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  1. Boundless Good.James Dreier - forthcoming - Ms.
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  2. Infinite Prospects.Jeffrey Sanford Russell & Yoaav Isaacs - forthcoming - Philosophy and Phenomenological Research.
    People with the kind of preferences that give rise to the St. Petersburg paradox are problematic---but not because there is anything wrong with infinite utilities. Rather, such people cannot assign the St. Petersburg gamble any value that any kind of outcome could possibly have. Their preferences also violate an infinitary generalization of Savage's Sure Thing Principle, which we call the *Countable Sure Thing Principle*, as well as an infinitary generalization of von Neumann and Morgenstern's Independence axiom, which we call *Countable (...)
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  3. Two Envelopes and Binding.Casper Storm Hansen - 2018 - Australasian Journal of Philosophy 96 (3):508-518.
    This paper describes a way of defending a modification of Eckhardt's [2013] solution to the Two Envelopes Paradox. The defence is based on ideas from Arntzenius, Elga, and Hawthorne [2004].
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  4. Essays on Paradoxes.Terry Horgan - 2017 - Oxford University Press USA.
    This volume brings together Terence Horgan's essays on paradoxes, both published and new. A common theme unifying these essays is that philosophically interesting paradoxes typically resist either easy solutions or solutions that are formally/mathematically highly technical. Another unifying theme is that such paradoxes often have deep-sometimes disturbing-philosophical morals.
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  5. Probabilistic Reasoning in the Two-Envelope Problem.Bruce D. Burns - 2015 - Thinking and Reasoning 21 (3):295-316.
    In the two-envelope problem, a reasoner is offered two envelopes, one containing exactly twice the money in the other. After observing the amount in one envelope, it can be traded for the unseen contents of the other. It appears that it should not matter whether the envelope is traded, but recent mathematical analyses have shown that gains could be made if trading was a probabilistic function of amount observed. As a problem with a purely probabilistic solution, it provides a potentially (...)
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  6. The Enigma Of Probability.Nick Ergodos - 2014 - Journal of Cognition and Neuroethics 2 (1):37-71.
    Using “brute reason” I will show why there can be only one valid interpretation of probability. The valid interpretation turns out to be a further refinement of Popper’s Propensity interpretation of probability. Via some famous probability puzzles and new thought experiments I will show how all other interpretations of probability fail, in particular the Bayesian interpretations, while these puzzles do not present any difficulties for the interpretation proposed here. In addition, the new interpretation casts doubt on some concepts often taken (...)
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  7. Keep or Trade? Effects of Pay-Off Range on Decisions with the Two-Envelopes Problem.Raymond S. Nickerson, Susan F. Butler, Nathaniel Delaney-Busch & Michael Carlin - 2014 - Thinking and Reasoning 20 (4):472-499.
    The "two-envelopes" problem has stimulated much discussion on probabilistic reasoning, but relatively little experimentation. The problem specifies two identical envelopes, one of which contains twice as much money as the other. You are given one of the envelopes and the option of keeping it or trading for the other envelope. Variables of interest include the possible amounts of money involved, what is known about the process by which the amounts of money were assigned to the envelopes, and whether you are (...)
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  8. The Two-Envelope Paradox: Asymmetrical Cases.Chunghyoung Lee - 2013 - Mind 122 (485):1-26.
    In the asymmetrical variant of the two-envelope paradox, the amount in envelope A is determined first, and then the amount in envelope B is determined to be either twice or half the amount in A by flipping a fair coin. Contra the common belief that B is preferable to A in this case, I show that the proposed arguments for this common belief all fail, and argue that B is not preferable to A if the expected values of the amounts (...)
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  9. Conditionals and a Two-Envelope Paradox.Byeong-Uk Yi - 2013 - Journal of Philosophy 110 (5):233-257.
