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. Three Puzzles About Lotteries.Julia Staffel - forthcoming - In Igor Douven (ed.), Lotteries, Knowledge, and Rational Belief. Cambridge University Press.
    In this article, I discuss three distinct but related puzzles involving lotteries: Kyburg’s lottery paradox, the statistical evidence problem, and the Harman-Vogel paradox. Kyburg’s lottery paradox is the following well-known problem: if we identify rational outright belief with a rational credence above a threshold, we seem to be forced to admit either that one can have inconsistent rational beliefs, or that one cannot rationally believe anything one is not certain of. The statistical evidence problem arises from the observation that people (...)
  2. Routes for Roots: A Mapping Shorthand Symbolism with Reference to Nelson Goodman’s Hidden Ars Combinatoria.Gerald Moshammer - 2017 - History and Philosophy of Logic 38 (3):263-281.
    A shorthand symbolism for the relational mapping of categories is introduced and developed on the basis of Nelson Goodman's structural methodology. Through a reconstruction of extensional isomorphism that Goodman introduces as a criterion for definitional accuracy, and a brief reminder of the argument structure behind his ‘new riddle of induction’, Goodman's radical ontological relativism is turned into a protological principle of what I call ‘domain constituting philosophy’. MSS is demonstrated with reference to Goodman's symbol theory, particularly his notion of exemplification, (...)
  3. Agreement Theorems for Self-Locating Belief.Michael Caie - 2016 - Review of Symbolic Logic 9 (2):380-407.
  4. Genuine Coherence as Mutual Confirmation Between Content Elements.Michael Schippers & Gerhard Schurz - 2017 - Studia Logica 105 (2):299-329.
    The concepts of coherence and confirmation are closely intertwined: according to a prominent proposal coherence is nothing but mutual confirmation. Accordingly, it should come as no surprise that both are confronted with similar problems. As regards Bayesian confirmation measures these are illustrated by the problem of tacking by conjunction. On the other hand, Bayesian coherence measures face the problem of belief individuation. In this paper we want to outline the benefit of an approach to coherence and confirmation based on content (...)
  5. Goodman's Extensional Isomorphism and Syntactical Interpretations.Marek Polanski - 2009 - Theoria: Revista de Teoría, Historia y Fundamentos de la Ciencia 24 (2):203-211.
    The aim of the present paper is to provide a model-theoretic explication of Nelson Goodman’s concept of extensional isomorphism. The term "extensional isomorphism" has been informally introduced by Nelson Goodman in the beginning paragraph of his The Structure of Appearance. After some conceptual clarications Goodman’s concept of isomorphy turns out to be closely related to some variant of set-theoretic denability and some variants of syntactical interpretability.
  6. A Shooting-Room View of Doomsday.William Eckhardt - 1997 - Journal of Philosophy 94 (5):244.
  7. Everettian Confirmation and Sleeping Beauty.A. Wilson - 2014 - British Journal for the Philosophy of Science 65 (3):573-598.
    Darren Bradley has recently appealed to observation selection effects to argue that conditionalization presents no special problem for Everettian quantum mechanics, and to defend the ‘halfer’ answer to the puzzle of Sleeping Beauty. I assess Bradley’s arguments and conclude that while he is right about confirmation in Everettian quantum mechanics, he is wrong about Sleeping Beauty. This result is doubly good news for Everettians: they can endorse Bayesian confirmation theory without qualification, but they are not thereby compelled to adopt the (...)
  8. Hempel Carl G. And Oppenheim Paul. Reply to David L. Miller's Comments. Philosophy of Science, Vol. 15 Pp. 350–352.Thomas Storer - 1949 - Journal of Symbolic Logic 14 (2):133.
  9. 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.
  10. Hempel Carl G.. Aspects of Scientific Explanation. Aspects of Scientific Explanation and Other Essays in the Philosophy of Science, by Hempel Carl G., The Free Press, New York, and Collier-Macmillan Ltd., London, 1965, Pp. 331–496. [REVIEW]Asa Kasher - 1972 - Journal of Symbolic Logic 37 (4):747-749.
  11. 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.
  12. 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.
  13. Goodman Nelson. The Test of Simplicity. Science, Vol. 128 , Pp. 1064–1069.Robert L. Causey - 1972 - Journal of Symbolic Logic 37 (1):176.
  14. Goodman Nelson. Condensation Versus Simplification. Theoria , Vol. 27 , Pp. 47–48.Robert L. Causey - 1972 - Journal of Symbolic Logic 37 (1):177.
  15. 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.
  16. Sharpe R. A.. Validity and the Paradox of Confirmation. The Philosophical Quarterly , Vol. 14 , Pp. 170–173. [REVIEW]David Kaplan - 1967 - Journal of Symbolic Logic 32 (2):251.
  17. Between Analytic and Empirical, by J. W. N. Watkins. [REVIEW]David Kaplan - 1967 - Journal of Symbolic Logic 32 (2):246-249.
  18. Leblanc Hugues. Évidence Logique Et Degré de Confirmation. Revue Philosophique de Louvain, Vol. 52 , Pp. 619–625.Richard Montague - 1960 - Journal of Symbolic Logic 25 (1):86.
  19. 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.
  20. 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.
  21. Hempel Carl G.. A Logical Appraisal of Operationism. The Scientific Monthly, Vol. 79 , Pp. 215–220.Henry Mehlberg - 1958 - Journal of Symbolic Logic 23 (3):354-356.
  22. Freund John E.. On the Problem of Confirmation. Methodos, Vol. 3 , Pp. 33–42Somenzi Vittorio. Discussion. Methodos, Vol. 3 , P. 42. [REVIEW]Hilary Putnam - 1958 - Journal of Symbolic Logic 23 (1):76-77.
