About this topic
Summary In this category belong a range of puzzles that are analysed using probabililty and have philosophical implications. Perhaps the best known is Goodman's New Riddle of Induction (Grue), which can be seen as a strengthened version of Hume's problem of induction. The Paradox of the Ravens (the paradox of confirmation) is one of the central problems for theories of confirmation. It seems to show that obvious principles of confirmation generate the result that a white sneaker confirms that all ravens are black. The Sleeping Beauty problem concerns an agent who is woken on either one day or two, and faces the question of whether the current waking is part of the single waking or the double waking. This raises the issue of incorporating self-locating beliefs into the Bayesian framework. The Doomsday Argument purports to show that humans will die out sooner than we previously thought, based merely on our own birth rank among humans. The Monty Hall Problem is about whether you should swap doors, after tentatively choosing one of the three doors, one of which contains a prize, and finding that the door you selected does not have the prize.
Key works The New Riddle of Induction was introduced in Goodman 1954. The Paradox of the Ravens was introduced by Hosiasson-Lindenbaum 1940 and influentially discussed by Hempel 1945 I and Hempel 1945 II. Sleeping Beauty was introduced by Elga 2000, shortly followed by Lewis 2001. The Doomsday Argument was popularized largely by Leslie 1989.
Introductions The new riddle of induction and the paradox of the ravens are explained in section 5 of Vickers 2008. This Bostrom manuscript explains the Doomsday Argument and Titelbaum forthcoming gives a summary of the responses to Sleeping Beauty
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  1. Nick Bostrom (2002). Self-Locating Belief in Big Worlds: Cosmology's Missing Link to Observation. Journal of Philosophy 99 (12):607-623.
    Current cosmological theories say that the world is so big that all possible observations are in fact made. But then, how can such theories be tested? What could count as negative evidence? To answer that, we need to consider observation selection effects.
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  2. C. A. Hooker (1968). Goodman, 'Grue' and Hempel. Philosophy of Science 35 (3):232-247.
    It is now commonly accepted that N. Goodman's predicate "grue" presents the theory of confirmation of C. G. Hempel (and other such theories) with grave difficulties. The precise nature and status of these "difficulties" has, however, never been made clear. In this paper it is argued that it is very unlikely that "grue" raises any formal difficulties for Hempel and appearances to the contrary are examined, rejected and an explanation of their intuitive appeal offered. However "grue" is shown to raise (...)
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  3. G. M. K. Hunt (1969). Further Ramifications of 'Grue'. British Journal for the Philosophy of Science 20 (3):257-259.
  4. Richard Jackson (1969). The Sleeping King. Bibliothèque d'Humanisme Et Renaissance 31 (3):525-551.
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  5. Francis J. Kovach (1985). About Beauty, A Thomistic Interpretation. Review of Metaphysics 38 (3):662-664.
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  6. Guy Lemieux (1935). Outline of the Problem of Beauty (First Part). Modern Schoolman 12 (4):93-94.
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  7. Guy Lemieux (1935). Outline of the Problem of Beauty, Conclusion. Modern Schoolman 12 (4):96-96.
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  8. Y. Liu, A. Bisazza, M. M. Botvinick, N. Chomsky, C. DiYanni, L. Feigenson, W. T. Fitch, J. I. Flombaum, U. Hahn & M. D. Hauser (2005). Leslie, AM, 153. Cognition 97:337.
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  9. Colin Lyas (1980). LESLIE, JOHN "Value and Existence". [REVIEW] Philosophy 55:275.
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  10. R. M. Martin (1960). Review: Nelson Goodman, Fact, Fiction, & Forecast. [REVIEW] Journal of Symbolic Logic 25 (3):250-251.
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  11. Robert M. Martin (1990). It's Not That Easy Being Grue. Philosophical Quarterly 40 (160):299-315.
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  12. Gerald J. Massey (1974). Oliver Leslie Reiser 1895-1974. Proceedings and Addresses of the American Philosophical Association 48:179 - 180.
