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Probability and Symmetry

Philosophy of Science 68 (S3):S109-S122 (2001)

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  1. Popper Functions, Uniform Distributions and Infinite Sequences of Heads.Alexander R. Pruss - 2015 - Journal of Philosophical Logic 44 (3):259-271.
    Popper functions allow one to take conditional probabilities as primitive instead of deriving them from unconditional probabilities via the ratio formula P=P/P. A major advantage of this approach is it allows one to condition on events of zero probability. I will show that under plausible symmetry conditions, Popper functions often fail to do what they were supposed to do. For instance, suppose we want to define the Popper function for an isometrically invariant case in two dimensions and hence require the (...)
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  • How and How Not to Make Predictions with Temporal Copernicanism.Kevin Nelson - 2009 - Synthese 166 (1):91-111.
    Gott (Nature 363:315–319, 1993) considers the problem of obtaining a probabilistic prediction for the duration of a process, given the observation that the process is currently underway and began a time t ago. He uses a temporal Copernican principle according to which the observation time can be treated as a random variable with uniform probability density. A simple rule follows: with a 95% probability.
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  • Epistemic Theories of Objective Chance.Richard Johns - forthcoming - Synthese.
    Epistemic theories of objective chance hold that chances are idealised epistemic probabilities of some sort. After giving a brief history of this approach to objective chance, I argue for a particular version of this view, that the chance of an event E is its epistemic probability, given maximal knowledge of the possible causes of E. The main argument for this view is the demonstration that it entails all of the commonly-accepted properties of chance. For example, this analysis entails that chances (...)
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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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  • Challenges to Bayesian Confirmation Theory.John D. Norton - 2011 - In Prasanta S. Bandyopadhyay & Malcolm R. Forster (eds.), Handbook of the Philosophy of Science, Vol. 7: Philosophy of Statistics. Elsevier B.V.. pp. 391-440.
    Proponents of Bayesian confirmation theory believe that they have the solution to a significant, recalcitrant problem in philosophy of science. It is the identification of the logic that governs evidence and its inductive bearing in science. That is the logic that lets us say that our catalog of planetary observations strongly confirms Copernicus’ heliocentric hypothesis; or that the fossil record is good evidence for the theory of evolution; or that the 3oK cosmic background radiation supports big bang cosmology. The definitive (...)
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  • On Bertrand's Paradox.Sorin Bangu - 2010 - Analysis 70 (1):30-35.
    The Principle of Indifference is a central element of the ‘classical’ conception of probability, but, for all its strong intuitive appeal, it is widely believed that it faces a devastating objection: the so-called (by Poincare´) ‘Bertrand paradoxes’ (in essence, cases in which the same probability question receives different answers). The puzzle has fascinated many since its discovery, and a series of clever solutions (followed promptly by equally clever rebuttals) have been proposed. However, despite the long-standing interest in this problem, an (...)
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  • Feminist Philosophy of Science1.Lynn Hankinson Nelson - 2002 - In Peter Machamer Michael Silberstein (ed.), The Blackwell Guide to the Philosophy of Science. Blackwell. pp. 312.
  • The Indifference Principle, its Paradoxes and Kolmogorov's Probability Space.Dan D. November - unknown
    In this paper I show that the validity of the Indifference Principle in light of its related paradoxes, is still an open question. I do so by offering an analysis of IP and its related paradoxes in the way they are manifested within the framework of Kolmogorov's probability theory. I describe the conditions that any mathematical formalization of IP must satisfy. Consequently, I show that IP's mathematical formalization has to be a set of constrains on probability spaces which mathematically describe (...)
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