The problem of perception and the no-miracles principle


The problem of perception is the problem of explaining how perceptual knowledge is possible. The skeptic has a simple solution: it is not possible. I analyze the weaknesses of one type of skeptical reasoning by making explicit a dynamic (or diachronic) epistemic principle from dynamic epistemic logic that is implicitly used in debating the problem, with the aim of offering a novel diagnosis to this skeptical argument. I argue (i) that prominent modest foundationalist responses to perceptual skepticism can be understood as rejecting the dynamic assumption made by the skeptic, (ii) that there are independent reasons to doubt the truth of such a principle in the context of skeptical reasoning, and (iii) that making the dynamic principle explicit allows for a better understanding of at least one objection to modest foundationalism.

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  1. 1.

    The answer to the question what counts as an epistemic event for an agent will depend in general on context. For example, in the context of a game of perfect information, the event of one player playing their turn will count as an epistemic event for the players of the game, as we assume (in such context) that all players are perfectly informed about every turn in the game. The same event might not be an epistemic event for a different agent who is not part of the game.

  2. 2.

    The connection I draw here between the No-Miracles principle and surprise is not meant to be an exhaustive account of surprise in epistemic logic. For different types of analyses of surprise in epistemic logic, see Lorini and Castelfranchi (2007), Demey (2015) and Vignero and Demey (2020).

  3. 3.

    The principle should not be associated with the no miracles argument from philosophy of science, nor with any other philosophical discussion about miracles for that matter. For a review of the principle in epistemic logic, see van Benthem et al. (2009), van Benthem (2012), and Wang and Cao (2013). For its role in game theory, see van Benthem and Klein (2019). It is worth noting that NM is the converse of a more familiar diachronic principle, known as Perfect-Recall, which can be stated as \(KE \varphi \rightarrow EK \varphi \). Versions of No-Miracles and Perfect-Recall can be used as axioms of the dynamic epistemic logic Public announcement logic (PAL). This alternative axiomatization is studied and compared to the standard reduction axioms of PAL in Wang and Cao (2013).

  4. 4.

    By using the expression being in a position to know we just guard against counterexamples to the NM principle that are based on the cognitive limitations of actual human subjects. If someone is distracted or not paying attention, they might not know \(\varphi \), even if they are in a position to know \(\varphi \). The way I use this term follows Williamson’s usage, according to which “If one is in a position to know p, and one has done what one is in a position to do to decide whether p is true, then one does know p” (2000: p 95).

  5. 5.

    Since much of this paper criticizes an unqualified NM principle, it is most charitable to consider the weakest interpretation of it.

  6. 6.

    Things are more complicated. Agents might be ‘surprised’ when we consider (i) Jeffrey conditionalization instead of standard conditionalization and (ii) when updating on event with probability 0 occurs. See Joyce (2003) for some overview.

  7. 7.

    Failures of the NM principle can lead to the failure of the probabilistic diachronic reflection principle (Briggs 2009; Arntzenius 2003). Informally, you might be uncertain whether your future self is more informed than your current self, even if your future self is indeed more informed. In such cases both NM and diachronic reflection will fail. Counterexamples to diachronic reflection are more familiar, however, when a different diachronic introspection principle fails, namely Perfect-Recall.

  8. 8.

    We do not assume here that the dependency between the event and Alice’s epistemic state can be completely analyzed in causal terms.

  9. 9.

    For a concrete example, consider the tic-tac-toe game from before. Even if in fact both players will never touch the board again , it is still the case that \(E K_O (\text {O can immediately win})\), where E is the event X plays bottom left. Thus, E should not be understood as denoting a particular moment in time. E is not a temporal modality per-se.

  10. 10.

    He also considers a more basic principle, the Indirectness principle, stating that nothing is directly presented to the mind. See the discussion in Lyons 2016: sec 1.

  11. 11.

    More accurately, we should distinguish between the event exp(p) and the propositional operator [exp(p)]. exp(p) just abbreviates the event of having the experience as of p; the propositional operator [exp(p)] allows us to formulate what happens as a result of the update.

  12. 12.

    Some coherentist and conservative responses to perceptual skepticism can be characterized as rejecting the Reasons claim. See Lyons (2016) for this path.

  13. 13.

    There is nothing implausible about the conjunction \(\lnot K [exp(p)]p \wedge [exp(p)]Kp\) from the perspective of epistemic logic. If we let [exp(p)] stand for the radical upgrade operator \([\Uparrow p]\) from dynamic epistemic logic (Baltag and Smets 2008; van Benthem 2012), and if we interpret K as the S4 defeasible knowledge operator of Baltag and Smets (2008), then such a conjunction is indeed satisfiable. See van Benthem (2012), Baltag and Smets (2008), Baltag and Renne (2016), for more about such formal systems.

  14. 14.

    See Lyons (2016: sec 3.4.2)

  15. 15.

    Fixing a context is important. Let \(E'\) be the experience of a hand in the epistemologically bad case, and E the experience of hand in the good case. Of course I can distinguish between E and \(E'\) in a context in which they are described the way I just described them: one is the good case, the other is the bad case. But there are other contexts in which I cannot distinguish between the two.

  16. 16.

    For suppose that there is a property P s.t. the agent knows that E has P while they do not know that \(E'\) has P. Then the agent’s epistemic state is (or evidence) makes a distinction between the two, contrary to what we assumed.

  17. 17.

    For further discussion, see Weatherson (2007), Pryor (2013), Miller (2016).

  18. 18.

    Of course, Bayesian epistemologists do offer arguments in favor of the norm of conditionalization (and so implicitly to NM), most prominently diachronic Dutch book arguments (Lewis 1999; van Fraassen 1984). The acceptance of NM is well motivated in certain Bayesian contexts.

  19. 19.

    Unlike Williamson (2000: ch 7), the account I present here does not involve the failure of the KK principle. The dynamic (or diachronic) dimension of the epistemology of perception I focus on is logically independent of the static (or synchronic) dimension of one’s higher-order mental states at a given time, which is the focus of the KK principle.

  20. 20.

    Logically, the connection between static and dynamic introspection runs deeper. In the possible world semantics of modal logic, assuming that the agent has full static introspection (i.e. both positive and negative introspection) amounts to the assumption that the set of worlds epistemically open to the agent is constant across the worlds the agent considers possible. Since that set is constant, the agent has no uncertainty about what they know. Similarly, assuming full dynamic introspection in the possible worlds semantics amounts to the assumption that the result of any given update is the same (i.e. constant) across the worlds in the model. Since the result of the update is constant across possible worlds, the agent has no uncertainty as to the effect of the update, and we can consider it transparent. For a logical framework for reasoning about failures of dynamic introspection, see Cohen (2020a). For more on the connection between the failure of static and dynamic introspection, see Cohen (2020b).


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I would like to thank Johan van Benthem, Ray Briggs, Krista Lawlor, the participants of the Stanford GSW, and two anonymous referees of this journal for many helpful comments, suggestions and corrections on earlier versions of this article.

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Correspondence to Michael Cohen.

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Cohen, M. The problem of perception and the no-miracles principle. Synthese (2020).

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  • Perceptual skepticism
  • Modest foundationalism
  • Dogmatism
  • Externalism
  • Disjunctivism
  • Introspection principles
  • Dynamic epistemic logic