A continuum-valued logic of degrees of probability. (English) Zbl 1329.03061
Summary: Leibniz seems to have been the first to suggest a logical interpretation of probability, but there have always seemed formidable mathematical and interpretational barriers to implementing the idea. De Finetti revived it only, it seemed, to reject it in favour of a purely decision-theoretic approach. In this paper I argue that not only is it possible to view (Bayesian) probability as a continuum-valued logic, but that it has a very close formal kinship with classical propositional logic.
MSC:
| 03B50 | Many-valued logic |
| 03B48 | Probability and inductive logic |
| 60A05 | Axioms; other general questions in probability |
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