Epistemic Logic, Monotonicity, and the Halbach–Welch Rapprochement Strategy
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Predicate approaches to modality have been a topic of increased interest in recent intensional logic. Halbach and Welch (Mind 118(469):71–100, 2009) have proposed a new formal technique to reduce the necessity predicate to an operator, demonstrating that predicate and operator methods are ultimately compatible. This article concerns the question of whether Halbach and Welch’s approach can provide a uniform formal treatment for intensionality. I show that the monotonicity constraint in Halbach and Welch’s proof for necessity fails for almost all possible-worlds theories of knowledge. The nonmonotonicity results demonstrate that the most obvious way of emulating Halbach and Welch’s rapprochement of the predicate and operator fails in the epistemic setting.
KeywordsEpistemic logic Intensional logic Modal logic
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I would like to thank Sean Walsh, David Woodruff Smith, Kai Wehmeier, and Brian Skyrms. Early versions of this work were presented at the following events: The Predicate Approaches to Modality Conference at the Munich Center for Mathematical Philosophy, LMU Munich, in September 2014; the C-ALPHA Logic Seminar, UC Irvine, in Winter 2016. I am grateful to the audiences for their responses. Thanks is owed in particular to the following people who gave me invaluable feedback and comments on these and other occasions: Tim Button, Volker Halbach, Greg Lauro, Richard Mendelsohn, Jeff Schaz, Johannes Stern, and Philip Welch.
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