Vagueness and Modality

Philosophical Perspectives 30 (1):1-39 (2016)
Authors
Juhani Yli-Vakkuri
University of Tartu
Jon Litland
University of Texas at Austin
Abstract
How does vagueness interact with metaphysical modality and with restrictions of it, such as nomological modality? In particular, how do definiteness, necessity (understood as restricted in some way or not), and actuality interact? This paper proposes a model-theoretic framework for investigating the logic and semantics of that interaction. The framework is put forward in an ecumenical spirit: it is intended to be applicable to all theories of vagueness that express vagueness using a definiteness (or: determinacy) operator. We will show how epistemicists, supervaluationists, and theorists of metaphysical vagueness like Barnes and Williams (2010) can interpret the framework.  We will also present a complete axiomatization of the logic we recommend to both epistemicists and local supervaluationists. 
Keywords Vagueness  Modality  Epistemicism  Supervaluationism  Ontic vagueness  Metaphysical possibility  Indeterminacy  Modal logic  Quantified modal logic  Free logic
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