{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,2,21]],"date-time":"2025-02-21T07:45:08Z","timestamp":1740123908610,"version":"3.37.3"},"reference-count":41,"publisher":"Springer Science and Business Media LLC","issue":"2","license":[{"start":{"date-parts":[[2020,8,20]],"date-time":"2020-08-20T00:00:00Z","timestamp":1597881600000},"content-version":"tdm","delay-in-days":0,"URL":"https:\/\/www.springer.com\/tdm"},{"start":{"date-parts":[[2020,8,20]],"date-time":"2020-08-20T00:00:00Z","timestamp":1597881600000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/www.springer.com\/tdm"}],"content-domain":{"domain":["link.springer.com"],"crossmark-restriction":false},"short-container-title":["J Philos Logic"],"published-print":{"date-parts":[[2021,4]]},"DOI":"10.1007\/s10992-020-09569-2","type":"journal-article","created":{"date-parts":[[2020,8,20]],"date-time":"2020-08-20T08:03:42Z","timestamp":1597910622000},"page":"395-414","update-policy":"https:\/\/doi.org\/10.1007\/springer_crossmark_policy","source":"Crossref","is-referenced-by-count":0,"title":["Convergence to the Truth Without Countable Additivity"],"prefix":"10.1007","volume":"50","author":[{"ORCID":"https:\/\/orcid.org\/0000-0002-3161-6823","authenticated-orcid":false,"given":"Michael","family":"Nielsen","sequence":"first","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"297","published-online":{"date-parts":[[2020,8,20]]},"reference":[{"issue":"11","key":"9569_CR1","doi-asserted-by":"publisher","first-page":"3725","DOI":"10.1257\/aer.104.11.3725","volume":"104","author":"N Al-Najjar","year":"2014","unstructured":"Al-Najjar, N., Pomatto, L., & Sandroni, A. (2014). Claim validation. American Economic Review, 104(11), 3725\u201336.","journal-title":"American Economic Review"},{"key":"9569_CR2","volume-title":"Infinite dimensional analysis: a hitchhiker\u2019s guide","author":"CD Aliprantis","year":"2006","unstructured":"Aliprantis, C.D., & Border, K.C. (2006). Infinite dimensional analysis: a hitchhiker\u2019s guide. Berlin: Springer-Verlag."},{"issue":"4","key":"9569_CR3","doi-asserted-by":"publisher","first-page":"483","DOI":"10.1086\/673249","volume":"80","author":"G Belot","year":"2013","unstructured":"Belot, G. (2013). Bayesian orgulity. Philosophy of Science, 80 (4), 483\u2013503.","journal-title":"Philosophy of Science"},{"issue":"503","key":"9569_CR4","doi-asserted-by":"publisher","first-page":"655","DOI":"10.1093\/mind\/fzv185","volume":"126","author":"G Belot","year":"2017","unstructured":"Belot, G. (2017). Objectivity and bias. Mind, 126(503), 655\u2013695.","journal-title":"Mind"},{"issue":"1","key":"9569_CR5","first-page":"1","volume":"5","author":"L Bienvenu","year":"2009","unstructured":"Bienvenu, L., Shafer, G., & Shen, A. (2009). On the history of martingales in the study of randomness. Electronic Journal for History of Probability and Statistics, 5(1), 1\u201340.","journal-title":"Electronic Journal for History of Probability and Statistics"},{"key":"9569_CR6","volume-title":"Probability and Measure","author":"P Billingsley","year":"2008","unstructured":"Billingsley, P. (2008). Probability and Measure. New Jersey: John Wiley & Sons."},{"issue":"3","key":"9569_CR7","doi-asserted-by":"publisher","first-page":"882","DOI":"10.1214\/aoms\/1177704456","volume":"33","author":"D Blackwell","year":"1962","unstructured":"Blackwell, D., & Dubins, L. (1962). Merging of opinions with increasing information. The Annals of Mathematical Statistics, 33(3), 882\u2013886.","journal-title":"The Annals of Mathematical Statistics"},{"issue":"4","key":"9569_CR8","doi-asserted-by":"publisher","first-page":"341","DOI":"10.1007\/BF00533425","volume":"37","author":"R Chen","year":"1977","unstructured":"Chen, R. (1977). On almost sure convergence in a finitely additive setting. Zeitschrift