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. Goldberg Samuel. Probability. An Introduction. Prentice-Hall, Inc., Englewood Cliffs, N.J., 1960, Xiv + 322 Pp. [REVIEW]Stefan Bauer-Mengelberg - 1971 - Journal of Symbolic Logic 36 (3):543-544.
  2. Review: C. G. Hempel, On the Nature of Mathematical Truth. [REVIEW]Charles A. Baylis - 1946 - Journal of Symbolic Logic 11 (3):100-100.
  3. On Hempel's Rejection of Complete Verifiability.Robert W. Beard & Robert W. Loftin - 1974 - Philosophical Studies 25 (3):227 - 229.
  4. Gott Und "Theoria" Bei Aristoteles.Seth Benardete - 1983 - Review of Metaphysics 37 (1):112-113.
  5. Goodman Nelson. On the Simplicity of Ideas.George D. W. Berry - 1944 - Journal of Symbolic Logic 9 (2):52-53.
  6. Goodman Nelson. A Query on Confirmation. The Journal of Philosophy, Vol. 43 , Pp. 383–385.Max Black - 1946 - Journal of Symbolic Logic 11 (3):81.
  7. Hempel Carl G. And Oppenheim Paul. A Definition of “Degree of Confirmation.” Philosophy of Science, Vol. 12 , Pp. 98–115. [REVIEW]Max Black - 1946 - Journal of Symbolic Logic 11 (1):18-19.
  8. Hempel Carl G.. A Note on the Paradoxes of Confirmation. Mind, N. S. Vol. 55 , Pp. 79–82.Max Black - 1946 - Journal of Symbolic Logic 11 (4):124.
  9. Review: C. H. Whiteley, Hempel's Paradoxes of Confirmation. [REVIEW]Max Black - 1945 - Journal of Symbolic Logic 10 (3):104-104.
  10. Whiteley C. H.. Hempel's Paradoxes of Confirmation. Mind, N. S. Vol. 54 , Pp. 156–158.Max Black - 1945 - Journal of Symbolic Logic 10 (3):104.
  11. Hempel. Carl G. A Purely Syntactical Definition of Confirmation.Max Black - 1944 - Journal of Symbolic Logic 9 (2):47.
  12. Review: Carl G. Hempel, A Purely Syntactical Definition of Confirmation. [REVIEW]Max Black - 1944 - Journal of Symbolic Logic 9 (2):47-47.
  13. How Unlikely is a Doomsday Catastrophe?, With Max Tegmark, Published In.Nick Bostrom - manuscript
  14. Self-Locating Belief in Big Worlds: Cosmology's Missing Link to Observation.Nick Bostrom - 2002 - 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.
  15. Agreement Theorems for Self-Locating Belief.Michael Caie - 2016 - Review of Symbolic Logic 9 (2):380-407.
  16. Goodman Nelson. Axiomatic Measurement of Simplicity. The Journal of Philosophy, Vol. 52 , Pp. 709–722.Robert L. Causey - 1972 - Journal of Symbolic Logic 37 (1):174-175.
  17. Goodman Nelson. Condensation Versus Simplification. Theoria , Vol. 27 , Pp. 47–48.Robert L. Causey - 1972 - Journal of Symbolic Logic 37 (1):177.
  18. Goodman Nelson. Recent Developments in the Theory of Simplicity. Philosophy and Phenomenological Research, Vol. 19 No. 4 , Pp. 429–446. [REVIEW]Robert L. Causey - 1972 - Journal of Symbolic Logic 37 (1):176-177.
  19. Goodman Nelson. The Test of Simplicity. Science, Vol. 128 , Pp. 1064–1069.Robert L. Causey - 1972 - Journal of Symbolic Logic 37 (1):176.
  20. Goodman Nelson. On Likeness of Meaning. Analysis , Vol. 10 No. 1 , Pp. 1–7.Alonzo Church - 1950 - Journal of Symbolic Logic 15 (2):150-151.
  21. Hempel C. G.. Geometry and Empirical Science. The American Mathematical Monthly, Vol. 52 , Pp. 7–17.Alonzo Church - 1946 - Journal of Symbolic Logic 11 (3):100.
  22. A Paradox of Conditional Probability.Michael Clark - 1989 - Analysis 49 (1):16 - 21.
  23. Adams E. M.. Hall's Analysis of “Ought.” The Journal of Philosophy, Vol. 55 , Pp. 73–75.Hall Everett W.. Existential Normatives. The Journal of Philosophy, Vol. 55 , Pp. 75–77. [REVIEW]Romane Clark - 1959 - Journal of Symbolic Logic 24 (3):265-266.
