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  1. Frank Arntzenius, Adam Elga & and John Hawthorne (2004). Bayesianism, Infinite Decisions, and Binding. Mind 113 (450):251-283.
    We pose and resolve several vexing decision theoretic puzzles. Some are variants of existing puzzles, such as ‘Trumped’ (Arntzenius and McCarthy 1997), ‘Rouble trouble’ (Arntzenius and Barrett 1999), ‘The airtight Dutch book’ (McGee 1999), and ‘The two envelopes puzzle’ (Broome 1999). Others are new. A unified resolution of the puzzles shows that Dutch book arguments have no force in infinite cases. It thereby provides evidence that reasonable utility functions may be unbounded and that reasonable credence functions need not be countably (...)
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  2. Andrew Bacon (2014). Giving Your Knowledge Half a Chance. Philosophical Studies (2):1-25.
    One thousand fair causally isolated coins will be independently flipped tomorrow morning and you know this fact. I argue that the probability, conditional on your knowledge, that any coin will land tails is almost 1 if that coin in fact lands tails, and almost 0 if it in fact lands heads. I also show that the coin flips are not probabilistically independent given your knowledge. These results are uncomfortable for those, like Timothy Williamson, who take these probabilities to play a (...)
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  3. Marc Burock, Indifference, Sample Space, and the Wine/Water Paradox.
    Von Mises’ wine/water paradox has served as a foundation for detractors of the Principle of Indifference and logical probability. Mikkelson recently proposed a first solution, and here several additional solutions to the paradox are explained. Learning from the wine/water paradox, I will argue that it is meaningless to consider a particular probability apart from the sample space containing the probabilistic event in question.
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  4. Marc Burock, An Outcome of the de Finetti Infinite Lottery is Not Finite.
    A randomly selected number from the infinite set of positive integers—the so-called de Finetti lottery—will not be a finite number. I argue that it is still possible to conceive of an infinite lottery, but that an individual lottery outcome is knowledge about set-membership and not element identification. Unexpectedly, it appears that a uniform distribution over a countably infinite set has much in common with a continuous probability density over an uncountably infinite set.
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  5. Jake Chandler (2007). Solving the Tacking Problem with Contrast Classes. British Journal for the Philosophy of Science 58 (3):489 - 502.
    The traditional Bayesian qualitative account of evidential support (TB) takes assertions of the form 'E evidentially supports H' to affirm the existence of a two-place relation of evidential support between E and H. The analysans given for this relation is $C(H,E) =_{def} Pr(H\arrowvertE) \models Pr(H)$ . Now it is well known that when a hypothesis H entails evidence E, not only is it the case that C(H,E), but it is also the case that C(H&X,E) for any arbitrary X. There is (...)
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  6. Cian Dorr (2010). The Eternal Coin: A Puzzle About Self-Locating Conditional Credence. Philosophical Perspectives 24 (1):189-205.
    The Eternal Coin is a fair coin has existed forever, and will exist forever, in a region causally isolated from you. It is tossed every day. How confident should you be that the Coin lands heads today, conditional on (i) the hypothesis that it has landed Heads on every past day, or (ii) the hypothesis that it will land Heads on every future day? I argue for the extremely counterintuitive claim that the correct answer to both questions is 1.
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  7. I. Douven (2012). The Sequential Lottery Paradox. Analysis 72 (1):55-57.
    The Lottery Paradox is generally thought to point at a conflict between two intuitive principles, to wit, that high probability is sufficient for rational acceptability, and that rational acceptability is closed under logical derivability. Gilbert Harman has offered a solution to the Lottery Paradox that allows one to stick to both of these principles. The solution requires the principle that acceptance licenses conditionalization. The present study shows that adopting this principle alongside the principle that high probability is sufficient for rational (...)
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  8. Igor Douven (2012). The Lottery Paradox and the Pragmatics of Belief. Dialectica 66 (3):351-373.
    The thesis that high probability suffices for rational belief, while initially plausible, is known to face the Lottery Paradox. The present paper proposes an amended version of that thesis which escapes the Lottery Paradox. The amendment is argued to be plausible on independent grounds.
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  9. Simone Duca & Hannes Leitgeb (2012). How Serious Is the Paradox of Serious Possibility? Mind 121 (481):1-36.
    The so-called Paradox of Serious Possibility is usually regarded as showing that the standard axioms of belief revision do not apply to belief sets that are introspectively closed. In this article we argue to the contrary: we suggest a way of dissolving the Paradox of Serious Possibility so that introspective statements are taken to express propositions in the standard sense, which may thus be proper members of belief sets, and accordingly the normal axioms of belief revision apply to them. Instead (...)
