## Probability and Conditionals: Belief Revision and Rational DecisionThis is a collection of essays on the relation between probabilities--especially conditional probabilities--and conditionals. It provides new negative results that sharply limit the ways conditionals can be related to conditional probabilities. There are also positive ideas and results that will open up new areas of research. The collection is intended to honor Ernest W. Adams, whose seminal work is largely responsible for creating this area of inquiry. As well as describing, evaluating, and applying Adams's work, the contributions extend his ideas in directions he may not have anticipated, but that he certainly inspired. |

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### Contents

Some questions about Adams conditionals | 5 |

Adams conditionals | 13 |

Brian Skyrms | 27 |

From Adams conditionals to default expressions | 47 |

The hypothesis of the conditional construal of conditional | 75 |

Triviality on the cheap? 3 | 113 |

Back in the CCCP | 141 |

The Hou sonirbach proofs of Bayesian principles | 161 |

Learning the impossible | 179 |

### Common terms and phrases

Adams agent's degrees algebra antecedent argument assumption atomic sentences axioms Bas van Fraassen Bayesian belief function version belief revision betting quotient Boolean Brian Skyrms causal CCCP holds conclusion conditional chance conditional probability conditional sentences Conditionalization consequent consistent constraints counterfactual counterfactual conditionals Decision Theory decision,making conditional default defined degrees of belief Dordrecht entailment epistemic equivalent example family of partitions finite Fraassen given Goldszmidt Hajek Howson and Urbach Hypothesis implies indicative conditional induction inference interpretation Jeffrey conditioning Lemma Lewis Logic of Conditionals McGee nonstandard probability obeys CCCP omonotonic orthogonal P,atom P(AT payoff Pearl perturbation Philosophical Popper function possible worlds principle Probabilities of Conditionals probability assignment probability function probability space probability theory problem proof propositions random variable ranking function rational agent real numbers reasoning Reidel Restricted CCCP Robert Stalnaker rule satisfy semantics simple conditional Suppose Theorem thesis triviality results true truth functional truth values W. L. Harper