Abstract
Let R(X, B) denote the class of probability functions that are defined on algebra X and that represent rationally permissible degrees of certainty for a person whose total relevant background evidence is B. This paper is concerned with characterizing R(X, B) for the case in whichX is an algebra of propositions involving two properties and B is empty. It proposes necessary conditions for a probability function to be in R(X, B), some of which involve the notion of statistical dependence. The class of probability functions that satisfy these conditions, here denoted PI, includes a class that Carnap once proposed for the same situation. Probability functions in PI violate Carnap's axiom of analogy but, it is argued, that axiom should be rejected. A derivation of Carnap's model by Hesse has limitations that are not present in the derivation of PI given here. Various alternative probability models are considered and rejected.
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Maher, P. Probabilities For Two Properties. Erkenntnis 52, 63–91 (2000). https://doi.org/10.1023/A:1005557828204
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DOI: https://doi.org/10.1023/A:1005557828204