 33 (3):521-537.

View all 11 citations / Add more citations

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