  23. Crawshay-Williams Rupert. Equivocal Confirmation. Analysis , Vol. 11 No. 4 , Pp. 73–79.Hilary Putnam - 1957 - Journal of Symbolic Logic 22 (4):406-407.
  24. Goodman Nelson. New Notes on Simplicity.Frederic B. Fitch - 1953 - Journal of Symbolic Logic 18 (2):179.
  25. 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.
  26. 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.
  27. Hempel Carl G. And Oppenheim Paul. Studies in the Logic of Explanation. Philosophy of Science, Vol. 15 , Pp. 135–175.Thomas Storer - 1949 - Journal of Symbolic Logic 14 (2):133.
  28. Morris Charles. Signs, Language, and Behavior. Prentice-Hall, Inc., New York 1946, V + 356 Pp. [REVIEW]Arthur Francis Smullyan - 1947 - Journal of Symbolic Logic 12 (2):49-51.
  29. 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.
  30. 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.
  31. 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.
  32. 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.
  33. 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.
  34. Hempel. Carl G. A Purely Syntactical Definition of Confirmation.Max Black - 1944 - Journal of Symbolic Logic 9 (2):47.
  35. Goodman Nelson. On the Simplicity of Ideas.George D. W. Berry - 1944 - Journal of Symbolic Logic 9 (2):52-53.
  36. Goodman Nelson. Sequences.J. C. C. McKinsey - 1942 - Journal of Symbolic Logic 7 (3):120.
  37. Leonard Henry S. And Goodman Nelson. The Calculus of Individuals and its Uses.Laurence J. Lafleur - 1940 - Journal of Symbolic Logic 5 (3):113-114.
  38. 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.
  39. Hempel C. G.. Le Problème de la Vérité. Theoria, Vol. 3 , Pp. 206–246.C. H. Langford - 1937 - Journal of Symbolic Logic 2 (4):170-171.
  40. The Sleeping Lord.René Hague - 1974 - New Blackfriars 55 (652):402-415.
  41. Updating a Progic.Eric Raidl - 2016 - Journal of Applied Logic 14:65-94.
  42. The Goodman Paradox: Three Different Problems and a Naturalistic Solution to Two of Them.Nathan Stemmer - 2004 - Journal for General Philosophy of Science / Zeitschrift für Allgemeine Wissenschaftstheorie 35 (2):351-370.
    It is now more than 50 years that the Goodman paradox has been discussed, and many different solutions have been proposed. But so far no agreement has been reached about which is the correct solution to the paradox. In this paper, I present the naturalistic solutions to the paradox that were proposed in Quine (1969, 1974), Quine and Ullian (1970/1978), and Stemmer (1971). At the same time, I introduce a number of modifications and improvements that are needed for overcoming shortcomings (...)
  43. A Defense of the Principle of Indifference.Greg Novack - 2010 - Journal of Philosophical Logic 39 (6):655-678.
    The principle of indifference (hereafter ‘Poi’) says that if one has no more reason to believe A than B (and vice versa ), then one ought not to believe A more than B (nor vice versa ). Many think it’s demonstrably false despite its intuitive plausibility, because of a particular style of thought experiment that generates counterexamples. Roger White ( 2008 ) defends Poi by arguing that its antecedent is false in these thought experiments. Like White I believe Poi, but (...)
  44. Testability and Ockham’s Razor: How Formal and Statistical Learning Theory Converge in the New Riddle of Induction.Daniel Steel - 2009 - Journal of Philosophical Logic 38 (5):471-489.
    Nelson Goodman's new riddle of induction forcefully illustrates a challenge that must be confronted by any adequate theory of inductive inference: provide some basis for choosing among alternative hypotheses that fit past data but make divergent predictions. One response to this challenge is to distinguish among alternatives by means of some epistemically significant characteristic beyond fit with the data. Statistical learning theory takes this approach by showing how a concept similar to Popper's notion of degrees of testability is linked to (...)
  45. 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 (...)
  46. Sleeping Beauty, Countable Additivity, and Rational Dilemmas.J. Ross - 2010 - Philosophical Review 119 (4):411-447.
    Currently, the most popular views about how to update de se or self-locating beliefs entail the one-third solution to the Sleeping Beauty problem.2 Another widely held view is that an agent‘s credences should be countably additive.3 In what follows, I will argue that there is a deep tension between these two positions. For the assumptions that underlie the one-third solution to the Sleeping Beauty problem entail a more general principle, which I call the Generalized Thirder Principle, and there are situations (...)
  47. An Empirical Critique of Two Versions of the Doomsday Argument – Gott's Line and Leslie's Wedge.E. Sober - 2003 - Synthese 135 (3):415-430.
    I discuss two versions of the doomsday argument. According to "Gott's Line", the fact that the human race has existed for 200,000 years licences the prediction that it will last between 5100 and 7.8 million more years. According to "Leslie's Wedge", the fact that I currently exist is evidence that increases the plausibility of the hypothesis that the human race will come to an end sooner rather than later. Both arguments rest on substantive assumptions about the sampling process that underlies (...)
  48. ‘Yes:—No:—I Have Been Sleeping—and Now—Now—I Am Dead’: Undeath, the Body and Medicine.Megan Stern - 2008 - Studies in History and Philosophy of Science Part C: Studies in History and Philosophy of Biological and Biomedical Sciences 39 (3):347-354.
  49. Incoherence and Inconsistency.Michael Schippers - 2014 - Review of Symbolic Logic 7 (3):511-528.
  50. 34. The Problem of the Enjoyment of Beauty.Guy Sircello - 2015 - In New Theory of Beauty. Princeton University Press. pp. 126-129.
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