f\u00fcr Wahrscheinlichkeitstheorie und verwandte Gebiete, 37 (4), 341\u2013356.","journal-title":"Zeitschrift f\u00fcr Wahrscheinlichkeitstheorie und verwandte Gebiete"},{"issue":"1","key":"9569_CR9","doi-asserted-by":"publisher","first-page":"53","DOI":"10.1086\/694836","volume":"85","author":"J Cisewski","year":"2018","unstructured":"Cisewski, J., Kadane, J.B., Schervish, M.J., Seidenfeld, T., & Stern, R. (2018). Standards for modest Bayesian credences. Philosophy of Science, 85(1), 53\u201378.","journal-title":"Philosophy of Science"},{"key":"9569_CR10","volume-title":"Probability, induction, and statistics","author":"B de Finetti","year":"1972","unstructured":"de Finetti, B. (1972). Probability, induction, and statistics. New Jersey: John Wiley & Sons."},{"key":"9569_CR11","volume-title":"Theory of Probability, Volume 1","author":"B de Finetti","year":"1974","unstructured":"de Finetti, B. (1974). Theory of Probability, Volume 1. New Jersey: John Wiley & Sons."},{"key":"9569_CR12","volume-title":"Stochastic Processes","author":"JL Doob","year":"1953","unstructured":"Doob, J.L. (1953). Stochastic Processes. Wiley: New York."},{"issue":"1","key":"9569_CR13","doi-asserted-by":"publisher","first-page":"89","DOI":"10.1214\/aop\/1176996451","volume":"3","author":"LE Dubins","year":"1975","unstructured":"Dubins, L.E. (1975). Finitely additive conditional probabilities, conglomerability and disintegrations. The Annals of Probability, 3(1), 89\u201399.","journal-title":"The Annals of Probability"},{"key":"9569_CR14","unstructured":"Dubins, L.E., & Savage, L.J. (1965). How to Gamble If You Must: Inequalities for Stochastic Processes. Dover Publications."},{"key":"9569_CR15","doi-asserted-by":"publisher","DOI":"10.1017\/CBO9780511779398","volume-title":"Probability: Theory and Examples","author":"R Durrett","year":"2010","unstructured":"Durrett, R. (2010). Probability: Theory and Examples. Cambridge: Cambridge University Press."},{"issue":"3","key":"9569_CR16","doi-asserted-by":"publisher","first-page":"193","DOI":"10.1037\/h0044139","volume":"70","author":"W Edwards","year":"1963","unstructured":"Edwards, W., Lindman, H., & Savage, L.J. (1963). Bayesian statistical inference for psychological research. Psychological review, 70(3), 193\u2013242.","journal-title":"Psychological review"},{"key":"9569_CR17","doi-asserted-by":"publisher","first-page":"305","DOI":"10.1086\/685740","volume":"83","author":"A Elga","year":"2016","unstructured":"Elga, A. (2016). Bayesian humility. Philosophy of Science, 83, 305\u2013323.","journal-title":"Philosophy of Science"},{"key":"9569_CR18","volume-title":"Fact, Fiction, and Forecast","author":"N Goodman","year":"1955","unstructured":"Goodman, N. (1955). Fact, Fiction, and Forecast. United States: Harvard University Press."},{"key":"9569_CR19","doi-asserted-by":"crossref","unstructured":"Halmos, P.R. (1950). Measure Theory D. Van Nostrand Company Inc.","DOI":"10.1007\/978-1-4684-9440-2"},{"key":"9569_CR20","doi-asserted-by":"crossref","unstructured":"Hume, D. (1748). An Enquiry Concerning Human Understanding. London: Millar.","DOI":"10.1093\/oseo\/instance.00032980"},{"issue":"4","key":"9569_CR21","doi-asserted-by":"publisher","first-page":"587","DOI":"10.1086\/682941","volume":"82","author":"SM Huttegger","year":"2015","unstructured":"Huttegger, S.M. (2015). Bayesian convergence to the truth and the metaphysics of possible worlds. Philosophy of Science, 82(4), 587\u2013601.","journal-title":"Philosophy of Science"},{"key":"9569_CR22","first-page":"181","volume":"1","author":"C Juhl","year":"1994","unstructured":"Juhl, C., & Kelly, K.T. (1994). Realism, convergence, and additivity. PSA: Proceedings of the Biennial Meeting of the Philosophy of Science Association, 1, 181\u2013189.","journal-title":"PSA: Proceedings of the Biennial Meeting of the Philosophy of Science Association,"},{"key":"9569_CR23","doi-asserted-by":"crossref","unstructured":"Kelly, K.T. (1996). The Logic of Reliable Inquiry, Oxford University Press, England.","DOI":"10.1093\/oso\/9780195091953.001.0001"},{"key":"9569_CR24","volume-title":"Foundations of the Theory of Probability","author":"AN Kolmogorov","year":"1950","unstructured":"Kolmogorov, A.N. (1950). Foundations of the Theory of Probability. New York: Chelsea Publishing Company."