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  13. Mary Kate McGowan (2003). Realism, Reference and Grue (Why Metaphysical Realism Cannot Solve the Grue Paradox). American Philosophical Quarterly 40 (1):47 - 57.
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  14. Mary Kate McGowan (2002). Gruesome Connections. Philosophical Quarterly 52 (206):21-33.
    It is widely recognized that Goodman's grue example demonstrates that the rules for induction, unlike those for deduction, cannot be purely syntactic. Ways in which Goodman's proof generalizes, however, are not widely recognized. Gruesome considerations demonstrate that neither theories of simplicity nor theories of empirical confirmation can be purely syntactic. Moreover, the grue paradox can be seen as an instance of a much more general phenomenon. All empirical investigations require semantic constraints, since purely structural constraints are inadequate. Both Russell's theory (...)
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  15. Henry Mehlberg (1958). Review: Carl G. Hempel, A Logical Appraisal of Operationism. [REVIEW] Journal of Symbolic Logic 23 (3):354-356.
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  16. Martine Mespoulet (2002). From Typical Areas to Random Sampling: Sampling Methods in Russia From 1875 to 1930. Science in Context 15 (3):411-425.
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  17. Ca Miller (1984). The Poet in the Poem: A Phenomenological Analysis of Anne Sexton's: Briar Rose (Sleeping Beauty) in The Existential Coordinates of the Human Condition: Poetic, Epic, Tragic. The Literary Genre. Analecta Husserliana 18:61-73.
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  18. Florian Mittl (2012). The Creeping Doomsday Named Finances. Disputatio Philosophica 13 (1):113-124.
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  19. Richard Montague (1960). Review: Hugues Leblanc, Evidence Logique Et Degre de Confirmation. [REVIEW] Journal of Symbolic Logic 25 (1):86-86.
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  20. Hilde Lindemann Nelson & Daniel Callahan (2005). Before He Wakes. Hastings Center Report 35 (4):15-16.
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  21. Harold W. Noonan (1982). Reply to Leslie Stevenson1. Philosophical Books 23 (1):7-12.
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  22. John O'Connor (1967). Differential Properties and Goodman's Riddle. Analysis 28 (2):59 -.
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  23. Temporal Horizons oj Justice (1997). A Shooting Room View Oj Doomsday, William Eckhardt. Mind 106 (421).
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  24. A. G. Padgett (1998). Leslie, J.-The End of the World. Philosophical Books 39:222-224.
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  25. J. V. Pickstone (1978). Locating Dutrochet. British Journal for the History of Science 11 (1):49-64.
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  26. V. T. Rajshekar (2004). Hindutva: Whipping Up Sleeping Slaves. Journal of Dharma 29 (1):73-78.
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  27. Baron Reed (2008). Fallibilism and the Lottery Paradox. Proceedings of the Xxii World Congress of Philosophy 53:217-225.
    Any theory of knowledge that is fallibilist—i.e., that allows for one to have knowledge that could have been false or accidentally true—faces the lottery paradox. The paradox arises from the combination of two plausible claims: first, no one can know that one’s lottery ticket will lose prior to learning that it in fact has lost, and, second, the justification one has for the belief that one’s ticket will lose is just as good as the justification one has for paradigmatic instances (...)
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  28. Arthur Rubinstein (1998). Induction, Grue Emeralds and Lady Macbeth's Fallacy. Philosophical Quarterly 48 (190):37-49.
    This paper does not purport to offer yet another ‘solution’ to the much discussed ‘new riddle’ of induction. The focus, instead, is on the genesis of Goodman's paradox and its relation to the classic problem of induction. In the arguments which led Goodman from the dissolution of Hume's problem to the discovery of the new riddle, I reveal a fundamentally flawed assumption about the nature of inductive inference which undermines Goodman's contention that the genuine problem of induction consists in distinguishing (...)