    C onsider two contrary conditionals 1 about two envelopes, Ali and Baba: (a) If Ali has more money than Baba, the difference between the amounts in them is $5. (b) If Ali has more money than Baba, the difference between the amounts in them is $10. Can these both be true? The answer is a resounding yes on the standard account of conditionals, which identifies indicative con- ditionals with material conditionals. It is not the same with many other contemporary accounts (...)
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  10. Repeated St Petersburg Two-Envelope Trials and Expected Value.Jeremy Gwiazda - 2012 - The Reasoner 6 (3).
    It is commonly believed that when a finite value is received in a game that has an infinite expected value, it is in one’s interest to redo the game. We have argued against this belief, at least in the repeated St Petersburg two-envelope case. We also show a case where repeatedly opting for a higher expected value leads to a worse outcome.
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  11. Conditionals, Probabilities, and Utilities: More on Two Envelopes.B. D. Katz & D. Olin - 2010 - Mind 119 (473):171-183.
    Sutton ( 2010 ) claims that on our analysis (2007), the problem in the two-envelope paradox is an error in counterfactual reasoning. In fact, we distinguish two formulations of the paradox, only one of which, on our account, involves an error in conditional reasoning. According to Sutton, it is conditional probabilities rather than subjunctive conditionals that are essential to the problem. We argue, however, that his strategy for assigning utilities on the basis of conditional probabilities leads to absurdity. In addition, (...)
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  12. The Epoch of Incredulity: A Response to Katz and Olin's 'A Tale of Two Envelopes'.P. A. Sutton - 2010 - Mind 119 (473):159-169.
    When David Lewis ( 1986 ) told us that possible worlds were a ‘paradise for philosophers’, he neglected to add that they are a minefield for decision theorists. Possibilities — be they nomological, metaphysical, or epistemic possibilities — have little to do with subjective probabilities, and it is these latter that matter most to decision theory. Bernard Katz and Doris Olin ( 2007 ) have tried to solve the two-envelope problem by appealing to possible worlds and counterfactual conditionals. In this (...)
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  13. The Epoch of Incredulity.P. A. Sutton - 2010 - Mind 119 (473):159-169.
    When David Lewis (1986) told us that possible worlds were a ‘paradise for philosophers,’ he neglected to add that they are a minefield for decision theorists. Possibilities—be they nomological, metaphysical, or epistemic possibilities—have little to do with subjective probabilities, and it is these latter that matter most to decision theory. Bernard Katz and Doris Olin (2007) have tried to solve the two-envelope problem by appealing to possible worlds and counterfactual conditionals. In this paper I explain why any such attempt is (...)
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  14. Opening Two Envelopes.Paul Syverson - 2010 - Acta Analytica 25 (4):479-498.
    In the two-envelope problem, one is offered a choice between two envelopes, one containing twice as much money as the other. After seeing the contents of the chosen envelope, the chooser is offered the opportunity to make an exchange for the other envelope. However, it appears to be advantageous to switch, regardless of what is observed in the chosen envelope. This problem has an extensive literature with connections to probability and decision theory. The literature is roughly divided between those that (...)
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  15. Taking the Two Envelope Paradox to the Limit.Don Fallis - 2009 - Southwest Philosophy Review 25 (2):95-111.
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  16. The Nonidentity Problem and the Two Envelope Problem: When is One Act Better for a Person Than Another?Melinda A. Roberts - 2009 - In David Wasserman & Melinda Roberts (eds.), Harming Future Persons. Springer. pp. 201--228.
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  17. Keep or Trade? An Experimental Study of the Exchange Paradox.Raymond S. Nickerson & Susan F. Butler - 2008 - Thinking and Reasoning 14 (4):365-394.
    The “exchange paradox”—also referred to in the literature by a variety of other names, notably the “two-envelopes problem”—is notoriously difficult, and experts are not all agreed as to its resolution. Some of the various expressions of the problem are open to more than one interpretation; some are stated in such a way that assumptions are required in order to fill in missing information that is essential to any resolution. In three experiments several versions of the problem were used, in each (...)
