20/03/22 10:02:49 TMbOZsnt.net
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>Of course, one could mean "independently" here in some non-mathematical causal sense. (And there may be philosophical reason for doing this: fitelson.org/doi.pdf )
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URLﾘﾝｸ(fitelson.org)
Synthese ・ September 2014?137 (3), 273-323
Declarations of Independence
Branden Fitelson and Alan Hajek
Abstract
According to orthodox (Kolmogorovian) probability theory, conditional probabilities are by definition certain ratios of unconditional probabilities. As a result, orthodox conditional probabilities are regarded as 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.
URLﾘﾝｸ(www.researchgate.net)
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URLﾘﾝｸ(fitelson.org)
Branden Fitelson is Distinguished Professor of Philosophy at Northeastern University.
Before teaching at Northeastern, Branden held teaching positions at Rutgers, UC-Berkeley, San Jose State, and Stanford and visiting positions at the Munich Center for Mathematical Philosophy at LMU-Munich (MCMP @ LMU) and the Institute for Logic, Language and Computation at the University of Amsterdam (ILLC @ UvA).
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