Probability Logic and Logical Probability

Abstract

Authors like Keynes, H. Jeffreys and Carnap advocated using a concept of "logical probability".  Logical probability had the following properties: (a) it was representable as a function from potential states of full belief (or "evidence") to states of subjective or credal probability judgment.  (b) Such functions were alleged to be constrained by principles of probability logic.  (c) All rational agents were supposed to be obliged to adopt the standard function that probability logic prescribed.  In this essay, it is argued that these three requirements could be satisfied only if probability logic prescribed that credal probability should be numerically determinate.  Keynes denied that it should numerically determinate and Carnap abandoned the idea that probability logic could supply a determinate function from states of full belief to numerically determinate credal states that all rational agents ought to adopt.   The paper explains that once this is conceded, logical probability ought to be interpreted rather differently than it is customarily is.