Richard Bradley

This paper examines Becker's thesis that the hypothesis that choices maximise expected utility relative to fixed and universal tastes provides a general framework for the explanation of behaviour. Three different models of preference revision are presented and their scope evaluated. The first, the classical conditioning model, explain all changes in preferences in terms of changes in the information held by the agent, holding fundamental beliefs and desires fixed. The second, the Jeffrey conditioning model, explains them in terms of changes in both the information held by the agent and changes in her prior beliefs, holding her fundamental desires fixed. The final model, that of generalised conditioning, allows for explanations in terms of changes in the values of all three variables.

Adams’ Thesis has much evidence in its favour, but DavidLewis famously showed that it cannot be true, in all but the most trivial of cases, if conditionals are proprositions and their probabilities are classical probabilities of truth. In this paper I show thatsimilar results can be constructed for a much wider class of conditionals. The fact that these results presupposethat the logic of conditionals is Boolean motivates a search for a non-Boolean alternative. It is arguedthat the exact proposition expressed by a conditional depends on the context in which it is uttered. Consequentlyits probability of truth will depend not only on the probabilities of the various propositions it mightexpress, but also on the probabilities of the contexts determining which proposition it does in fact express.The semantic theory developed from this is then shown to explain why agents’ degrees of belief satisfyAdams’ Thesis. Finally the theory is compared with proposals for a three-valued logic of conditionals.

According to the Ramsey Test hypothesis the conditional claim that if A then B is credible just in case it is credible that B, on the supposition that A. If true the hypothesis helps explain the way in which we evaluate and use ordinary language conditionals. But impossibility results for the Ramsey Test hypothesis in its various forms suggest that it is untenable. In this paper, I argue that these results do not in fact have this implication, on the grounds that similar results can be proved without recourse to the Ramsey test hypothesis. Instead they show that a number of well entrenched principles of rational belief and belief revision do not apply to conditionals.

Richard Jeffrey regarded the version of Bayesian decision theory he floated in ‘The Logic of Decision’ and the idea of a probability kinematics—a generalisation of Bayesian conditioning to contexts in which the evidence is ‘uncertain’—as his two most important contributions to philosophy. This paper aims to connect them by developing kinematical models for the study of preference change and practical deliberation. Preference change is treated in a manner analogous to Jeffrey’s handling of belief change: not as mechanical outputs of combinations of intrinsic desires plus information, but as a matter of judgement and of making up one’s mind. In the first section Jeffrey’s probability kinematics is motivated and extended to the treatment of changes in conditional belief. In the second, analogous kinematical models are developed for preference change and in particular belief-induced change that depends on an invariance condition for conditional preference. The two are the brought together in the last section in a tentative model of pratical deliberation.

In this paper Richard Jeffrey's 'Logic of Decision' is extended by examination of agents' attitudes to the sorts of possibilities identified by indicative conditional sentences. An expression for the desirability of conditionals is proposed and, along with Adams' thesis that the probability of a conditional equals the conditional probability of its antecedent given its consequent, is defended by informally deriving it from Jeffrey's notion of desirability and some weak constraints on rational preference for conditional possibilities. Finally a statement is given of a representation theorem establishing the conditions under which a rational agent's preferences for conditionals determines the existence of unique measures (up to choice of scale) of her degrees of belief and desire.

Bayesian models typically assume that agents are rational, logically omniscient and opinionated. The last of these has little descriptive or normative appeal, however, and limits our ability to describe how agents make up their minds (as opposed to changing them) or how they can suspend or withdraw their opinions. To address these limitations this paper represents the attitudinal states of non-opinionated agents by sets of (permissible) probability and desirability functions. Several basic ways in which such states of mind can be changed are then characterised and compared with those found in AGM style models of attitude revision. Finally these models are employed to describe how agents make up their mind when deliberating.

This paper investigates the role of conditionals in hypothetical reasoning and rational decision making. Its main result is a proof of a representation theorem for preferences defined on sets of sentences (and, in particular, conditional sentences), where an agent’s preference for one sentence over another is understood to be a preference for receiving the news conveyed by the former. The theorem shows that a rational preference ordering of conditional sentences determines probability and desirability representations of the agent’s degrees of belief and desire that satisfy, in the case of non-conditional sentences, the axioms of Jeffrey’s decision theory and, in the case of conditional sentences, Adams’ expression for the probabilities of conditionals. Furthermore, the probability representation is shown to be unique and the desirability representation unique up to positive linear transformation.