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  10. Alan Hájek & Michael Smithson (2012). Rationality and Indeterminate Probabilities. Synthese 187 (1):33-48.
    We argue that indeterminate probabilities are not only rationally permissible for a Bayesian agent, but they may even be rationally required . Our first argument begins by assuming a version of interpretivism: your mental state is the set of probability and utility functions that rationalize your behavioral dispositions as well as possible. This set may consist of multiple probability functions. Then according to interpretivism, this makes it the case that your credal state is indeterminate. Our second argument begins with our (...)
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  11. Ned Hall (1999). How to Set a Surprise Exam. Mind 108 (432):647-703.
    The professor announces a surprise exam for the upcoming week; her clever student purports to demonstrate by reductio that she cannot possibly give such an exam. Diagnosing his puzzling argument reveals a deeper puzzle: Is the student justified in believing the announcement? It would seem so, particularly if the upcoming 'week' is long enough. On the other hand, a plausible principle states that if, at the outset, the student is justified in believing some proposition, then he is also justified in (...)
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  12. James Hawthorne & Luc Bovens (1999). The Preface, the Lottery, and the Logic of Belief. Mind 108 (430):241-264.
    John Locke proposed a straightforward relationship between qualitative and quantitative doxastic notions: belief corresponds to a sufficiently high degree of confidence. Richard Foley has further developed this Lockean thesis and applied it to an analysis of the preface and lottery paradoxes. Following Foley's lead, we exploit various versions of these paradoxes to chart a precise relationship between belief and probabilistic degrees of confidence. The resolutions of these paradoxes emphasize distinct but complementary features of coherent belief. These features suggest principles that (...)
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  13. Cory Juhl (2006). Fine-Tuning is Not Surprising. Analysis 66 (292):269–275.
    This paper is a response to Stephen Leeds’s "Juhl on Many Worlds". Contrary to what Leeds claims, we can legitimately argue for nontrivial conclusions by appeal to our existence. The ’problem of old evidence’, applied to the ’old evidence’ that we exist, seems to be a red herring in the context of determining whether there is a rationally convincing argument for the existence of many universes. A genuinely salient worry is whether multiversers can avoid illicit reuse of empirical evidence in (...)
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  14. Brian Kierland & Bradley Monton (2006). How to Predict Future Duration From Present Age. Philosophical Quarterly 56 (January):16-38.
    Physicist J. Richard Gott has given an argument that, if good, allows one to make accurate predictions for the future longevity of a process, based solely on its present age. We show that there are problems with some of the details of Gott’s argument, but we defend the crucial insight: in many circumstances, the greater the present age of a process, the more likely a longer future duration.
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  15. Wang-Yen Lee (2013). Akaike's Theorem and Weak Predictivism in Science. Studies in History and Philosophy of Science Part A 44 (4):594-599.
  16. Keith Lehrer & Vann McGee (1991). An Epistemic Principle Which Solves Newcomb's Paradox. Grazer Philosophische Studien 40:197-217.
    If it is certain that performing an observation to determine whether P is true will in no way influence whether P is tme, then the proposition that the observation is performed ought to be probabilistically independent of P. Applying the notion of "observation" liberally, so that a wide variety of actions are treated as observations, this proposed new principle of belief revision yields the result that simple utihty maximization gives the correct solution to the Fisher smoking paradox and the two-box (...)
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  17. Peter J. Lewis (2013). The Doomsday Argument and the Simulation Argument. Synthese 190 (18):4009-4022.
    The Simulation Argument and the Doomsday Argument share certain structural similarities, and hence are often discussed together (Bostrom 2003, Aranyosi 2004, Richmond 2008, Bostrom and Kulczycki 2011). Both are cases where reflecting on one’s location among a set of possibilities yields a counter-intuitive conclusion—in one case that the end of humankind is closer than you initially thought, and in the second case that it is more likely than you initially thought that you are living in a computer simulation. Indeed, the (...)
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  18. Peter J. Lewis, Credence for Whom?
    There is an important sense in which an agent’s credences are universal: while they reflect an agent’s own judgments, those judgments apply equally to everyone’s bets. This point, while uncontentious, has been overlooked; people automatically assume that credences concern an agent’s own bets, perhaps just because of the name “subjective” that is typically applied to this account of belief. This oversight has had unfortunate consequences for recent epistemology, in particular concerning the Sleeping Beauty case and its myriad variants.
