On background: Using two-argument chance

Synthese 166 (1):165 - 186 (2009)
Abstract
I follow Hájek (Synthese 137:273–323, 2003c) by taking objective probability to be a function of two propositional arguments—that is, I take conditional probability as primitive. Writing the objective probability of q given r as P(q, r), I argue that r may be chosen to provide less than a complete and exact description of the world’s history or of its state at any time. It follows that nontrivial objective probabilities are possible in deterministic worlds and about the past. A very simple chance–credence relation is also then natural, namely that reasonable credence equals objective probability. In other words, we should set our actual credence in a proposition equal to the proposition’s objective probability conditional on available background information. One advantage of that approach is that the background information is not subject to an admissibility requirement, as it is in standard formulations of the Principal Principle. Another advantage is that the “undermining” usually thought to follow from Humean supervenience can be avoided. Taking objective probability to be a two-argument function is not merely a technical matter, but provides us with vital flexibility in addressing significant philosophical issues.
Keywords Conditional probability  Principal principle  Direct inference  Objective Bayesianism
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References found in this work BETA
Frank Arntzenius & Ned Hall (2003). On What We Know About Chance. British Journal for the Philosophy of Science 54 (2):171-179.
Robert Black (1998). Chance, Credence, and the Principal Principle. British Journal for the Philosophy of Science 49 (3):371-385.
Arthur W. Burks (1977). Chance, Cause, Reason. Chicago,University of Chicago Press.

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Citations of this work BETA
Christopher J. G. Meacham (2010). Two Mistakes Regarding the Principal Principle. British Journal for the Philosophy of Science 61 (2):407-431.
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