The Reflection Principle

Edited by Anna Mahtani (London School of Economics, London School of Economics And Political Science)
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  1. Too clever by halving.Tim Button, Daniel Rothschild & Levi Spectre - manuscript
    We argue against the halving response to Sleeping Beauty. First, we outline an appealing constraint on probability assignments: the Principle of Irrelevant Information. Roughly, this says: if you don’t know whether C, but you would assign probability p to X regardless of whether C or not-C, then you should assign p to X. This Principle is deeply plausible, but we show that it contradicts halving. Second, we show that halving either violates solid statistical reasoning or draws absurd distinctions.
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  2. Revealing the Beauty behind the Sleeping Beauty Problem.Ioannis Mariolis - manuscript
    A large number of essays address the Sleeping Beauty problem, which undermines the validity of Bayesian inference and Bas Van Fraassen's 'Reflection Principle'. In this study a straightforward analysis of the problem based on probability theory is presented. The key difference from previous works is that apart from the random experiment imposed by the problem's description, a different one is also considered, in order to negate the confusion on the involved conditional probabilities. The results of the analysis indicate that no (...)
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  3. Random and Systematic Error in the Puzzle of the Unmarked Clock.Randall G. McCutcheon - manuscript
    A puzzle of an unmarked clock, used by Timothy Williamson to question the KK principle, was separately adapted by David Christensen and Adam Elga to critique a principle of Rational Reflection. Both authors, we argue, flout the received relationship between ideal agency and the classical distinction between systematic and random error, namely that ideal agents are subject only to the latter. As a result, these criticisms miss their mark.
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  4. A Liar-Like Paradox for Rational Reflection Principles.Joshua Schechter - forthcoming - Analysis.
    This article shows that there is a liar-like paradox that arises for rational credence that relies only on very weak logical and credal principles. The paradox depends on a weak rational reflection principle, logical principles governing conjunction, and principles governing the relationship between rational credence and proof. To respond to this paradox, we must either reject even very weak rational reflection principles or reject some highly plausible logical or credal principle.
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  5. Epistemic characterizations of validity and level-bridging principles.Joshua Schechter - 2024 - Philosophical Studies 181 (1):153-178.
    How should we understand validity? A standard way to characterize validity is in terms of the preservation of truth (or truth in a model). But there are several problems facing such characterizations. An alternative approach is to characterize validity epistemically, for instance in terms of the preservation of an epistemic status. In this paper, I raise a problem for such views. First, I argue that if the relevant epistemic status is factive, such as being in a position to know or (...)
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  6. Rational Polarization.Kevin Dorst - 2023 - Philosophical Review 132 (3):355-458.
    Predictable polarization is everywhere: we can often predict how people’s opinions, including our own, will shift over time. Extant theories either neglect the fact that we can predict our own polarization, or explain it through irrational mechanisms. They needn’t. Empirical studies suggest that polarization is predictable when evidence is ambiguous, that is, when the rational response is not obvious. I show how Bayesians should model such ambiguity and then prove that—assuming rational updates are those which obey the value of evidence—ambiguity (...)
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  7. Local and global deference.J. Dmitri Gallow - 2023 - Philosophical Studies 180 (9):2753-2770.
    A norm of local expert deference says that your credence in an arbitrary proposition A, given that the expert's probability for A is n, should be n. A norm of global expert deference says that your credence in A, given that the expert's entire probability function is E, should be E(A). Gaifman (1988) taught us that these two norms are not equivalent. Stalnaker (2019) conjectures that Gaifman's example is "a loophole". Here, I substantiate Stalnaker's suspicions by providing characterisation theorems which (...)
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  8. Bayesian updating when what you learn might be false.Richard Pettigrew - 2023 - Erkenntnis 88 (1):309-324.
