David Bourget (Western Ontario)
David Chalmers (ANU, NYU)
Rafael De Clercq
Ezio Di Nucci
Jonathan Jenkins Ichikawa
Jack Alan Reynolds
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According to orthodox (Kolmogorovian) probability theory, conditional probabilities are by definition certain ratios of unconditional probabilities. As a result, orthodox conditional probabilities are undefined whenever their antecedents have zero unconditional probability. This has important ramifications for the notion of probabilistic independence. Traditionally, independence is defined in terms of unconditional probabilities (the factorization of the relevant joint unconditional probabilities). Various “equivalent” formulations of independence can be given using conditional probabilities. But these “equivalences” break down if conditional probabilities are permitted to have conditions with zero unconditional probability. We reconsider probabilistic independence in this more general setting. We argue that a less orthodox but more general (Popperian) theory of conditional probability should be used, and that much of the conventional wisdom about probabilistic independence needs to be rethought.
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References found in this work BETA
Rudolf Carnap (1962). Logical Foundations of Probability. Chicago]University of Chicago Press.
David Lewis (1979). Counterfactual Dependence and Time's Arrow. Noûs 13 (4):455-476.
Alan Hájek (2003). What Conditional Probability Could Not Be. Synthese 137 (3):273--323.
Kenny Easwaran (2014). Regularity and Hyperreal Credences. Philosophical Review 123 (1):1-41.
Citations of this work BETA
Jonathan Weisberg (forthcoming). You’Ve Come a Long Way, Bayesians. Journal of Philosophical Logic:1-18.
Bradley Darren (forthcoming). Deutsch on the Epistemic Problem in Everettian Quantum Theory. Studies in History and Philosophy of Science Part B: Studies in History and Philosophy of Modern Physics.
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