David Bourget (Western Ontario)
David Chalmers (ANU, NYU)
Rafael De Clercq
Jack Alan Reynolds
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Mind 106 (424):641-660 (1997)
One of the few points of agreement to be found in mainstream responses to the logical and semantic problems generated by vagueness is the view that if any modification of classical logic and semantics is required at all then it will only be such as to admit underdetermined reference and truth-value gaps. Logics of vagueness including many valued logics, fuzzy logics, and supervaluation logics all provide responses in accord with this view. The thought that an adequate response might require the recognition of cases of overdetermination and truth value gluts has few supporters. This imbalance lacks justification. As it happens, Jaskowski's paraconsistent discussive logic-a logic which admits truth value gluts-can be defended by reflecting on similarities between it and the popular supervaluationist analysis of vagueness already in the philosophical literature. A simple dualisation of supervaluation semantics results in a paraconsistent logic of vagueness based on what has been termed subvaluational semantics.
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Pablo Cobreros (2013). Vagueness: Subvaluationism. Philosophy Compass 8 (5):472-485.
Pablo Cobreros, Paul Egré, David Ripley & Robert van Rooij (2010). Tolerant, Classical, Strict. Journal of Philosophical Logic 41 (2):347-385.
Lewis Powell (2012). How to Refrain From Answering Kripke's Puzzle. Philosophical Studies 161 (2):287-308.
Ken Akiba (2004). Vagueness in the World. Noûs 38 (3):407–429.
Elia Zardini (2013). Higher-Order Sorites Paradox. Journal of Philosophical Logic 42 (1):25-48.
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