Declarations of independence Article First Online: 02 October 2014 Received: 18 June 2014 Accepted: 09 September 2014 DOI :
10.1007/s11229-014-0559-2

Cite this article as: Fitelson, B. & Hájek, A. Synthese (2014). doi:10.1007/s11229-014-0559-2
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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.

Keywords Conditional probability Independence Popper Confirmation

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Authors and Affiliations 1. Department of Philosophy Rutgers University New Brunswick USA 2. School of Philosophy Australian National University Canberra Australia