Opaque Updates


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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  1. 1.

    Arntzenius, F. (2003). Some problems for conditionalization and reflection. Journal of Philosophy, 100(7), 356–370.

    Article  Google Scholar 

  2. 2.

    Aucher, G., & Herzig, A. (2010). Exploring the power of converse events in dynamic epistemology: contemporary perspectives. In Dynamic epistemology: contemporary perspectives. Synthese Library: Springer.

  3. 3.

    Baltag, A. (2016). To know is to know the value of variable. In Beklemishev, L., Demri, S., & Máté, A. (Eds.) Advances in modal logic, (Vol. 11 pp. 135–155): CSLI Publications.

  4. 4.

    Baltag, A., & Renne, B. (2016). Dynamic epistemic logic. The stanford encyclopedia of philosophy. (Winter 2016 Edition).

  5. 5.

    Baltag, A., & Smets, S. (2008) In Bonanno, G., van der Hoek, W., & Wooldridge, M. (Eds.), A qualitative theory of dynamic interactive belief revision, (pp. 11–58). Amsterdam: Amsterdam University Press.

  6. 6.

    van Benthem, J., Gerbrandy, J., Hoshi, T., & Pacuit, E. (2009). Merging frameworks for interaction. Journal of Philosophical Logic, 38 (5), 491–526.

    Article  Google Scholar 

  7. 7.

    van Benthem, J. (2012). Logical dynamics of information and interaction. Cambridge: Cambridge University Press.

    Google Scholar 

  8. 8.

    van Benthem, J. (2014). Logic in games. Cambridge, MA: The MIT Press.

    Google Scholar 

  9. 9.

    van Benthem, J., & Klein, D. (2019). Logics for analyzing games. The Stanford Encyclopedia of Philosophy, (Spring 2019 Edition), Zalta, E.N. (Eds.)

  10. 10.

    van Benthem, J., van Eijck, J., & Kooi, B. (2006). Logics of communication and change. Information and Computation, 204(11), 1620–1662.

    Article  Google Scholar 

  11. 11.

    Bird, A. (2018). Evidence and inference. Philosophy and Phenomenological Research, 96, 299–317.

    Article  Google Scholar 

  12. 12.

    Bird, A., & Pettigrew, R. (2019). Internalism, Externalism, and the KK Principle. Erkenntnis:1–20.

  13. 13.

    Bjorndahl, A. (2018). The epistemology of nondeterminism. In Moss, L., de Queiroz, R., & Martinez, M (Eds.) Logic, language, information, and computation. WoLLIC 2018. Lecture notes in computer science, Vol. 10944. Berlin: Springer.

  14. 14.

    Carter, A.J., Gordon, C.E, & Jarvis B. (Eds.). (2017). Knowledge first: approaches in epistemology and mind. Oxford: Oxford University Press.

    Google Scholar 

  15. 15.

    van Cleve, J. (2003). Is knowledge easy — or impossible? externalism as the only alternative to skepticism. In The skeptics: contemporary essays. Aldershot: Ashgate Publishing.

  16. 16.

    Cohen, M. (2020). The problem of perception and the no-miracles principle. Synthese. https://doi.org/10.1007/s11229-020-02772-3.

  17. 17.

    Cohen, S. (2002). Basic knowledge and the problem of easy knowledge. Philosophy and Phenomenological Research, 65(2), 309–329.

    Article  Google Scholar 

  18. 18.

    Comesaña, J., & Kantin, H. (2010). Is evidence knowledge?. Philosophy and Phenomenological Research, 80, 447–454.

    Article  Google Scholar 

  19. 19.

    van Ditmarsch, H.P. (2000). Knowledge games. Ph.D. thesis, University of Groningen, ILLC Dissertation Series DS-2000-06.

  20. 20.

    van Eijck, J., Gattinger, M., & Wang, Y. (2017). Knowing values and public inspection. In Ghosh, S., & Prasad, S. (Eds.) Logic and its applications. ICLA 2017. Lecture notes in computer science, Vol. 10119. Berlin, Heidelberg: Springer.

  21. 21.

    Fratantonio, G., & McGlynn, A. (2018). Reassessing the case against evidential externalism. In Mitova, V. (Ed.) The factive turn in epistemology (pp. 84–101). Cambridge: Cambridge University Press.

  22. 22.

    Girard, P., Liu, F., & Seligman, J. (2012). General dynamic dynamic logic. In Bolander, T., Brauner, T., Ghilardi, S., & Moss, L. (Eds.) Proceedings of the 9th international conference on advances in modal logic (AiML’12) (pp. 239–260). London: College Publications.

  23. 23.

    Goldman, A. Greenough, P., Pritchard, D., & Goldman, A (Eds.). (2009). Williamson on knowledge and evidence. Oxford: Oxford University Press.

  24. 24.

    Goldman, A., & Beddor, B. (2016). Reliabilist Epistemology. The Stanford Encyclopedia of Philosophy, Edward N. Zalta (ed.)

  25. 25.

    Halpern, J. (2004). Sleeping beauty reconsidered: conditioning and reflection in asynchronous systems. In Gendler, T.S., & Hawthorne, J. (Eds.) Proceedings of the twentieth conference on uncertainty in Ai (pp. 111–142): Oxford University Press.

  26. 26.

