Some epistemological ramifications of the Borel–Kolmogorov paradox

Synthese 192 (3):735-767 (2015)
Authors
Michael Rescorla
University of California, Los Angeles
Abstract
This paper discusses conditional probability $$P$$ P , or the probability of A given B. When $$P>0$$ P > 0 , the ratio formula determines $$P$$ P . When $$P=0$$ P = 0 , the ratio formula breaks down. The Borel–Kolmogorov paradox suggests that conditional probabilities in such cases are indeterminate or ill-posed. To analyze the paradox, I explore the relation between probability and intensionality. I argue that the paradox is a Frege case, similar to those that arise in many probabilistic and non-probabilistic contexts. The paradox vividly illustrates how an agent’s way of representing an entity can rationally influence her credal assignments. I deploy my analysis to defend Kolmogorov’s relativistic treatment of conditional probability
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DOI 10.1007/s11229-014-0586-z
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References found in this work BETA

What Conditional Probability Could Not Be.Alan Hájek - 2003 - Synthese 137 (3):273--323.
Truth and the Absence of Fact.Hartry Field - 2001 - Oxford University Press.
Problems of Rationality.Donald Davidson - 2004 - Oxford University Press.

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