Levi, Isaac
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.
BibTeX  Entry
@InProceedings{levi:DSP:2007:1210,
author = {Isaac Levi},
title = {Probability Logic and Logical Probability},
booktitle = {Formal Models of Belief Change in Rational Agents},
year = {2007},
editor = {Giacomo Bonanno and James Delgrande and J{\'e}r{\^o}me Lang and Hans Rott},
number = {07351},
series = {Dagstuhl Seminar Proceedings},
ISSN = {18624405},
publisher = {Internationales Begegnungs und Forschungszentrum f{\"u}r Informatik (IBFI), Schloss Dagstuhl, Germany},
address = {Dagstuhl, Germany},
URL = {http://drops.dagstuhl.de/opus/volltexte/2007/1210},
annote = {Keywords: Probability, full belief, logic, evidence}
}
Keywords: 

Probability, full belief, logic, evidence 
Seminar: 

07351  Formal Models of Belief Change in Rational Agents

Issue date: 

2007 
Date of publication: 

20.11.2007 