Some epistemological ramifications of the Borel-Kolmogorov paradox

摘要

This paper discusses conditional probability , or the probability of A given B. When , the ratio formula determines . When , 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.