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There are many possible reductionist theories of chance, differing as to which possible pattern of events they take to be chance-making. It is also widely taken to be a norm of rationality that credence should defer to chance: special cases aside, rationality requires that one\u2019s credence function, when conditionalized on the chance-making facts, should coincide with the objective chance function. It is a shortcoming of a theory of chance if it implies that this norm of rationality is unsatisfiable. The primary goal of this paper is to show, on the basis of considerations concerning computability and inductive learning, that this shortcoming is more common than one would have hoped.<\/jats:p>","DOI":"10.1017\/s1755020323000151","type":"journal-article","created":{"date-parts":[[2023,6,13]],"date-time":"2023-06-13T10:27:30Z","timestamp":1686652050000},"page":"435-474","update-policy":"http:\/\/dx.doi.org\/10.1017\/policypage","source":"Crossref","is-referenced-by-count":1,"title":["UNPRINCIPLED"],"prefix":"10.1017","volume":"17","author":[{"given":"GORDON","family":"BELOT","sequence":"first","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"56","published-online":{"date-parts":[[2023,6,13]]},"reference":[{"key":"S1755020323000151_r29","doi-asserted-by":"publisher","DOI":"10.1016\/j.geb.2009.03.013"},{"key":"S1755020323000151_r6","first-page":"81","volume-title":"Information Processing \u201971","volume":"1","author":"B\u0101rzdi\u0146\u0161","year":"1972"},{"key":"S1755020323000151_r42","doi-asserted-by":"publisher","DOI":"10.4115\/jla.2010.2.10"},{"key":"S1755020323000151_r8","doi-asserted-by":"publisher","DOI":"10.1080\/00048402.2016.1139604"},{"key":"S1755020323000151_r16","doi-asserted-by":"publisher","DOI":"10.1016\/S0019-9958(75)90261-2"},{"key":"S1755020323000151_r33","doi-asserted-by":"publisher","DOI":"10.1017\/9781108781718.005"},{"key":"S1755020323000151_r38","doi-asserted-by":"publisher","DOI":"10.1016\/0304-4068(94)90037-X"},{"key":"S1755020323000151_r56","first-page":"247","volume-title":"Logic Colloquium \u201906","author":"Reimann","year":"2009"},{"key":"S1755020323000151_r4","doi-asserted-by":"publisher","DOI":"10.1017\/9781108781718.007"},{"key":"S1755020323000151_r50","volume-title":"Classical Recursion Theory II","author":"Odifreddi","year":"1999"},{"key":"S1755020323000151_r48","doi-asserted-by":"publisher","DOI":"10.1016\/S0019-9958(66)80018-9"},{"key":"S1755020323000151_r20","first-page":"131","volume-title":"The Open Handbook of Formal Epistemology","author":"Easwaran","year":"2019"},{"key":"S1755020323000151_r54","first-page":"761","volume-title":"The Philosophy of Rudolf Carnap","author":"Putnam","year":"1963a"},{"key":"S1755020323000151_r12","volume-title":"Theory of Charges: A Study of Finitely Additive Measures","author":"Bhaskara Rao","year":"1983"},{"key":"S1755020323000151_r39","doi-asserted-by":"publisher","DOI":"10.1007\/978-3-030-61871-1"},{"key":"S1755020323000151_r51","doi-asserted-by":"publisher","DOI":"10.1215\/00318108-1539098"},{"key":"S1755020323000151_r2","doi-asserted-by":"publisher","DOI":"10.1145\/356914.356918"},{"key":"S1755020323000151_r1","doi-asserted-by":"publisher","DOI":"10.2307\/2275058"},{"key":"S1755020323000151_r3","doi-asserted-by":"publisher","DOI":"10.1093\/bjps\/54.2.171"},{"key":"S1755020323000151_r37","doi-asserted-by":"publisher","DOI":"10.2307\/2951492"},{"key":"S1755020323000151_r18","doi-asserted-by":"publisher","DOI":"10.1007\/978-0-387-68441-3"},{"key":"S1755020323000151_r24","doi-asserted-by":"publisher","DOI":"10.1214\/aoms\/1177700068"},{"key":"S1755020323000151_r58","first-page":"581","article-title":"On finding predictors for arbitrary families of processes","volume":"11","author":"Ryabko","year":"2010","journal-title":"Journal of Machine Learning Research"},{"key":"S1755020323000151_r44","doi-asserted-by":"publisher","DOI":"10.1214\/lnms\/1215453571"},{"key":"S1755020323000151_r35","doi-asserted-by":"publisher","DOI":"10.1111\/j.1468-0068.2008.00681.x"},{"key":"S1755020323000151_r61","volume-title":"Quitting Certainties: A Bayesian Framework for Modeling Degrees of Belief","author":"Titelbaum","year":"2013"},{"key":"S1755020323000151_r19","volume-title":"Bayes or Bust? 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