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)
  Copy   BIBTEX


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.)



External links

Setup an account with your affiliations in order to access resources via your University's proxy server

Through your library

Similar books and articles

The Problem with Truthmaker-Gap Epistemicism.Mark Jago - 2012 - Thought: A Journal of Philosophy 1 (4):320-329.
The Illusion of Higher-Order Vagueness.Crispin Wright - 2009 - In Richard Dietz & Sebastiano Moruzzi (eds.), Cuts and Clouds. Vagueness, its Nature and its Logic. Oxford University Press.
Demoting higher-order vagueness.Diana Raffman - 2009 - In Sebastiano Moruzzi & Richard Dietz (eds.), Cuts and Clouds. Vaguenesss, its Nature and its Logic. Oxford University Press. pp. 509--22.
Chrysippus and the epistemic theory of vagueness.Susanne Bobzien - 2002 - Proceedings of the Aristotelian Society 102 (1):217-238.
How vagueness could cut out at any order.Cian Dorr - 2015 - Review of Symbolic Logic 8 (1):1-10.
Contextualism about vagueness and higher-order vagueness.Patrick Greenough - 2005 - Aristotelian Society Supplementary Volume 79 (1):167–190.
Russell’s Leibnizian Concept of Vagueness.Larry M. Jorgensen - 2011 - History of Philosophy Quarterly 28 (3):289-301.


Added to PP

995 (#10,370)

6 months
56 (#54,193)

Historical graph of downloads
How can I increase my downloads?

Author's Profile

Susanne Bobzien
Oxford University

References found in this work

Scorekeeping in a language game.David Lewis - 1979 - Journal of Philosophical Logic 8 (1):339--359.
Vagueness, truth and logic.Kit Fine - 1975 - Synthese 30 (3-4):265-300.
Assertion.Robert Stalnaker - 1978 - Syntax and Semantics (New York Academic Press) 9:315-332.
Assertion.Robert Stalnaker - 1978 - In Maite Ezcurdia & Robert J. Stainton (eds.), The Semantics-Pragmatics Boundary in Philosophy. Broadview Press. pp. 179.
Scorekeeping in a Language Game.David Lewis - 1979 - Journal of Philosophical Logic 8 (3):339.

View all 23 references / Add more references