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  18. The Two Envelope Paradox and Using Variables Within the Expectation Formula.Eric Schwitzgebel & Josh Dever - 2008 - Sorites:135-140.
    You are presented with a choice between two envelopes. You know one envelope contains twice as much money as the other, but you don't know which contains more. You arbitrarily choose one envelope -- call it Envelope A -- but don't open it. Call the amount of money in that envelope X. Since your choice was arbitrary, the other envelope (Envelope B) is 50% likely to be the envelope with more and 50% likely to be the envelope with less. But, (...)
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  19. A Three-Step Solution to the Two-Envelope Paradox.Igor Douven - 2007 - Logique Et Analyse 50 (200):359.
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  20. A Tale of Two Envelopes.Bernard D. Katz & Doris Olin - 2007 - Mind 116 (464):903-926.
    This paper deals with the two-envelope paradox. Two main formulations of the paradoxical reasoning are distinguished, which differ according to the partition of possibilities employed. We argue that in the first formulation the conditionals required for the utility assignment are problematic; the error is identified as a fallacy of conditional reasoning. We go on to consider the second formulation, where the epistemic status of certain singular propositions becomes relevant; our diagnosis is that the states considered do not exhaust the possibilities. (...)
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  21. Two Envelope Problems.Gary Malinas - 2006 - The Proceedings of the Twenty-First World Congress of Philosophy 9:153-158.
    When decision makers have more to gain than to lose by changing their minds, and that is the only relevant fact, they thereby have a reason to change their minds. While this is sage advice, it is silent on when one stands more to gain than to lose. The two envelope paradox provides a case where the appearance of advantage in changing your mind is resilient despite being a chimera. Setups that are unproblematically modeled by decision tables that are used (...)
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  22. The Exchange Paradox: Probabilistic and Cognitive Analysis of a Psychological Conundrum.Raymond S. Nickerson & Ruma Falk - 2006 - Thinking and Reasoning 12 (2):181 – 213.
    The term “exchange paradox” refers to a situation in which it appears to be advantageous for each of two holders of an envelope containing some amount of money to always exchange his or her envelope for that of the other individual, which they know contains either half or twice their own amount. We review several versions of the problem and show that resolving the paradox depends on the specifics of the situation, which must be disambiguated, and on the player's beliefs. (...)
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  23. Philosophical Perspectives on Infinity.Graham Oppy - 2006 - Cambridge University Press.
    This book is an exploration of philosophical questions about infinity. Graham Oppy examines how the infinite lurks everywhere, both in science and in our ordinary thoughts about the world. He also analyses the many puzzles and paradoxes that follow in the train of the infinite. Even simple notions, such as counting, adding and maximising present serious difficulties. Other topics examined include the nature of space and time, infinities in physical science, infinities in theories of probability and decision, the nature of (...)
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  24. Trying to Resolve the Two-Envelope Problem.Casper J. Albers, Barteld P. Kooi & Willem Schaafsma - 2005 - Synthese 145 (1):89-109.
    After explaining the well-known two-envelope paradox by indicating the fallacy involved, we consider the two-envelope problem of evaluating the factual information provided to us in the form of the value contained by the envelope chosen first. We try to provide a synthesis of contributions from economy, psychology, logic, probability theory (in the form of Bayesian statistics), mathematical statistics (in the form of a decision-theoretic approach) and game theory. We conclude that the two-envelope problem does not allow a satisfactory solution. An (...)
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  25. Casper J. Albers, Barteld P. Kooi and Willem Schaafsma/Trying to Resolve the Two-Envelope Problem Edwin H.-C. Hung/Projective Explanation: How Theories Explain Empirical Data in Spite of Theory. [REVIEW]Fc Boogerd, Fj Bruggeman & Rc Richardson - 2005 - Synthese 145 (1):499-500.
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  26. The Two-Envelope Paradox: An Axiomatic Approach.Franz Dietrich & Christian List - 2005 - Mind 114 (454):239-248.
