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A Review of the Lottery Paradox

In William Harper & Gregory Wheeler (eds.), Probability and Inference: Essays in Honour of Henry E. Kyburg, Jr. College Publications (2007)

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  1. The Psychological Dimension of the Lottery Paradox.Jennifer Nagel - 2021 - In Igor Douven (ed.), The Lottery Paradox. Cambridge University Press.
    The lottery paradox involves a set of judgments that are individually easy, when we think intuitively, but ultimately hard to reconcile with each other, when we think reflectively. Empirical work on the natural representation of probability shows that a range of interestingly different intuitive and reflective processes are deployed when we think about possible outcomes in different contexts. Understanding the shifts in our natural ways of thinking can reduce the sense that the lottery paradox reveals something problematic about our concept (...)
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  • On the Rationality of Inconsistent Predictions: The March Madness Paradox.Rory Smead - 2016 - Journal of the Philosophy of Sport 43 (1):163-169.
    There are circumstances in which we want to predict a series of interrelated events. Faced with such a prediction task, it is natural to consider logically inconsistent predictions to be irrational. However, it is possible to find cases where an inconsistent prediction has higher expected accuracy than any consistent prediction. Predicting tournaments in sports provides a striking example of such a case and I argue that logical consistency should not be a norm of rational predictions in these situations.
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  • Logical questions behind the lottery and preface paradoxes: lossy rules for uncertain inference.David Makinson - 2012 - Synthese 186 (2):511-529.
    We reflect on lessons that the lottery and preface paradoxes provide for the logic of uncertain inference. One of these lessons is the unreliability of the rule of conjunction of conclusions in such contexts, whether the inferences are probabilistic or qualitative; this leads us to an examination of consequence relations without that rule, the study of other rules that may nevertheless be satisfied in its absence, and a partial rehabilitation of conjunction as a ‘lossy’ rule. A second lesson is the (...)
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  • Reducing belief simpliciter to degrees of belief.Hannes Leitgeb - 2013 - Annals of Pure and Applied Logic 164 (12):1338-1389.
    Is it possible to give an explicit definition of belief in terms of subjective probability, such that believed propositions are guaranteed to have a sufficiently high probability, and yet it is neither the case that belief is stripped of any of its usual logical properties, nor is it the case that believed propositions are bound to have probability 1? We prove the answer is ‘yes’, and that given some plausible logical postulates on belief that involve a contextual “cautiousness” threshold, there (...)
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  • Closure and Epistemic Modals.Justin Bledin & Tamar Lando - 2018 - Philosophy and Phenomenological Research 97 (1):3-22.
    According to a popular closure principle for epistemic justification, if one is justified in believing each of the premises in set Φ and one comes to believe that ψ on the basis of competently deducing ψ from Φ—while retaining justified beliefs in the premises—then one is justified in believing that ψ. This principle is prima facie compelling; it seems to capture the sense in which competent deduction is an epistemically secure means to extend belief. However, even the single-premise version of (...)
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  • How bad is the postulation of a low entropy initial state of the universe?Aldo Filomeno - 2023 - Aphex 27:141-158.
    I summarize, in this informal interview, the main approaches to the ‘Past Hypothesis’, the postulation of a low-entropy initial state of the universe. I’ve chosen this as an open problem in the philosophical foundations of physics. I hope that this brief overview helps readers in gaining perspective and in appreciating the diverse range of approaches in this fascinating unresolved debate.
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  • Probability of Guilt.Mario Günther - manuscript
    In legal proceedings, a fact-finder needs to decide whether a defendant is guilty or not based on probabilistic evidence. We defend the thesis that the defendant should be found guilty just in case it is rational for the fact-finder to believe that the defendant is guilty. We draw on Leitgeb’s stability theory for an appropriate notion of rational belief and show how our thesis solves the problem of statistical evidence. Finally, we defend our account of legal proof against challenges from (...)
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  • On argument strength.Niki Pfeifer - 2013 - In Frank Zenker (ed.), Bayesian argumentation. The practical side of probability. Dordrecht, Netherlands: pp. 185-193.
    Everyday life reasoning and argumentation is defeasible and uncertain. I present a probability logic framework to rationally reconstruct everyday life reasoning and argumentation. Coherence in the sense of de Finetti is used as the basic rationality norm. I discuss two basic classes of approaches to construct measures of argument strength. The first class imposes a probabilistic relation between the premises and the conclusion. The second class imposes a deductive relation. I argue for the second class, as the first class is (...)
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