David Bourget (Western Ontario)
David Chalmers (ANU, NYU)
Rafael De Clercq
Jack Alan Reynolds
Learn more about PhilPapers
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.
|Keywords||No keywords specified (fix it)|
|Categories||categorize this paper)|
Setup an account with your affiliations in order to access resources via your University's proxy server
Configure custom proxy (use this if your affiliation does not provide a proxy)
|Through your library||
References found in this work BETA
No references found.
Citations of this work BETA
No citations found.
Similar books and articles
Richard Bradley (2006). Adams Conditionals and Non-Monotonic Probabilities. Journal of Logic, Language and Information 15 (1-2):65-81.
Charles G. Morgan & Edwin D. Mares (1995). Conditionals, Probability, and Non-Triviality. Journal of Philosophical Logic 24 (5):455-467.
Alan Hájek (2012). The Fall of “Adams' Thesis”? Journal of Logic, Language and Information 21 (2):145-161.
Richard Jeffrey (1996). Unknown Probabilities. Erkenntnis 45 (2-3):327 - 335.
James Hawthorne (1996). On the Logic of Nonmonotonic Conditionals and Conditional Probabilities. Journal of Philosophical Logic 25 (2):185-218.
Wolfgang Spohn (1994). On the Properties of Conditional Independence. In Paul Humphreys (ed.), Patrick Suppes, Scientific Philosopher Vol. 1: Probability and Probabilistic Causality. Kluwer.
Paul Weirich (1983). Conditional Probabilities and Probabilities Given Knowledge of a Condition. Philosophy of Science 50 (1):82-95.
Robert C. Stalnaker (1970). Probability and Conditionals. Philosophy of Science 37 (1):64-80.
Added to index2009-03-17
Total downloads65 ( #23,160 of 1,102,700 )
Recent downloads (6 months)4 ( #84,424 of 1,102,700 )
How can I increase my downloads?