    There has been much discussion on the two-envelope paradox. Clark and Shackel (2000) have proposed a solution to the paradox, which has been refuted by Meacham and Weisberg (2003). Surprisingly, however, the literature still contains no axiomatic justification for the claim that one should be indifferent between the two envelopes before opening one of them. According to Meacham and Weisberg, "decision theory does not rank swapping against sticking [before opening any envelope]" (p. 686). To fill this gap in the literature, (...)
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  27. Bayesianism, Infinite Decisions, and Binding.Frank Arntzenius, Adam Elga & John Hawthorne - 2004 - 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 1995). 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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  28. The Classical and Maximin Versions of the Two-Envelope Paradox.Bruce Langtry - 2004 - Australasian Journal of Logic 2:30-43.
    The Two-Envelope Paradox is classically presented as a problem in decision theory that turns on the use of probabilities in calculating expected utilities. I formulate a Maximin Version of the paradox, one that is decision-theoretic but omits considerations of probability. I investigate the source of the error in this new argument, and apply the insights thereby gained to the analysis of the classical version.
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  29. Decision Theory, Symmetry and Causal Structure: Reply to Meacham and Weisberg.Michael Clark & Nicholas Shackel - 2003 - Mind 112 (448):691-701.
  30. Two Envelope Problems and the Roles of Ignorance.Gary Malinas - 2003 - Acta Analytica 18 (1-2):217-225.
    Four variations on Two Envelope Paradox are stated and compared. The variations are employed to provide a diagnosis and an explanation of what has gone awry in the paradoxical modeling of the decision problem that the paradox poses. The canonical formulation of the paradox underdescribes the ways in which one envelope can have twice the amount that is in the other. Some ways one envelope can have twice the amount that is in the other make it rational to prefer the (...)
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  31. Clark and Shackel on the Two‐Envelope Paradox.Jonathan Weisberg & Christopher Meacham - 2003 - Mind 112 (448):685-689.
    Clark and Shackel have recently argued that previous attempts to resolve the two-envelope paradox fail, and that we must look to symmetries of the relevant expected-value calculations for a solution. Clark and Shackel also argue for a novel solution to the peeking case, a variant of the two-envelope scenario in which you are allowed to look in your envelope before deciding whether or not to swap. Whatever the merits of these solutions, they go beyond accepted decision theory, even contradicting it (...)
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  32. The St. Petersburg Two-Envelope Paradox.David J. Chalmers - 2002 - Analysis 62 (2):155–157.
    I reason: (1) For any x, if I knew that A contained x, then the odds are even that B contains either 2x or x/2, so the expected amount in B would be 5x/4. So (2) for all x, if I knew that A contained x, I would have an expected gain in switching to B. So (3) I should switch to B. But this seems clearly wrong, as my information about A and B is symmetrical.
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  33. The Non-Probabilistic Two Envelope Paradox.James Chase - 2002 - Analysis 62 (2):157–160.
    Given a choice between two sealed envelopes, one of which contains twice as much money as the other (and in any case some), you don't know which contains the larger sum and so choose one at random. You are then given the option of taking the other envelope instead. Is it rational to do so? Surely not. but a specious line of reasoning suggests otherwise.
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  34. Getting Clear on the Two-Envelope Paradox.Monte Cook - 2002 - Southwest Philosophy Review 18 (1):45-51.
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  35. Paradox Lost, but in Which Envelope?Olav Gjelsvik - 2002 - Croatian Journal of Philosophy 2 (3):353-362.
    The aim of this paper is to diagnose the so-called two envelopes paradox. Many writers have claimed that there is something genuinely paradoxical in the situation with the two envelopes, and some writers are now developing non-standards theories of expected utility. I claim that there is no paradox for expected utility theory as I understand that theory, and that contrary claims are confused. Expected utility theory is completely unaffected by the two-envelope paradox.
