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(2015) Synthese 192 (3).
This paper discusses conditional probability (P(A{vert }B)), or the probability of A given B. When (P(B)>0), the ratio formula determines (P(A {vert } B)). When (P(B)=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.
Publication details
DOI: 10.1007/s11229-014-0586-z
Full citation:
Rescorla, M. (2015). Some epistemological ramifications of the Borel–Kolmogorov paradox. Synthese 192 (3), pp. 735-767.
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