Declarations of independence

Synthese (forthcoming)
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.
What Conditional Probability Could Not Be.Alan Hájek - 2003 - Synthese 137 (3):273--323.
Regularity and Hyperreal Credences.Kenny Easwaran - 2014 - Philosophical Review 123 (1):1-41.

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Citations of this work BETA
You’Ve Come a Long Way, Bayesians.Jonathan Weisberg - forthcoming - Journal of Philosophical Logic:1-18.
Deutsch on the Epistemic Problem in Everettian Quantum Theory.Bradley Darren - forthcoming - Studies in History and Philosophy of Science Part B: Studies in History and Philosophy of Modern Physics.

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