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  36. A Commentary on Cook’s “Getting Clear on the Two-Envelope Paradox”.William L. Vanderburgh - 2002 - Southwest Philosophy Review 18 (2):95-99.
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  37. The Two-Envelope Paradox.Michael Clark & Nicholas Shackel - 2000 - Mind 109 (435):415--442.
    Previous claims to have resolved the two-envelope paradox have been premature. The paradoxical argument has been exposed as manifestly fallacious if there is an upper limit to the amount of money that may be put in an envelope; but the paradoxical cases which can be described if this limitation is removed do not involve mathematical error, nor can they be explained away in terms of the strangeness of infinity. Only by taking account of the partial sums of the infinite series (...)
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  38. The Exchange Paradox, Finite Additivity, and the Principle of Dominance Commentary.R. B. Gardner - 2000 - Poznan Studies in the Philosophy of the Sciences and the Humanities 71:49-76.
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  39. The Two-Envelope Paradox, Nonstandard Expected Utility, and the Intensionality of Probability.Terry Horgan - 2000 - Noûs 34 (4):578–603.
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  40. The Exchange Paradox, Finite Additivity, and the Principle of Dominance.Piers Rawling - 2000 - Poznan Studies in the Philosophy of the Sciences and the Humanities 71:49-76.
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  41. Misadventures in Conditional Expectation: The Two-Envelope Problem. [REVIEW]Carl G. Wagner - 1999 - Erkenntnis 51 (2-3):233-241.
    Several fallacies of conditionalization are illustrated, using the two-envelope problem as a case in point.
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  42. Where the Sum of Our Expectation Fails Us: The Exchange Paradox.Norton John - 1998 - Pacific Philosophical Quarterly 79 (1):34–58.
    In the exchange paradox, two players receive envelopes containing different amounts of money. The assignment of the amounts ensures each player has the same probability of receiving each possible amount. Nonetheless, for each specific amount a player may find in his envelope, there is a positive expectation of gain if the player swaps envelopes with the other player, in apparent contradiction with the symmetry of the game. I consider a variant form of the paradox that avoids problems with improper probabilities (...)
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  43. The Two Envelope Paradox and Infinite Expectations.Frank Arntzenius & David McCarthy - 1997 - Analysis 57 (1):42–50.
    The two envelope paradox can be dissolved by looking closely at the connection between conditional and unconditional expectation and by being careful when summing an infinite series of positive and negative terms. The two envelope paradox is not another St. Petersburg paradox and that one does not need to ban talk of infinite expectation values in order to dissolve it. The article ends by posing a new puzzle to do with infinite expectations.
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  44. The Two Envelope Paradox and Infinite Expectations.Frank Arntzenius & David McCarthy - 1997 - Analysis 57 (1):42-50.
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  45. The Two-Envelope Paradox Resolved.Timothy J. McGrew, David Shier & Harry S. Silverstein - 1997 - Analysis 57 (1):28–33.
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  46. Perspectives on a Pair of Envelopes.Piers Rawling - 1997 - Theory and Decision 43 (3):253-277.
    The two envelopes problem has generated a significant number of publications (I have benefitted from reading many of them, only some of which I cite; see the epilogue for a historical note). Part of my purpose here is to provide a review of previous results (with somewhat simpler demonstrations). In addition, I hope to clear up what I see as some misconceptions concerning the problem. Within a countably additive probability framework, the problem illustrates a breakdown of dominance with respect to (...)
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  47. What’s in the Two Envelope Paradox?Alexander D. Scott & Michael Scott - 1997 - Analysis 57 (1):34–41.
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  48. The Two-Envelope Paradox.John Broome - 1995 - Analysis 55 (1):6 - 11.
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  49. The Mystery of Julius: A Paradox in Decision Theory.Charles S. Chihara - 1995 - Philosophical Studies 80 (1):1 - 16.
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  50. The Two Envelope Paradox: The Infinite Case.Paul Castell & Diderik Batens - 1994 - Analysis 54 (1):46 - 49.
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