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  1. Frank Arntzenius (2003). Self-Locating Beliefs, Reflection, Conditionalization and Dutch Books. Journal of Philosophy 100:356-370.
  2. Frank Arntzenius (2003). Some Problems for Conditionalization and Reflection. Journal of Philosophy 100 (7):356-370.
  3. Paul Bartha, How to Put Self-Locating Information in its Place.
    How can self-locating propositions be integrated into normal patterns of belief revision? Puzzles such as Sleeping Beauty seem to show that such propositions lead to violation of ordinary principles for reasoning with subjective probability, such as Conditionalization and Reflection. I show that sophisticated forms of Conditionalization and Reflection are not only compatible with self-locating propositions, but also indispensable in understanding how they can function as evidence in Sleeping Beauty and similar cases.
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  4. Stephanie Beardman (2013). A Non-Factualist Defense of the Reflection Principle. Synthese 190 (15):2981-2999.
    Are there plausible synchronic constraints on how a subject thinks of herself extended over time? At first glance, Bas van Fraassen’s principle of Reflection seems to prescribe the sort of epistemic authority one’s future self should be taken by one to have over one’s current epistemic states. (The gist of this principle is that I should now believe what I’m convinced I will believe tomorrow.) There has been a general consensus that, as a principle concerning epistemic authority, Reflection does not (...)
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  5. Rachael Briggs (2009). Distorted Reflection. Philosophical Review 118 (1):59-85.
    Diachronic Dutch book arguments seem to support both conditionalization and Bas van Fraassen's Reflection principle. But the Reflection principle is vulnerable to numerous counterexamples. This essay addresses two questions: first, under what circumstances should an agent obey Reflection, and second, should the counterexamples to Reflection make us doubt the Dutch book for conditionalization? In response to the first question, this essay formulates a new "Qualified Reflection" principle, which states that an agent should obey Reflection only if he or she is (...)
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  6. John Cantwell (2002). The Pragmatic Stance. Croatian Journal of Philosophy 2 (3):319-336.
    The view that decision methods can only be justified by appeal to pragmatic considerations is defended. Pragmatic considerations are viewed as providing the underlying subject matter (“semantics”) of decision theories. It is argued that other approaches (e.g. justifying principles by appeal to obviousness, common usage, etc.) fail to provide grounds for a normative decision theory.It is argued that preferences that can lead to pragmatically adverse outcomes in a relevantly similar possible decision situation are pragmatically unsound, even if the decision situation (...)
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  7. Jake Chandler & Adam Rieger (2011). Self-Respect Regained. Proceedings of the Aristotelian Society 111 (2pt2):311-318.
    In a recent article, David Christensen casts aspersions on a restricted version of van Fraassen's Reflection principle, which he dubs ‘Self-Respect’(sr). Rejecting two possible arguments for sr, he concludes that the principle does not constitute a requirement of rationality. In this paper we argue that not only has Christensen failed to make a case against the aforementioned arguments, but that considerations pertaining to Moore's paradox indicate that sr, or at the very least a mild weakening thereof, is indeed a plausible (...)
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  8. David Christensen (2007). Epistemic Self-Respect. Proceedings of the Aristotelian Society 107 (1pt3):319-337.
  9. Kenny Easwaran (2013). Expected Accuracy Supports Conditionalization—and Conglomerability and Reflection. Philosophy of Science 80 (1):119-142.
  10. Adam Elga (2007). Reflection and Disagreement. Noûs 41 (3):478–502.
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  11. Simon J. Evnine (2007). Personhood and Future Belief: Two Arguments for Something Like Reflection. Erkenntnis 67 (1):91 - 110.
    This paper offers two new arguments for a version of Reflection, the principle that says, roughly, that if one knew now what one would believe in the future, one ought to believe it now. The most prominent existing argument for the principle is the coherence-based Dutch Strategy argument advanced by Bas van Fraassen (and others). My two arguments are quite different. The first is a truth-based argument. On the basis of two substantive premises, that people’s beliefs generally get better over (...)
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  12. Simon J. Evnine (2005). Containing Multitudes: Reflection, Expertise and Persons as Groups. Episteme 2 (1):57-64.