    Rescorla (Erkenntnis, 2020) has recently pointed out that the standard arguments for Bayesian Conditionalization assume that whenever I become certain of something, it is true. Most people would reject this assumption. In response, Rescorla offers an improved Dutch Book argument for Bayesian Conditionalization that does not make this assumption. My purpose in this paper is two-fold. First, I want to illuminate Rescorla’s new argument by giving a very general Dutch Book argument that applies to many cases of updating beyond those (...)
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  9. Bounded Reflectivism and Epistemic Identity.Nick Byrd - 2022 - Metaphilosophy 53 (1):53-69.
    Reflectivists consider reflective reasoning crucial for good judgment and action. Anti-reflectivists deny that reflection delivers what reflectivists seek. Alas, the evidence is mixed. So, does reflection confer normative value or not? This paper argues for a middle way: reflection can confer normative value, but its ability to do this is bound by such factors as what we might call epistemic identity: an identity that involves particular beliefs—for example, religious and political identities. We may reflectively defend our identities’ beliefs rather than (...)
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  10. Be modest: you're living on the edge.Kevin Dorst - 2022 - Analysis 81 (4):611-621.
    Many have claimed that whenever an investigation might provide evidence for a claim, it might also provide evidence against it. Similarly, many have claimed that your credence should never be on the edge of the range of credences that you think might be rational. Surprisingly, both of these principles imply that you cannot rationally be modest: you cannot be uncertain what the rational opinions are.
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  11. Comparative Opinion Loss.Benjamin Eva & Reuben Stern - 2022 - Philosophy and Phenomenological Research 107 (3):613-637.
    It is a consequence of the theory of imprecise credences that there exist situations in which rational agents inevitably become less opinionated toward some propositions as they gather more evidence. The fact that an agent's imprecise credal state can dilate in this way is often treated as a strike against the imprecise approach to inductive inference. Here, we show that dilation is not a mere artifact of this approach by demonstrating that opinion loss is countenanced as rational by a substantially (...)
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  12. Accuracy-First Epistemology Without Additivity.Richard Pettigrew - 2022 - Philosophy of Science 89 (1):128-151.
    Accuracy arguments for the core tenets of Bayesian epistemology differ mainly in the conditions they place on the legitimate ways of measuring the inaccuracy of our credences. The best existing arguments rely on three conditions: Continuity, Additivity, and Strict Propriety. In this paper, I show how to strengthen the arguments based on these conditions by showing that the central mathematical theorem on which each depends goes through without assuming Additivity.
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  13. Transformative Experience, Awareness Growth, and the Limits of Rational Planning.Katie Steele & H. Orri Stefánsson - 2022 - Philosophy of Science 89 (5):939-948.
    Laurie Paul argues that, when it comes to many of your most significant life-changing decisions, the principles of rational choice are silent. That is because, in these cases, you anticipate that one of your choice options would yield a transformative experience. We argue that such decisions are best seen as ones in which you anticipate awareness growth. You do not merely lack knowledge about which possible outcome will arise from a transformative option; you lack knowledge about what are the possible (...)
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  14. Deference Done Better.Kevin Dorst, Benjamin A. Levinstein, Bernhard Salow, Brooke E. Husic & Branden Fitelson - 2021 - Philosophical Perspectives 35 (1):99-150.
    There are many things—call them ‘experts’—that you should defer to in forming your opinions. The trouble is, many experts are modest: they’re less than certain that they are worthy of deference. When this happens, the standard theories of deference break down: the most popular (“Reflection”-style) principles collapse to inconsistency, while their most popular (“New-Reflection”-style) variants allow you to defer to someone while regarding them as an anti-expert. We propose a middle way: deferring to someone involves preferring to make any decision (...)
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  15. Dutch Books and Logical Form.Joel Pust - 2021 - Philosophy of Science 88 (5):961-970.
