Synthese 194 (10):3979-3995 (2017)

Authors
Branden Fitelson
Northeastern University
Abstract
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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DOI 10.1007/s11229-014-0559-2
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References found in this work BETA

Logical Foundations of Probability.Rudolf Carnap - 1950 - Chicago]University of Chicago Press.
A Subjectivist’s Guide to Objective Chance.David K. Lewis - 1980 - In Richard C. Jeffrey (ed.), Studies in Inductive Logic and Probability, Volume II. Berkeley: University of California Press. pp. 263-293.
What Conditional Probability Could Not Be.Alan Hájek - 2003 - Synthese 137 (3):273--323.

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Citations of this work BETA

Conditional Probabilities.Kenny Easwaran - 2019 - In Richard Pettigrew & Jonathan Weisberg (eds.), The Open Handbook of Formal Epistemology. PhilPapers Foundation. pp. 131-198.
Conditional Degree of Belief and Bayesian Inference.Jan Sprenger - 2020 - Philosophy of Science 87 (2):319-335.
Bayesian Decision Theory and Stochastic Independence.Philippe Mongin - 2020 - Philosophy of Science 87 (1):152-178.
You’Ve Come a Long Way, Bayesians.Jonathan Weisberg - 2015 - Journal of Philosophical Logic 44 (6):817-834.

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