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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 (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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  2. 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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  3. Menachem Fisch (1984). Hempel's Ravens, the Natural Classification of Hypotheses and the Growth of Knowledge. Erkenntnis 21 (1):45 - 62.
  4. Branden Fitelson, Goodman's “Grue” Argument in Historical Perspective.
    The talk is mainly defensive. I won’t offer positive accounts of the “paradoxical” cases I will discuss (but, see “Extras”). I’ll begin with Harman’s defense of classical deductive logic against certain (epistemological) “relevantist” arguments.
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  5. Antony Flew (1997). The End of the World: The Science and Ethics of Human Extinction By Leslie John Routledge, 1996, Vii+310 Pp. £16.99. [REVIEW] Philosophy 72 (279):158-.
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  6. P. Franceschi (1999). How the Urn of Carter and Leslie Flows Into That of Hempel. Canadian Journal of Philosophy 29 (1):139-156.
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  7. Paul Franceschi, 8qh 6roxwlrq Srxu o¶$Ujxphqw Gh o¶$Srfdo\Svh.
    Attribué à Brandon Carter, l'DUJXPHQW GH O$SRFDO\SVH ('RRPVGD\ $UJXPHQW, soit DA, dans ce qui suit) a été décrit par John Leslie (1992). On peut formuler ainsi cet argument. Soit $ l'événement: O$SRFDO\SVH VH SURGXLUD DYDQW ODQ ; et % l'événement: O$SRFDO\SVH QH VH SURGXLUD SDV DYDQW . Soit également = l'événement: MDL FRQQX OHV DQQpHV . On peut par ailleurs estimer à 40 milliards le nombre d'humains ayant existé depuis la naissance de l'humanité.
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  8. D. Goldstick (1989). The Meaning of “Grue”. Erkenntnis 31 (1):139 - 141.
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  9. Ian Hacking (1993). On Kripke's and Goodman's Uses of 'Grue'. Philosophy 68 (265):269-295.
    Kripke's lectures, published as Wittgenstein on Rules and Private Language , posed a sceptical problem about following a rule, which he cautiously attributed to Wittgenstein. He briefly noticed an analogy between his new kind of scepticism and Goodman's riddle of induction. ‘Grue’, he said, could be used to formulate a question not about induction but about meaning: the problem would not be Goodman's about induction—‘Why not predict that grass, which has been grue in the past, will be grue in the (...)
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  10. Marvin Henberg (1986). Letting Sleeping Truths Lie. Canadian Journal of Philosophy 16 (2):281 - 295.
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  11. Paul Henle (1938). Review: Carl G. Hempel, Ein System Verallgemeinerter Negationen. [REVIEW] Journal of Symbolic Logic 3 (4):164-164.
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  12. Mary Hesse (1969). Ramifications of 'Grue'. British Journal for the Philosophy of Science 20 (1):13-25.
  13. C. A. Hooker (1971). The Ravens, Hempel and Goodman. Australasian Journal of Philosophy 49 (1):82 – 89.
  14. 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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  15. G. M. K. Hunt (1969). Further Ramifications of 'Grue'. British Journal for the Philosophy of Science 20 (3):257-259.
  16. Francis J. Kovach (1985). About Beauty, A Thomistic Interpretation. Review of Metaphysics 38 (3):662-664.
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  17. Stefan Krauss & X. T. Wang (2003). The Psychology of the Monty Hall Problem: Discovering Psychological Mechanisms for Solving a Tenacious Brain Teaser. Journal of Experimental Psychology: General 132 (1):3.
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  18. Guy Lemieux (1935). Outline of the Problem of Beauty (First Part). Modern Schoolman 12 (4):93-94.
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  19. Guy Lemieux (1935). Outline of the Problem of Beauty, Conclusion. Modern Schoolman 12 (4):96-96.
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  20. Ken Levy (2007). Single Case Probabilities and the Case of Monty Hall: Baumann's View. Synthese 158:139-151.
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  21. 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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  22. R. M. Martin (1960). Review: Nelson Goodman, Fact, Fiction, & Forecast. [REVIEW] Journal of Symbolic Logic 25 (3):250-251.
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  23. Robert M. Martin (1990). It's Not That Easy Being Grue. Philosophical Quarterly 40 (160):299-315.
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  24. Gerald J. Massey (1974). Oliver Leslie Reiser 1895-1974. Proceedings and Addresses of the American Philosophical Association 48:179 - 180.
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  25. 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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  26. 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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  27. 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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  28. 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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  29. 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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  30. Florian Mittl (2012). The Creeping Doomsday Named Finances. Disputatio Philosophica 13 (1):113-124.
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  31. 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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  32. Hilde Lindemann Nelson & Daniel Callahan (2005). Before He Wakes. Hastings Center Report 35 (4):15-16.
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  33. Harold W. Noonan (1982). Reply to Leslie Stevenson1. Philosophical Books 23 (1):7-12.
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  34. John O'Connor (1967). Differential Properties and Goodman's Riddle. Analysis 28 (2):59 -.
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  35. Temporal Horizons oj Justice (1997). A Shooting Room View Oj Doomsday, William Eckhardt. Mind 106 (421).
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  36. A. G. Padgett (1998). Leslie, J.-The End of the World. Philosophical Books 39:222-224.
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  37. V. T. Rajshekar (2004). Hindutva: Whipping Up Sleeping Slaves. Journal of Dharma 29 (1):73-78.
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  38. 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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  39. 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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  40. 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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  41. Oscar Seminar (2008). An Objectivist Argument for Thirdism. Analysis 68 (2):149-155.
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  42. 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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  43. Michael A. Slote (1968). A General Solution to Goodman's Riddle? Analysis 29 (2):55 - 58.
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  44. Michael Anthony Slote (1967). Some Thoughts on Goodman's Riddle. Analysis 27 (4):128 - 132.
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  45. 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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  46. Alfred J. Stenner (1967). A Note on Grue. Philosophical Studies 18 (5):76 - 78.
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  47. Judith Jarvis Thomson (1966). Grue. Journal of Philosophy 63 (11):289-309.
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  48. Judith Jarvis Thomson (1966). More Grue. Journal of Philosophy 63 (18):528-534.
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  49. J. S. Ullian (1961). More on "Grue" and Grue. Philosophical Review 70 (3):386-389.
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  50. Simon Johnson Williams & Nick Crossley (2008). Introduction: Sleeping Bodies. Body and Society 14 (4):1-13.
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