    Dutch Book Arguments (DBAs) have been invoked to support various requirements of rationality. Some are plausible: probabilism and conditionalization. Others are less so: credal transparency and reflection. Anna Mahtani has argued for a new understanding of DBAs which, she claims, allow us to keep the DBAs for probabilism (and perhaps conditionalization) and reject the DBAs for credal transparency and reflection. I argue that Mahtani’s new account fails as (a) it does not support highly plausible requirements of rational coherence and (b) (...)
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  16. Bayesian Beauty.Silvia Milano - 2020 - Erkenntnis 87 (2):657-676.
    The Sleeping Beauty problem has attracted considerable attention in the literature as a paradigmatic example of how self-locating uncertainty creates problems for the Bayesian principles of Conditionalization and Reflection. Furthermore, it is also thought to raise serious issues for diachronic Dutch Book arguments. I show that, contrary to what is commonly accepted, it is possible to represent the Sleeping Beauty problem within a standard Bayesian framework. Once the problem is correctly represented, the ‘thirder’ solution satisfies standard rationality principles, vindicating why (...)
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  17. Evidence: A Guide for the Uncertain.Kevin Dorst - 2019 - Philosophy and Phenomenological Research 100 (3):586-632.
    Assume that it is your evidence that determines what opinions you should have. I argue that since you should take peer disagreement seriously, evidence must have two features. (1) It must sometimes warrant being modest: uncertain what your evidence warrants, and (thus) uncertain whether you’re rational. (2) But it must always warrant being guided: disposed to treat your evidence as a guide. Surprisingly, it is very difficult to vindicate both (1) and (2). But diagnosing why this is so leads to (...)
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  18. Basic‐Know And Super‐Know.Anna Mahtani - 2019 - Philosophy and Phenomenological Research 98 (2):375-391.
    Sometimes a proposition is ‘opaque’ to an agent: he doesn't know it, but he does know something about how coming to know it should affect his or her credence function. It is tempting to assume that a rational agent's credence function coheres in a certain way with his or her knowledge of these opaque propositions, and I call this the ‘Opaque Proposition Principle’. The principle is compelling but demonstrably false. I explain this incongruity by showing that the principle is ambiguous: (...)
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  19. Идентификация сегментов матрицы: два плана рефлексии.Vitalii Shymko - 2019 - Pro|Stranstvo.
    Публикация (#6) из научно-популярного цикла: "Структурная онтология познания с доктором Шимко".
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  20. Examinei Live: An Epistemological Exchange Between Philosophy and Cultural Psychology on Reflection.Waldomiro Silva Filho - 2019 - In W. & Tateo Silva-Filho (ed.), Thinking about Oneself. Chan, Switzerland: Springer. pp. 1-18.
    Since the famous passage in which Socrates (Plato 38a5-6) says that the unexamined, and therefore non-reflected, life is not worth living, “reflection” has been a diffuse and iterant term in ethics, moral philosophy, epistemology, political philosophy (Tiberius 2008; Skorupski 2010), but also in psychology (Marsico, Andrisano Ruggieri & Salvatore 2015). This chapter outlines the discussion of reflection and presents the book "Thinking about Onself", a volume that opens a new perspective on the topic of reflection, considering the most recent approaches (...)
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  21. Chance, Credence and Circles.Fabrizio Cariani - 2017 - Episteme 14 (1):49-58.
    This is a discussion of Richard Pettigrew's book "Accuracy and the Laws of Credence". I target Pettigrew's application of the accuracy framework to derive chance-credence principles. My principal contention is that Pettigrew's preferred version of the argument might in one sense be circular and, moreover, that Pettigrew's premises have content that go beyond that of standard chance-credence principles.
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  22. Dutch Books, Coherence, and Logical Consistency.Anna Mahtani - 2015 - Noûs 49 (3):522-537.
    In this paper I present a new way of understanding Dutch Book Arguments: the idea is that an agent is shown to be incoherent iff he would accept as fair a set of bets that would result in a loss under any interpretation of the claims involved. This draws on a standard definition of logical inconsistency. On this new understanding, the Dutch Book Arguments for the probability axioms go through, but the Dutch Book Argument for Reflection fails. The question of (...)