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  29. Ruth Rubinstein (1986). Michelangelo's Lost Sleeping Cupid and Fetti's Vertumnus and Pomona. Journal of the Warburg and Courtauld Institutes 49:257-259.
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  30. Oscar Seminar (2008). An Objectivist Argument for Thirdism. Analysis 68 (2):149-155.
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  31. J. R. Shoenfield (1971). Review: Leslie H. Tharp, On a Set Theory of Bernays. [REVIEW] Journal of Symbolic Logic 36 (4):682-682.
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  32. Michael A. Slote (1968). A General Solution to Goodman's Riddle? Analysis 29 (2):55 - 58.
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  33. Michael Anthony Slote (1967). Some Thoughts on Goodman's Riddle. Analysis 27 (4):128 - 132.
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  34. Gary Sollazzo (1972). Barker and Achinstein on Goodman. Philosophical Studies 23 (1-2):91 - 97.
    Barker and Achinstein think that it is not possible for a predicate like grue to serve as well as a predicate like green in the role of a qualitative or non-positional predicate. Their arguments consist in a number of attempts to show that one who possesses green in his language can do things with that predicate which one who must work with grue instead cannot do. However, they succeed in showing only that a qualitative predicate is better adapted to our (...)
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  35. Alfred J. Stenner (1967). A Note on Grue. Philosophical Studies 18 (5):76 - 78.
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  36. Judith Jarvis Thomson (1966). Grue. Journal of Philosophy 63 (11):289-309.
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  37. Judith Jarvis Thomson (1966). More Grue. Journal of Philosophy 63 (18):528-534.
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  38. J. S. Ullian (1961). More on "Grue" and Grue. Philosophical Review 70 (3):386-389.
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  39. Simon Johnson Williams & Nick Crossley (2008). Introduction: Sleeping Bodies. Body and Society 14 (4):1-13.
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Doomsday Argument
  1. Tom Adams (2007). Sorting Out the Anti-Doomsday Arguments: A Reply to Sowers. Mind 116 (462):269-273.
    claim that his thought experiment shows that a currently living person is not a random sample is refuted. His thought experiment is reduced to a probability model, and is shown to be identical to one previously developed by Dieks. The status of the Doomsday Argument is left unresolved, since Dieks's refutation attempt is disputed in the literature.
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  2. Mr István A. Aranyosi, The Doomsday Simulation Argument. Or Why Isn't the End Nigh, and You're Not Living in a Simulation.
    According to the Carter-Leslie Doomsday Argument, we should assign a high probability to the hypothesis that the human species will go extinct very soon. The argument is based on the application of Bayes’s theo-rem and a certain indifference principle with respect to the temporal location of our observed birth rank within the totality of birth ranks of all humans who will ever have lived. According to Bostrom’s Simulation Argument, which appeals to a weaker indifference principle than the Doomsday Argument, at (...)
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  3. Paul Bartha & Christopher Hitchcock (1999). No One Knows the Date or the Hour: An Unorthodox Application of Rev. Bayes's Theorem. Philosophy of Science 66 (3):353.
    Carter and Leslie (1996) have argued, using Bayes's theorem, that our being alive now supports the hypothesis of an early 'Doomsday'. Unlike some critics (Eckhardt 1997), we accept their argument in part: given that we exist, our existence now indeed favors 'Doom sooner' over 'Doom later'. The very fact of our existence, however, favors 'Doom later'. In simple cases, a hypothetical approach to the problem of 'old evidence' shows that these two effects cancel out: our existence now yields no information (...)
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  4. Paul Bartha & Christopher Hitchcock (1999). The Shooting-Room Paradox and Conditionalizing on Measurably Challenged Sets. Synthese 118 (3):403-437.
