What are conditional probabilities conditional upon?


Abstract
This paper rejects a traditional epistemic interpretation of conditional probability. Suppose some chance process produces outcomes X, Y,..., with probabilities P(X), P(Y),... If later observation reveals that outcome Y has in fact been achieved, then the probability of outcome X cannot normally be revised to P(X|Y) ['P&Y)/P(Y)]. This can only be done in exceptional circumstances - when more than just knowledge of Y-ness has been attained. The primary reason for this is that the weight of a piece of evidence varies with the means by which it is provided, so knowledge of Y-ness does not have uniform impact on the probability of X. A better updating of the probability of X is provided by P(X|Y*), where Y* is not an outcome of the chance process being observed, but the sentence 'the outcome Y has been observed', an 'outcome' of the subsequent observation process. This alternative formula is widely endorsed in practice, but not well recognized in theory, where the oversight has generated some unsatisfactory consequences.
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DOI 10.1093/bjps/50.4.665
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References found in this work BETA

Betting on Theories.Patrick Maher - 2008 - Cambridge University Press.
Belief and the Will.Bas C. van Fraassen - 2010 - In Antony Eagle (ed.), Philosophy of Probability: Contemporary Readings. Routledge. pp. 235-256.
The Foundations of Statistics.Leonard J. Savage - 1954 - Philosophy of Science 23 (2):166-166.

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Citations of this work BETA

Confirmation in a Branching World: The Everett Interpretation and Sleeping Beauty.Darren Bradley - 2011 - British Journal for the Philosophy of Science 62 (2):323-342.
Four Problems About Self-Locating Belief.D. Bradley - 2012 - Philosophical Review 121 (2):149-177.
Conditionalization and Belief De Se.Darren Bradley - 2010 - Dialectica 64 (2):247-250.

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