, Volume 186, Issue 2, pp 511–529

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


DOI: 10.1007/s11229-011-9997-2

Cite this article as:
Makinson, D. Synthese (2012) 186: 511. doi:10.1007/s11229-011-9997-2


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.


Lottery paradoxPreface paradoxUncertain inferenceConjunctionRationalityInconsistencyLossy rules

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© Springer Science+Business Media B.V. 2011

Authors and Affiliations

  1. 1.Department of Philosophy, Logic & Scientific MethodLondon School of EconomicsLondonUK