Some epistemological ramifications of the Borel–Kolmogorov paradox

Michael Rescorla

pp. 735-767

in: Bjørn Jespersen, Marie Duží (eds), Hyperintensionality, Synthese 192 (3), 2015.

Abstract

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.

Cited authors

Frege Gottlob