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  23. In Search of Enlightenment by Reading Samuel Beckett’s Waiting for Godot.Syed Ismyl Mahmood Rizvi - 2015 - Literaria: An International Journal of New Literature Across the World 5 (1-2):37-55.
    Beckett’s philosophical indebtedness has long been recognised – especially in conjunction with Dante, Descartes and Geulincx. In this article, I examine Beckettian universal values of Enlightenment, which will be exposed as self-serving mystifications that rationalize and instrumentalize the meaning of life. In this context, the awareness of the Enlightenment nature of Beckett’s writing in Waiting for Godot will be analysed along with the freedom appeal of his reader as he strives to attain the enlightenment.
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  24. Reflection, Conditionalization and Indeterminacy about the Future.Michael J. Shaffer - 2014 - The Reasoner 8:65-66.
    This paper shows that any view of future contingent claims that treats such claims as having indeterminate truth values or as simply being false implies probabilistic irrationality. This is because such views of the future imply violations of reflection, special reflection and conditionalization.
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  25. Bayesian conditioning, the reflection principle, and quantum decoherence.Christopher A. Fuchs & Rüdiger Schack - 2012 - In Yemima Ben-Menahem & Meir Hemmo (eds.), Probability in Physics. Springer. pp. 233--247.
    The probabilities a Bayesian agent assigns to a set of events typically change with time, for instance when the agent updates them in the light of new data. In this paper we address the question of how an agent's probabilities at different times are constrained by Dutch-book coherence. We review and attempt to clarify the argument that, although an agent is not forced by coherence to use the usual Bayesian conditioning rule to update his probabilities, coherence does require the agent's (...)
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  26. Reflection, Disagreement, and Context.Edward Hinchman - 2012 - American Philosophical Quarterly 49 (2):95.
    How far, if at all, do our intrapersonal and our interpersonal epistemic obligations run in parallel? This paper treats the question as addressing the stability of doxastic commitment in the two dimensions. In the background lies an analogy between doxastic and practical commitment. We’ll pursue the question of doxastic stability by coining a doxastic analogue of Gregory Kavka’s much-discussed toxin case. In this new case, you foresee that you will rationally abandon a doxastic commitment by undergoing a shift in the (...)
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  27. Diachronic Dutch Book Arguments.Anna Mahtani - 2012 - Philosophical Review 121 (3):443-450.
    The Reflection Principle can be defended with a Diachronic Dutch Book Argument (DBA), but it is also defeated by numerous compelling counter-examples. It seems then that Diachronic DBAs can lead us astray. Should we reject them en masse—including Lewis’s Diachronic DBA for Conditionalization? Rachael Briggs’s “suppositional test” is supposed to differentiate between Diachronic DBAs that we can safely ignore (including the DBA for Reflection) and Diachronic DBAs that we should find compelling (including the DBA for Conditionalization). I argue that Brigg’s (...)
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  28. Coin flips, credences and the Reflection Principle.Brett Topey - 2012 - Analysis 72 (3):478-488.
    One recent topic of debate in Bayesian epistemology has been the question of whether imprecise credences can be rational. I argue that one account of imprecise credences, the orthodox treatment as defended by James M. Joyce, is untenable. Despite Joyce’s claims to the contrary, a puzzle introduced by Roger White shows that the orthodox account, when paired with Bas C. van Fraassen’s Reflection Principle, can lead to inconsistent beliefs. Proponents of imprecise credences, then, must either provide a compelling reason to (...)
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  29. Rational Reflection.David Christensen - 2010 - Philosophical Perspectives 24 (1):121-140.
    This paper explores an initially attractive principle connecting beliefs in general with beliefs about what beliefs are rational. The principle turns out to be violated by intuitively rational beliefs in some situations. The paper lays out some options for reacting to this fact.