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  19. Peter J. Lewis, A Note on the Simulation Argument.
    The point of this note is to compare the Doomsday Argument to the Simulation Argument. The latter, I maintain, is a better argument than the former.
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  20. Hanti Lin & Kevin T. Kelly (2012). A Geo-Logical Solution to the Lottery Paradox, with Applications to Conditional Logic. Synthese 186 (2):531-575.
  21. David C. Makinson (1965). The Paradox of the Preface. Analysis 25 (6):205-207.
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  22. Radford M. Neal, Puzzles of Anthropic Reasoning Resolved Using Full Non-Indexical Conditioning.
    I consider the puzzles arising from four interrelated problems involving `anthropic' reasoning, and in particular the `Self-Sampling Assumption' (SSA) - that one should reason as if one were randomly chosen from the set of all observers in a suitable reference class. The problem of Freak Observers might appear to force acceptance of SSA if any empirical evidence is to be credited. The Sleeping Beauty problem arguably shows that one should also accept the `Self-Indication Assumption' (SIA) - that one should take (...)
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  23. Dana K. Nelkin (2000). The Lottery Paradox, Knowledge, and Rationality. Philosophical Review 109 (3):373-409.
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  24. Alexander R. Pruss (2012). Infinite Lotteries, Perfectly Thin Darts and Infinitesimals. Thought: A Journal of Philosophy 1 (2):81-89.
    One of the problems that Bayesian regularity, the thesis that all contingent propositions should be given probabilities strictly between zero and one, faces is the possibility of random processes that randomly and uniformly choose a number between zero and one. According to classical probability theory, the probability that such a process picks a particular number in the range is zero, but of course any number in the range can indeed be picked. There is a solution to this particular problem on (...)
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  25. Grant Reaber (2012). Rational Feedback. Philosophical Quarterly 62 (249):797-819.
    Suppose you think that whether you believe some proposition A at some future time t might have a causal influence on whether A is true. For instance, maybe you think a woman can read your mind, and either (1) you think she will snap her fingers shortly after t if and only if you believe at t that she will, or (2) you think she will snap her fingers shortly after t if and only if you don't believe at t (...)
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  26. John Roberts (2012). Fine-Tuning and the Infrared Bull's-Eye. Philosophical Studies 160 (2):287-303.
    I argue that the standard way of formalizing the fine-tuning argument for design is flawed, and I present an alternative formalization. On the alternative formalization, the existence of life is not treated as the evidence that confirms design; instead it is treated as part of the background knowledge, while the fact that fine tuning is required for life serves as the evidence. I argue that the alternative better captures the informal line of thought that gives the fine-tuning argument its intuitive (...)
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  27. Glenn Ross (2012). Reconsidering the Lessons of the Lottery for Knowledge and Belief. Philosophical Studies 161 (1):37-46.
    In this paper, I propose that one can have reason to choose a few tickets in a very large lottery and arbitrarily believe of them that they will lose. Such a view fits nicely within portions of Lehrer's theory of rational acceptance. Nonetheless, the reasonability of believing a lottery ticket will lose should not be taken to constitute the kind of justification required in an analysis of knowledge. Moreover, one should not accept what one takes to have a low chance (...)
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  28. Tamas Rudas (ed.) (2008). Handbook of Probability Theory with Applications.
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  29. Sharon Ryan (1996). The Epistemic Virtues of Consistency. Synthese 109 (2):121-141.
    The lottery paradox has been discussed widely. The standard solution to the lottery paradox is that a ticket holder is justified in believing each ticket will lose but the ticket holder is also justified in believing not all of the tickets will lose. If the standard solution is true, then we get the paradoxical result that it is possible for a person to have a justified set of beliefs that she knows is inconsistent. In this paper, I argue that the (...)
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  30. Sharon Ryan (1991). The Preface Paradox. Philosophical Studies 64 (3):293-307.
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  31. Daniele Sgaravatti (2014). Scepticism, Defeasible Evidence and Entitlement. Philosophical Studies 168 (2):439-455.
    The paper starts by describing and clarifying what Williamson calls the consequence fallacy. I show two ways in which one might commit the fallacy. The first, which is rather trivial, involves overlooking background information; the second way, which is the more philosophically interesting, involves overlooking prior probabilities. In the following section, I describe a powerful form of sceptical argument, which is the main topic of the paper, elaborating on previous work by Huemer. The argument attempts to show the impossibility of (...)
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  32. Nicholas Shackel (2008). Paradoxes of Probability. In Tamas Rudas (ed.), Handbook of Probability Theory with Applications.
