Logical questions behind the lottery and preface paradoxes: lossy rules for uncertain inference

Synthese 186 (2):511-529 (2012)
Abstract
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 in its absence, and a partial rehabilitation of conjunction as a ‘lossy’ rule. A second lesson is the possibility of rational inconsistent belief; this leads us to formulate criteria for deciding when an inconsistent set of beliefs may reasonably be retained
Keywords Lottery paradox  Preface paradox  Uncertain inference  Conjunction  Rationality  Inconsistency  Lossy rules
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Kevin B. Korb (1992). The Collapse of Collective Defeat: Lessons From the Lottery Paradox. PSA: Proceedings of the Biennial Meeting of the Philosophy of Science Association 1992:230 - 236.
Igor Douven (2002). A New Solution to the Paradoxes of Rational Acceptability. British Journal for the Philosophy of Science 53 (3):391-410.
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