  24. Hall Everett W.. What is Value? An Essay in Philosophical Analysis. The Humanities Press, New York 1952, and Routledge & Kegan Paul, London 1952, Xi + 255 Pp.Hochberg Herbert. ‘Fitting’ as a Semantical Predicate. Mind, N.S. Vol. 65 , Pp. 530–533.Hall Everett W.. Hochberg on What is ‘Fitting’ for Ewing and Hall. Mind, N.S. Vol. 67 , Pp. 104–106.Adams E. M.. The Nature of Ought. Philosophical Studies , Vol. 7 , Pp. 36–42.Hall Everett W.. Further Words on ‘Ought.’ Philosophical Studies , Vol. 7 , Pp. 74–78.Adams E. M.. ‘Ought’ Again. Philosophical Studies , Vol. 8 , Pp. 86–89. [REVIEW]Romane Clark - 1959 - Journal of Symbolic Logic 24 (1):89-91.
  25. The Disordered Bedin the Sleeping Venus.Jodi Cranston - 2013 - In Iris Wenderholm, Jörg Trempler & Markus Rath (eds.), Das Haptische Bild: Körperhafte Bilderfahrung in der Neuzeit. De Gruyter. pp. 31-50.
  26. A Remark on Hempel's Replies to His Critics.Stephens M. Dietz - 1970 - Philosophy of Science 37 (4):614-617.
  27. A Shooting-Room View of Doomsday.William Eckhardt - 1997 - Journal of Philosophy 94 (5):244.
  28. Problem Decomposition for Problem Solution.Leona F. Fass - 2001 - Bulletin of Symbolic Logic 7 (3):431-432.
  29. Goodman Nelson. New Notes on Simplicity.Frederic B. Fitch - 1953 - Journal of Symbolic Logic 18 (2):179.
  30. Goodman Nelson. Some Reflections of the Theory of Systems. English with Spanish Abstract. Philosophy and Phenomenological Research, Vol. 9 No. 3 , Pp. 620–626. [REVIEW]Frederic B. Fitch - 1950 - Journal of Symbolic Logic 15 (3):218.
  31. Goodman’s “New Riddle”.Branden Fitelson - 2008 - Journal of Philosophical Logic 37 (6):613-643.
    First, a brief historical trace of the developments in confirmation theory leading up to Goodman's infamous "grue" paradox is presented. Then, Goodman's argument is analyzed from both Hempelian and Bayesian perspectives. A guiding analogy is drawn between certain arguments against classical deductive logic, and Goodman's "grue" argument against classical inductive logic. The upshot of this analogy is that the "New Riddle" is not as vexing as many commentators have claimed. Specifically, the analogy reveals an intimate connection between Goodman's problem, and (...)
  32. On the Problem of Confirmation.John E. Freund - 1958 - Journal of Symbolic Logic 23 (1):76-77.
  33. La Ramification Selon Everett: Une Interprétation Critiquée Mais Logiquement Impeccable de la Mécanique Quantique.Roland Frïasé - 1987 - History and Philosophy of Logic 8 (2):215-241.
    Pour résoudre les paradoxes bien connus de la mécanique quantique, on propose une interprétation par ramification (ou univers parallèles) analogue à celle d?Everett, mais avec des différences: (i) on propose une infinité continue de branches, dont les poids (o[ugrave] probabilités) se calculent par intégrale; (ii) les branches sont séparées par des ramifieurs qui se propagent à la vitesse de la lumière. Lorsqu?est négligeable la composante d?énergie négative de la fonction d?onde, le poids de chaque branche en un point donné u (...)
  34. Lewis Harry R. And Papadimitriou Christos H.. Elements of the Theory of Computation. Prentice-Hall Software Series. Prentice-Hall, Inc., Englewood Cliffs, N.J., 1981, Xiv + 466 Pp. [REVIEW]Jean H. Gallier - 1984 - Journal of Symbolic Logic 49 (3):989-990.
  35. A Laplacean Formal Semantics for Single-Case Propensities.Ronald N. Giere - 1976 - Journal of Philosophical Logic 5 (3):321 - 353.
