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We reflect on lessons that the lottery and preface paradoxes provide for the logic of uncertain inference. One of these lessons is the unreliability of the rule of conjunction of conclusions in such contexts, whether the inferences are probabilistic or qualitative; this leads us to an examination of consequence relations without that rule, the study of other rules that may nevertheless be satisfied...
This paper explores how the Bayesian program benefits from allowing for objective chance as well as subjective degree of belief. It applies David Lewis’s Principal Principle and David Christensen’s principle of informed preference to defend Howard Raiffa’s appeal to preferences between reference lotteries and scaling lotteries to represent degrees of belief. It goes on to outline the role of objective...
This paper analyzes concepts of independence and assumptions of convexity in the theory of sets of probability distributions. The starting point is Kyburg and Pittarelli’s discussion of “convex Bayesianism” (in particular their proposals concerning E-admissibility, independence, and convexity). The paper offers an organized review of the literature on independence for sets of probability distributions;...
The rule of adjunction is intuitively appealing and uncontroversial for deductive inference, but in situations where information can be uncertain, the rule is neither needed nor wanted for rational acceptance, as illustrated by the lottery paradox. Practical certainty is the acceptance of statements whose chances of error are smaller than a prescribed threshold parameter, when evaluated against an...
Though he maintained a significant interest in theoretical aspects of measurement, Henry E. Kyburg, Jr. was critical of the representational theory that in many ways has come to dominate discussions concerning the foundations of measurement. In particular, Kyburg (in Savage and Ehrlich (eds) Philosophical and foundational issues in measurement theory, 1992) asserts that the representational theory...
This is a brief review of issues over which Henry Kyburg and I differed concerning the requirement that full beliefs should be closed under deductive consequence.
We defend a set of acceptance rules that avoids the lottery paradox, that is closed under classical entailment, and that accepts uncertain propositions without ad hoc restrictions. We show that the rules we recommend provide a semantics that validates exactly Adams’ conditional logic and are exactly the rules that preserve a natural, logical structure over probabilistic credal states that we call...
Kyburg’s opposition to the subjective Bayesian theory, and in particular to its advocates’ indiscriminate and often questionable use of Dutch Book arguments, is documented and much of it strongly endorsed. However, it is argued that an alternative version, proposed by both de Finetti at various times during his long career, and by Ramsey, is less vulnerable to Kyburg’s misgivings. This is a logical...
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