    The thesis of the paper is that persons are similar to a kind of group: multiple-expert epistemic unities (MEUs). MEUs are groups in which there are multiple experts on whom other members of the group model their opinion. An example would be a group of children playing Telephone. Any child nearer the source is an 'expert' for any child further away. I argue that, with certain important qualifications, it is both rational and necessary for persons to treat their future selves (...)
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  13. Simon J. Evnine (2003). Epistemic Unities. Erkenntnis 59 (3):365 - 388.
    I bring together social ontology and social epistemology by consideringsocial entities (``epistemic unities'') that are constituted by the holdingof epistemic relations between their members. In particular, I focus onthe relation of taking someone as an expert. Among the types of structuresexamined are ones with a single expert and one or more non-experts whomay or may not know of each other's situation; and ones with more thanone expert, including cases in which the relation between the experts ishierarchical and cases in which (...)
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  14. Christopher A. Fuchs & Rüdiger Schack (2012). Bayesian Conditioning, the Reflection Principle, and Quantum Decoherence. In. In Yemima Ben-Menahem & Meir Hemmo (eds.), Probability in Physics. Springer. 233--247.
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  15. Mitchell S. Green & Christopher R. Hitchcock (1994). Reflections on Reflection: Van Fraassen on Belief. Synthese 98 (2):297 - 324.
    In Belief and the Will, van Fraassen employed a diachronic Dutch Book argument to support a counterintuitive principle called Reflection. There and subsequently van Fraassen has put forth Reflection as a linchpin for his views in epistemology and the philosophy of science, and for the voluntarism (first-person reports of subjective probability are undertakings of commitments) that he espouses as an alternative to descriptivism (first-person reports of subjective probability are merely self-descriptions). Christensen and others have attacked Reflection, taking it to have (...)
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  16. Berry Groisman (2008). The End of Sleeping Beauty's Nightmare. British Journal for the Philosophy of Science 59 (3):409-416.
    The way a rational agent changes her belief in certain propositions/hypotheses in the light of new evidence lies at the heart of Bayesian inference. The basic natural assumption, as summarized in van Fraassen's Reflection Principle ([1984]), would be that in the absence of new evidence the belief should not change. Yet, there are examples that are claimed to violate this assumption. The apparent paradox presented by such examples, if not settled, would demonstrate the inconsistency and/or incompleteness of the Bayesian approach, (...)
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  17. Edward Hinchman (2012). Reflection, Disagreement, and Context. 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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  18. Brian Kierland, Bradley Monton & Samuel Ruhmkorff (2008). Avoiding Certain Frustration, Reflection, and the Cable Guy Paradox. 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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  19. Patrick Maher (1992). Diachronic Rationality. Philosophy of Science 59 (1):120-141.
    This is an essay in the Bayesian theory of how opinions should be revised over time. It begins with a discussion of the principle that van Fraassen has dubbed "Reflection". This principle is not a requirement of rationality; a diachronic Dutch argument, that purports to show the contrary, is fallacious. But under suitable conditions, it is irrational to actually implement shifts in probability that violate Reflection. Conditionalization and probability kinematics are special cases of the principle not to implement shifts that (...)
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  20. Anna Mahtani (2014). Dutch Books, Coherence, and Logical Consistency. Noûs 48 (3).
    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 (s)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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  21. Anna Mahtani (2012). Diachronic Dutch Book Arguments. 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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  22. Bradley Monton (2002). Sleeping Beauty and the Forgetful Bayesian. Analysis 62 (1):47–53.
    1. Consider the case of Sleeping Beauty: on Sunday she is put to sleep, and she knows that on Monday experimenters will wake her up, and then put her to sleep with a memory-erasing drug that causes her to forget that waking-up. The researchers will then flip a fair coin; if the result is Heads, they will allow her to continue to sleep, and if the result is Tails, they will wake her up again on Tuesday. Thus, when she is (...)
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  23. Ilho Park (2012). Rescuing Reflection. Philosophy of Science 79 (4):473-489.
    In this article, I suggest an argument that seems to show a conflict between the reflection principle and conditionalization. In particular, I show that when the reflection principle is formulated in a standard way, the principle conflicts with Jeffrey conditionalization. And it is argued that the source of the conflict resides in an ambiguity of the standard formulation. Furthermore, I attempt to rescue the principle using Bayes factors. That is, I suggest a new formulation of the principle so as to (...)