    Even those generally skeptical of propensity interpretations of probability must now grant the following two points. First, the above single-case propensity interpretation meets recognized formal conditions for being a genuine interpretation of probability. Second, this interpretation is not logically reducible to a hypothetical relative frequency interpretation, nor is it only vacuously different from such an interpretation.The main objection to this propensity interpretation must be not that it is too vague or vacuous, but that it is metaphysically too extravagant. It asserts (...)
  36. The Paradox of Confirmation.I. J. Good - 1961 - British Journal for the Philosophy of Science 12 (45):63-64.
  37. The Paradox of Confirmation.L. J. Good - 1960 - British Journal for the Philosophy of Science 11 (42):145-b-145.
  38. Reden von Gott. Reflexionen Zur Analytischen Philosophie der Religiösen Sprache.G. H. H. - 1976 - Review of Metaphysics 29 (4):732-733.
  39. The Sleeping Lord.René Hague - 1974 - New Blackfriars 55 (652):402-415.
  40. Three Models of Sequential Belief Updating on Uncertain Evidence.James Hawthorne - 2004 - Journal of Philosophical Logic 33 (1):89-123.
    Jeffrey updating is a natural extension of Bayesian updating to cases where the evidence is uncertain. But, the resulting degrees of belief appear to be sensitive to the order in which the uncertain evidence is acquired, a rather un-Bayesian looking effect. This order dependence results from the way in which basic Jeffrey updating is usually extended to sequences of updates. The usual extension seems very natural, but there are other plausible ways to extend Bayesian updating that maintain order-independence. I will (...)
  41. Review: Hans Reichenbach, The Verifiability Theory of Meaning; Carl G. Hempel, The Concept of Cognitive Significance: A Reconsideration; Gustav Bergmann, Comments on Professor Hempel's "The Concept of Cognitive Significance.". [REVIEW]William H. Hay - 1952 - Journal of Symbolic Logic 17 (2):134-136.
  42. Welsh Prose Versions of the Fifteen Signs Before Doomsday.William W. Heist - 1944 - Speculum 19 (4):421-432.
  43. Hempel Carl G.. Ein System Verallgemeinerter Negationen. Travaux du IXe Congrès International de Philosophie, VI Logique Et Mathématiques, Actualités Scientifiques Et Industrielles 535, Hermann Et Cie, Paris 1937, Pp. 26–32. [REVIEW]Paul Henle - 1938 - Journal of Symbolic Logic 3 (4):164.
  44. Synchronic Bayesian Updating and the Sleeping Beauty Problem: Reply to Pust.Terry Horgan - 2008 - Synthese 160 (2):155-159.
    I maintain, in defending “thirdism,” that Sleeping Beauty should do Bayesian updating after assigning the “preliminary probability” 1/4 to the statement S: “Today is Tuesday and the coin flip is heads.” (This preliminary probability obtains relative to a specific proper subset I of her available information.) Pust objects that her preliminary probability for S is really zero, because she could not be in an epistemic situation in which S is true. I reply that the impossibility of being in such an (...)
  45. On Confirmation.Janina Hosiasson-Lindenbaum - 1940 - Journal of Symbolic Logic 5 (4):133-148.
  46. The Logic of Theory Assessment.Franz Huber - 2007 - Journal of Philosophical Logic 36 (5):511-538.
    This paper starts by indicating the analysis of Hempel's conditions of adequacy for any relation of confirmation (Hempel, 1945) as presented in Huber (submitted). There I argue contra Carnap (1962, Section 87) that Hempel felt the need for two concepts of confirmation: one aiming at plausible theories and another aiming at informative theories. However, he also realized that these two concepts are conflicting, and he gave up the concept of confirmation aiming at informative theories. The main part of the paper (...)
  47. The Sleeping King.Richard Jackson - 1969 - Bibliothèque d'Humanisme Et Renaissance 31 (3):525-551.
  48. Sharpe R. A.. Validity and the Paradox of Confirmation. The Philosophical Quarterly , Vol. 14 , Pp. 170–173.David Kaplan - 1967 - Journal of Symbolic Logic 32 (2):251.
  49. Vincent R. H.. The Paradoxes of Confirmation. Mind, N.S. Vol. 73 , Pp. 273–279.David Kaplan - 1967 - Journal of Symbolic Logic 32 (2):250-251.
  50. Between Analytic and Empirical, by J. W. N. Watkins. [REVIEW]David Kaplan - 1967 - Journal of Symbolic Logic 32 (2):246-249.
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