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  30. Avoiding certain frustration, reflection, and the cable guy paradox.Brian Kierland, Bradley Monton & Samuel Ruhmkorff - 2008 - Philosophical Studies 138 (3):317 - 333.
    We discuss the cable guy paradox, both as an object of interest in its own right and as something which can be used to illuminate certain issues in the theories of rational choice and belief. We argue that a crucial principle—The Avoid Certain Frustration (ACF) principle—which is used in stating the paradox is false, thus resolving the paradox. We also explain how the paradox gives us new insight into issues related to the Reflection principle. Our general thesis is that principles (...)
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  31. Epistemic Self-respect.David Christensen - 2007 - Proceedings of the Aristotelian Society 107 (1pt3):319-337.
    Certain situations seem to call for acknowledging the possibility that one’s own beliefs are biased or distorted. On the other hand, certain sorts of epistemic self-doubts (such as ‘I believe it’s raining, but it’s not’) seem paradoxical. And some have put forth epistemic principles requiring rational agents to regard their own credences as so-called ‘expert functions’. This paper examines the question of whether rationality requires agents to respect their own credences in a way in which they need not respect the (...)
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  32. Sleeping beauty and the forgetful bayesian.Bradley Monton - 2002 - Analysis 62 (1):47–53.
    Adam Elga takes the Sleeping Beauty example to provide a counter-example to Reflection, since on Sunday Beauty assigns probability 1/2 to H, and she is certain that on Monday she will assign probability 1/3. I will show that there is a natural way for Bas van Fraassen to defend Reflection in the case of Sleeping Beauty, building on van Fraassen’s treatment of forgetting. This will allow me to identify a lacuna in Elga’s argument for 1/3. I will then argue, however, (...)
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  33. Dutch-book arguments depragmatized: Epistemic consistency for partial believers.David Christensen - 1996 - Journal of Philosophy 93 (9):450-479.
    The most immediately appealing model for formal constraints on degrees of belief is provided by probability theory, which tells us, for instance, that the probability of P can never be greater than that of (P v Q). But while this model has much intuitive appeal, many have been concerned to provide arguments showing that ideally rational degrees of belief would conform to the calculus of probabilities. The arguments most frequently used to make this claim plausible are the so-called "Dutch Book" (...)
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  34. A small reflection principle for bounded arithmetic.Rineke Verbrugge & Albert Visser - 1994 - Journal of Symbolic Logic 59 (3):785-812.
    We investigate the theory IΔ 0 + Ω 1 and strengthen [Bu86. Theorem 8.6] to the following: if NP ≠ co-NP. then Σ-completeness for witness comparison formulas is not provable in bounded arithmetic. i.e. $I\delta_0 + \Omega_1 + \nvdash \forall b \forall c (\exists a(\operatorname{Prf}(a.c) \wedge \forall = \leq a \neg \operatorname{Prf} (z.b))\\ \rightarrow \operatorname{Prov} (\ulcorner \exists a(\operatorname{Prf}(a. \bar{c}) \wedge \forall z \leq a \neg \operatorname{Prf}(z.\bar{b})) \urcorner)).$ Next we study a "small reflection principle" in bounded arithmetic. We prove that for (...)
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  35. Clever bookies and coherent beliefs.David Christensen - 1991 - Philosophical Review 100 (2):229-247.
    A critical examination of the Reflection principle in Bayesian epistemology, and of the diachronic Dutch-book-style arguments that have been invoked to support Reflection and Conditionalization.
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  36. Is there a dutch book argument for probability kinematics?Brad Armendt - 1980 - Philosophy of Science 47 (4):583-588.
    Dutch Book arguments have been presented for static belief systems and for belief change by conditionalization. An argument is given here that a rule for belief change which under certain conditions violates probability kinematics will leave the agent open to a Dutch Book.
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