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  1. Standard Decision Theory Corrected: Assessing Options When Probability is Infinitely and Uniformly Spread.Peter Vallentyne - 2000 - Synthese 122 (3):261-290.
    Where there are infinitely many possible [equiprobable] basic states of the world, a standard probability function must assign zero probability to each state—since any finite probability would sum to over one. This generates problems for any decision theory that appeals to expected utility or related notions. For it leads to the view that a situation in which one wins a million dollars if any of a thousand of the equally probable states is realized has an expected value of zero (since (...)
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  • Scientific Reasoning: The Bayesian Approach.Peter Urbach & Colin Howson - 1993 - Open Court.
    Scientific reasoning is—and ought to be—conducted in accordance with the axioms of probability. This Bayesian view—so called because of the central role it accords to a theorem first proved by Thomas Bayes in the late eighteenth ...
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  • Countable Additivity and the de Finetti Lottery.Paul Bartha - 2004 - British Journal for the Philosophy of Science 55 (2):301-321.
    De Finetti would claim that we can make sense of a draw in which each positive integer has equal probability of winning. This requires a uniform probability distribution over the natural numbers, violating countable additivity. Countable additivity thus appears not to be a fundamental constraint on subjective probability. It does, however, seem mandated by Dutch Book arguments similar to those that support the other axioms of the probability calculus as compulsory for subjective interpretations. These two lines of reasoning can be (...)
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  • Indifference, Sample Space, and the Wine/Water Paradox.Marc Burock - unknown
    Von Mises’ wine/water paradox has served as a foundation for detractors of the Principle of Indifference and logical probability. Mikkelson recently proposed a first solution, and here several additional solutions to the paradox are explained. Learning from the wine/water paradox, I will argue that it is meaningless to consider a particular probability apart from the sample space containing the probabilistic event in question.
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  • The Shooting-Room Paradox and Conditionalizing on Measurably Challenged Sets.Paul Bartha & Christopher Hitchcock - 1999 - 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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  • What Conditional Probability Could Not Be.Alan Hájek - 2003 - Synthese 137 (3):273--323.
    Kolmogorov''s axiomatization of probability includes the familiarratio formula for conditional probability: 0).$$ " align="middle" border="0">.
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  • God’s Lottery.Storrs McCall & D. M. Armstrong - 1989 - Analysis 49 (4):223 - 224.