Opaque Updates

Abstract

If updating with E has the same result across all epistemically possible worlds, then the agent has no uncertainty as to the behavior of the update, and we may call it a transparent update. If an agent is uncertain about the behavior of an update, we may call it opaque. In order to model the uncertainty an agent has about the result of an update, the same update must behave differently across different possible worlds. In this paper, I study opaque updates using a simple system of dynamic epistemic logic suitably modified for that purpose. The paper highlights the connection between opaque updates and the dynamic-epistemic principles Perfect-Recall and No-Miracles. I argue that opaque updates are central to contemporary discussions in epistemology, in particular to externalist theories of knowledge and to the related problem of epistemic bootstrapping, or easy knowledge. Opaque updates allow us to explicitly investigate a dynamic (or diachronic) form of uncertainty, using simple and precise logical tools.

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Acknowledgments

I would like to thank Johan van Benthem, Ray Briggs, and Krista Lawlor for their tremendous help in the process of developing and writing this paper. I also thank two anonymous reviewers of this journal for many helpful comments, suggestions, and corrections on an earlier version of this paper. Their valuable comments helped in clarifying the goal and scope of this paper.

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Correspondence to Michael Cohen.

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Cohen, M. Opaque Updates. J Philos Logic (2020). https://doi.org/10.1007/s10992-020-09571-8

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Keywords

  • Dynamic epistemic logic
  • Externalism
  • Basic knowledge
  • Bootstrapping
  • Introspection
  • Perfect-recall
  • No-miracles
  • Bayesian update
  • Opacity