    We call something a paradox if it strikes us as peculiar in a certain way, if it strikes us as something that is not simply nonsense, and yet it poses some difficulty in seeing how it could make sense. When we examine paradoxes more closely, we find that for some the peculiarity is relieved and for others it intensifies. Some are peculiar because they jar with how we expect things to go, but the jarring is to do with imprecision and (...)
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  33. Paul D. Thorn (2012). Two Problems of Direct Inference. Erkenntnis 76 (3):299-318.
    The article begins by describing two longstanding problems associated with direct inference. One problem concerns the role of uninformative frequency statements in inferring probabilities by direct inference. A second problem concerns the role of frequency statements with gerrymandered reference classes. I show that past approaches to the problem associated with uninformative frequency statements yield the wrong conclusions in some cases. I propose a modification of Kyburg’s approach to the problem that yields the right conclusions. Past theories of direct inference have (...)
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  34. Paul D. Thorn (2007). Three Problems of Direct Inference. Dissertation, University of Arizona
  35. Marcelo Tsuji (2000). Partial Structures and Jeffrey-Keynes Algebras. Synthese 125 (1-2):283-299.
    In Tsuji 1997 the concept of Jeffrey-Keynes algebras was introduced in order to construct a paraconsistent theory of decision under uncertainty. In the present paper we show that these algebras can be used to develop a theory of decision under uncertainty that measures the degree of belief on the quasi (or partial) truth of the propositions. As applications of this new theory of decision, we use it to analyze Popper's paradox of ideal evidence and to indicate a possible way of (...)
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  36. Hans Van Den Berg, Dick Hoekzema & Hans Radder (1990). Accardi on Quantum Theory and the "Fifth Axiom" of Probability. Philosophy of Science 57 (1):149-157.
    In this paper we investigate Accardi's claim that the "quantum paradoxes" have their roots in probability theory and that, in particular, they can be evaded by giving up Bayes' rule, concerning the relation between composite and conditional probabilities. We reach the conclusion that, although it may be possible to give up Bayes' rule and define conditional probabilities differently, this contributes nothing to solving the philosophical problems which surround quantum mechanics.
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  37. Jonathan Weisberg (2012). The Argument From Divine Indifference. Analysis 72 (4):707-714.
    I argue that the rationale behind the fine-tuning argument for design is self-undermining, refuting the argument’s own premise that fine-tuning is to be expected given design. In (Weisberg 2010) I argued on informal grounds that this premise is unsupported. White (2011) countered that it can be derived from three plausible assumptions. But White’s third assumption is based on a fallacious rationale, and is even objectionable by the design theorist’s own lights. The argument that shows this, the argument from divine indifference, (...)
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  38. Sylvia Wenmackers (2013). Ultralarge Lotteries: Analyzing the Lottery Paradox Using Non-Standard Analysis. Journal of Applied Logic 11 (4):452-467.
    A popular way to relate probabilistic information to binary rational beliefs is the Lockean Thesis, which is usually formalized in terms of thresholds. This approach seems far from satisfactory: the value of the thresholds is not well-specified and the Lottery Paradox shows that the model violates the Conjunction Principle. We argue that the Lottery Paradox is a symptom of a more fundamental and general problem, shared by all threshold-models that attempt to put an exact border on something that is intrinsically (...)
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  39. Sylvia Wenmackers (2012). Ultralarge and Infinite Lotteries. In B. Van Kerkhove, T. Libert, G. Vanpaemel & P. Marage (eds.), Logic, Philosophy and History of Science in Belgium II (Proceedings of the Young Researchers Days 2010). Koninklijke Vlaamse Academie van België Voor Wetenschappen En Kunsten
    By exploiting the parallels between large, yet finite lotteries on the one hand and countably infinite lotteries on the other, we gain insights in the foundations of probability theory as well as in epistemology. We solve the 'adding problems' that occur in these two contexts using a similar strategy, based on non-standard analysis.
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  40. Sylvia Wenmackers & Leon Horsten (2013). Fair Infinite Lotteries. Synthese 190 (1):37-61.
    This article discusses how the concept of a fair finite lottery can best be extended to denumerably infinite lotteries. Techniques and ideas from non-standard analysis are brought to bear on the problem.
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  41. Gregory Wheeler (2007). Two Puzzles Concerning Measures of Uncertainty and the Positive Boolean Connectives. In Progress in Artificial Intelligence (EPIA 2007). Springer
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  42. Gregory Wheeler (ed.) (2007). Progress in Artificial Intelligence (EPIA 2007). Springer.
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