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  24. Wlodek Rabinowicz (2006). Levi on Money Pumps and Diachronic Dutch Books. In Erik J. Olsson (ed.), Knowledge and Inquiry: Essays on the Pragmatism of Isaac Levi. Cambridge University Press.
    The paper's focus is on pragmatic arguments for various ‘rationality constraints’ on a decision maker’s state of mind: on his beliefs or preferences. An argument of this kind purports to show that a violator of a given constraint can be exposed to a decision problem in which he will act to his guaranteed disadvantage. Dramatically put, he can be exploited by a clever bookie who doesn’t know more than the agent himself. Examples of pragmatic arguments of this kind are synchronic (...)
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  25. Wlodek Rabinowicz & Luc Bovens (2011). Bets on Hats: On Dutch Books Against Groups, Degrees of Belief as Betting Rates, and Group-Reflection. Episteme 8 (3):281-300.
    The Story of the Hats is a puzzle in social epistemology. It describes a situation in which a group of rational agents with common priors and common goals seems vulnerable to a Dutch book if they are exposed to different information and make decisions independently. Situations in which this happens involve violations of what might be called the Group-Reflection Principle. As it turns out, the Dutch book is flawed. It is based on the betting interpretation of the subjective probabilities, but (...)
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  26. James H. Schmerl (1995). A Reflection Principle and its Applications to Nonstandard Models. Journal of Symbolic Logic 60 (4):1137-1152.
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  27. Michael J. Shaffer (2014). Reflection, Conditionalization and Indeterminacy About the Future. 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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  28. W. J. Talbott (1991). Two Principles of Bayesian Epistemology. Philosophical Studies 62 (2):135-150.
  29. B. Topey (2012). Coin Flips, Credences and the Reflection Principle. 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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  30. Soshichi Uchii (1973). Higher Order Probabilities and Coherence. Philosophy of Science 40 (3):373-381.
    It is well known that a degree-of-belief function P is coherent if and only if it satisfies the probability calculus. In this paper, we show that the notion of coherence can be extended to higher order probabilities such as P(P(h)=p)=q, and that a higher order degree-of-belief function P is coherent if and only if it satisfies the probability calculus plus the following axiom: P(h)=p iff P(P(h)=p)=1. Also, a number of lemmata which extend an incomplete probability function to a complete one (...)
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  31. Bas C. van Fraassen (2010). Belief and the Will. In Antony Eagle (ed.), Philosophy of Probability: Contemporary Readings. Routledge. 235-256.
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  32. Bas C. Van Fraassen (1999). A New Argument for Conditionalization. Topoi 18:93-96.
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  33. Bas C. van Fraassen (1995). Belief and the Problem of Ulysses and the Sirens. Philosophical Studies 77 (1):7-37.
    This is surely a bit of Socrates' famous irony. He draws the analogy to explain how his friends should regard poetry as they regretfully banish it from the ideal state. But lovers were no more sensible then than they are now. The advice to banish poetry, undermined already by Plato's own delight and skill in drama, is perhaps undermined still further by this evocation of a 'sensible' lover who counts love so well lost. Yet Socrates' image is one of avowed (...)
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  34. Rineke Verbrugge & Albert Visser (1994). A Small Reflection Principle for Bounded Arithmetic. 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. Jonathan Weisberg, Conditionalization Without Reflection.
    Conditionalization is an intuitive and popular epistemic principle. By contrast, the Reflection principle is well known to have some very unappealing consequences. But van Fraassen argues that Conditionalization entails Reflection, so that proponents of Conditionalization must accept Reflection and its consequences. Van Fraassen also argues that Reflection implies Conditionalization, thus offering a new justification for Conditionalization. I argue that neither principle entails the other, and thus neither can be used to motivate the other in the way van Fraassen says. I (...)
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  36. Timothy Williamson (2000). Knowledge and its Limits. Oxford University Press.
    Knowledge and its Limits presents a systematic new conception of knowledge as a kind of mental stage sensitive to the knower's environment. It makes a major contribution to the debate between externalist and internalist philosophies of mind, and breaks radically with the epistemological tradition of analyzing knowledge in terms of true belief. The theory casts new light on such philosophical problems as scepticism, evidence, probability and assertion, realism and anti-realism, and the limits of what can be known. The arguments are (...)
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