    We provide a solution to the well-known “Shooting-Room” paradox, developed by John Leslie in connection with his Doomsday Argument. In the “Shooting-Room” paradox, the death of an individual is contingent upon an event that has a 1/36 chance of occurring, yet the relative frequency of death in the relevant population is 0.9. There are two intuitively plausible arguments, one concluding that the appropriate subjective probability of death is 1/36, the other that this probability is 0.9. How are these two values (...)
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  5. Yann Benétreau-Dupin (forthcoming). Blurring Out Cosmic Puzzles. Philosophy of Science.
    The Doomsday argument and anthropic reasoning are two puzzling examples of probabilistic confirmation. In both cases, a lack of knowledge apparently yields surprising conclusions. Since they are formulated within a Bayesian framework, they constitute a challenge to Bayesianism. Several attempts, some successful, have been made to avoid these conclusions, but some versions of these arguments cannot be dissolved within the framework of orthodox Bayesianism. I show that adopting an imprecise framework of probabilistic reasoning allows for a more adequate representation of (...)
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  6. Yann Benétreau-Dupin (2015). The Bayesian Who Knew Too Much. Synthese 192 (5):1527-1542.
    In several papers, John Norton has argued that Bayesianism cannot handle ignorance adequately due to its inability to distinguish between neutral and disconfirming evidence. He argued that this inability sows confusion in, e.g., anthropic reasoning in cosmology or the Doomsday argument, by allowing one to draw unwarranted conclusions from a lack of knowledge. Norton has suggested criteria for a candidate for representation of neutral support. Imprecise credences (families of credal probability functions) constitute a Bayesian-friendly framework that allows us to avoid (...)
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  7. N. Bostrom (1999). The Doomsday Argument is Alive and Kicking. Mind 108 (431):539-551.
    A recent paper by Korb and Oliver in this journal attempts to refute the Carter-Leslie Doomsday argument. I organize their remarks into five objections and show that they all fail. Further efforts are thus called upon to find out what, if anything, is wrong with Carter and Leslie's disturbing reasoning. While ultimately unsuccessful, Korb and Oliver's objections do however in some instances force us to become clearer about what the Doomsday argument does and doesn't imply.
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  8. Nick Bostrom, A Doomsday Argument Primer.
    Rarely does philosophy produce empirical predictions. The Doomsday argument is an important exception. From seemingly trivial premises it seeks to show that the risk that humankind will go extinct soon has been systematically underestimated. Nearly everybody's first reaction is that there must be something wrong with such an argument. Yet despite being subjected to intense scrutiny by a growing number of philosophers, no simple flaw in the argument has been identified.
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  9. Nick Bostrom, Beyond the Doomsday Argument: Reply to Sowers and Further Remarks.
    George Sowers tries to refute the Doomsday argument on grounds that true random sampling requires all possible samples to be equally probable the time when the sample is taken. Yet the Doomsday argument does not rely on true random sampling. It presupposes random sampling only in a metaphorical sense. After arguing that Sowers’ critique fails, I outline my own view on the matter, which is that the Doomsday argument is inconclusive and that by developing a theory of observation selection effects (...)
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  10. Nick Bostrom (2008). The Doomsday Argument. Think 6 (17-18):23-28.
    A recent paper by Korb and Oliver in this journal attempts to refute the Carter-Leslie Doomsday argument. I organize their remarks into five objections and show that they all fail. Further efforts are thus called upon to find out what, if anything, is wrong with Carter and Leslie’s disturbing reasoning. While ultimately unsuccessful, Korb and Oliver’s objections do however in some instances force us to become clearer about what the Doomsday argument does and doesn’t imply.
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  11. Nick Bostrom (2003). The Mysteries of Self-Locating Belief and Anthropic Reasoning. The Harvard Review of Philosophy 11 (1):59-73.
    1. How big is the smallest fish in the pond? You take your wide-meshed fishing net and catch one hundred fishes, every one of which is greater than six inches long. Does this evidence support the hypothesis that no fish in the pond is much less than six inches long? Not if your wide-meshed net can’t actually catch smaller fish...
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