Probabilities for two properties

Erkenntnis 52 (1):63-91 (2000)
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.
Keywords Philosophy   Philosophy   Epistemology   Ethics   Logic   Ontology
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DOI 10.1023/A:1005557828204
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C. J. Nix & J. B. Paris (2007). A Note on Binary Inductive Logic. Journal of Philosophical Logic 36 (6):735 - 771.

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