    Hintikka, J. (1962). Knowledge and belief. New York: Cornell University Press.

    Google Scholar 

  27. 27.

    Kremer, P., & Mints, G. (2005). Dynamic topological logic. Annals of Pure and Applied Logic, 131, 133–158.

    Article  Google Scholar 

  28. 28.

    Lyons, J. (2016). Epistemological Problems of Perception. The Stanford Encyclopedia of Philosophy.

  29. 29.

    Ichikawa, J.J., & Steup, M. (2018). The analysis of knowledge. The Stanford Encyclopedia of Philosophy (Summer 2018 Edition), Zalta, E.N. (ed.)

  30. 30.

    Littlejohn, C. (2009). The new evil demon problem. Internet Encyclopedia of Philosophy.

  31. 31.

    Littlejohn, C. (2013). No evidence is false. Acta Analytica, 28 (2), 145–159.

    Article  Google Scholar 

  32. 32.

    Miller, J.S., & Moss, L.S. (2005). The undecidability of iterated modal relativization. Studia Logica, 79(3), 373–407.

    Article  Google Scholar 

  33. 33.

    Nagel, J. (2013). Knowledge as a mental state. Oxford Studies in Epistemology, 4, 275–310.

    Google Scholar 

  34. 34.

    Neta, R. (2018). Your evidence is the set of facts that are manifest to you. In Mitova, V. (Ed.) The factive turn in epistemology (pp. 32–49). Cambridge: Cambridge University Press.

  35. 35.

    Okasha, S. (2013). On a flawed argument against the KK principle. Analysis, 73(1), 80–86.

    Article  Google Scholar 

  36. 36.

    Pettigrew, R. (2019). What is conditionalization, and why should we do it? Philosophical Studies: 1–37.

  37. 37.

    Pryor, J. (2013). Problems for Credulism. In Chris Tucker (Ed.) Seemings and justification: new essays on dogmatism and phenomenal conservatism.

  38. 38.

    Rizzieri, A. (2011). Evidence does not equal knowledge. Philosophical Studies, 153, 235–242.

    Article  Google Scholar 

  39. 39.

    Rott, H. (2004). Stability, strength and sensitivity: converting belief into knowledge. Erkenntnis, 61, 469–493.

    Article  Google Scholar 

  40. 40.

    Salow, B. (2018). The externalist’s guide to fishing for compliments. Mind, 127(507), 691–728.

    Article  Google Scholar 

  41. 41.

    Sietsma, F., & van Eijck, J. (2012). Action emulation between canonical models. In Proceedings of the 10th conference on logic and the foundations of game and decision theory (LOFT 10). Spain: Sevilla.

  42. 42.

    Stalnaker, R. (2006). On logics of knowledge and belief. Philosophical Studies, 128, 169–199.

    Article  Google Scholar 

  43. 43.

    Titelbaum, M.G. (2010). Tell me you love me: bootstrapping, externalism, and no-lose epistemology. Philosophical Studies, 149, 119–134.

    Article  Google Scholar 

  44. 44.

    Troquard, N., & Balbiani, P. (2019). Propositional dynamic logic. The stanford encyclopedia of philosophy (Spring 2019 Edition), Zalta, E.N. (ed.)

  45. 45.

    Vogel, J. (2000). Reliabilism leveled. The Journal of Philosophy, 97(1), 602–623.

    Article  Google Scholar 

  46. 46.

    Vogel, J. (2008). Epistemic bootstrapping. The Journal of Philosophy, 105(9), 518–539.

    Article  Google Scholar 

  47. 47.

    Wang, Y., Kuppusamy, L., & van Eijck, J. (2009). Verifying epistemic protocols under common knowledge. In TARK ’09, pp 257–266.

  48. 48.

    Wang, Y., & Cao, Q. (2013). On axiomatizations of public announcement logic. Synthese 190(S1).

  49. 49.

    Wang, Y. (2018). Beyond knowing that: a new generation of epistemic logics. In van Ditmarsch, H., & Sandu, G. (Eds.) Jaakko hintikka on knowledge and game theoretical semantics (pp. 499–533): Springer.

  50. 50.

    Weatherson, B. (2007). The bayesian and the dogmatist. Proceedings of the Aristotelian Society, 107, 169–185.

    Article  Google Scholar 

  51. 51.

    Weisberg, J. (2010). Bootstrapping in general. Philosophy and Phenomenological Research, 81(3), 525–548.

    Article  Google Scholar 

  52. 52.

    Weisberg, J. (2012). The bootstrapping problem. Philosophy Compass, 7(9), 597–610.

    Article  Google Scholar 

  53. 53.

    White, R. (2006). Problems for dogmatism. Philosophical Studies, 131(3), 525–557.

    Article  Google Scholar 

  54. 54.

    Williamson, T. (2000). Knowledge and its limits. Oxford: Oxford University Press.

    Google Scholar 

  55. 55.

    Williamson, T. (2013). Gettier cases in epistemic logic. Inquiry, 56, 1–14.

    Article  Google Scholar 

  56. 56.

    Williamson, T. (2014). Very improbable knowing. Erkenntnis, 79, 971–999.

    Article  Google Scholar 

  57. 57.

    Yap, A., & Hoshi, T. (2009). Dynamic epistemic logic and branching temporal structures. Synthese, 169, 259–281.

    Article  Google Scholar 

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