},{"key":"9569_CR25","volume-title":"Theorie de l\u2019addition des variables al\u00e9atoires\u0301","author":"P L\u00e9vy","year":"1937","unstructured":"L\u00e9vy, P. (1937). Theorie de l\u2019addition des variables al\u00e9atoires\u0301. Paris: Gauthiers-Villars."},{"issue":"3","key":"9569_CR26","doi-asserted-by":"publisher","first-page":"333","DOI":"10.1007\/s002290170031","volume":"104","author":"Z Lipecki","year":"2001","unstructured":"Lipecki, Z. (2001). Cardinality of the set of extreme extensions of a quasi-measure. Manuscripta Mathematica, 104(3), 333\u2013341.","journal-title":"Manuscripta Mathematica"},{"key":"9569_CR27","doi-asserted-by":"crossref","unstructured":"Nielsen, M., & Stewart, R.T. (2019). Obligation, permission, and Bayesian orgulity. Ergo, 6(3).","DOI":"10.3998\/ergo.12405314.0006.003"},{"issue":"1","key":"9569_CR28","doi-asserted-by":"publisher","first-page":"193","DOI":"10.1090\/S0002-9939-1976-0419711-3","volume":"54","author":"D Plachky","year":"1976","unstructured":"Plachky, D. (1976). Extremal and monogenic additive set functions. Proceedings of the American Mathematical Society, 54(1), 193\u2013196.","journal-title":"Proceedings of the American Mathematical Society"},{"issue":"3","key":"9569_CR29","doi-asserted-by":"publisher","first-page":"1003","DOI":"10.1214\/14-AOS1212","volume":"42","author":"L Pomatto","year":"2014","unstructured":"Pomatto, L., Al-Najjar, N., Sandroni, A., & et al. (2014). Merging and testing opinions. The Annals of Statistics, 42(3), 1003\u20131028.","journal-title":"The Annals of Statistics"},{"issue":"2","key":"9569_CR30","doi-asserted-by":"publisher","first-page":"293","DOI":"10.1086\/696386","volume":"85","author":"L Pomatto","year":"2018","unstructured":"Pomatto, L., & Sandroni, A. (2018). An axiomatic theory of inductive inference. Philosophy of Science, 85(2), 293\u2013315.","journal-title":"Philosophy of Science"},{"issue":"2","key":"9569_CR31","doi-asserted-by":"publisher","first-page":"259","DOI":"10.1214\/aop\/1176996133","volume":"4","author":"RA Purves","year":"1976","unstructured":"Purves, R.A., & Sudderth, W.D. (1976). Some finitely additive probability. The Annals of Probability, 4(2), 259\u2013276.","journal-title":"The Annals of Probability"},{"issue":"1","key":"9569_CR32","first-page":"32","volume":"45","author":"RA Purves","year":"1983","unstructured":"Purves, R.A., & Sudderth, W.D. (1983). Finitely additive zero-one laws. Sankhy$\\bar {a}$: The Indian Journal of Statistics Series A, 45(1), 32\u201337.","journal-title":"Sankhy$\\bar {a}$\u0101: The Indian Journal of Statistics Series A"},{"key":"9569_CR33","volume-title":"The Foundations of Statistics","author":"LJ Savage","year":"1972","unstructured":"Savage, L.J. (1972). The Foundations of Statistics. John Wiley & Sons: New York."},{"key":"9569_CR34","volume-title":"Handbook of Analysis and its Foundations","author":"E Schechter","year":"1996","unstructured":"Schechter, E. (1996). Handbook of Analysis and its Foundations. United States: Academic Press."},{"issue":"3","key":"9569_CR35","doi-asserted-by":"publisher","first-page":"429","DOI":"10.1007\/s10959-007-0066-1","volume":"20","author":"O Schirokauer","year":"2007","unstructured":"Schirokauer, O., & Kadane, J.B. (2007). Uniform distributions on the natural numbers. Journal of Theoretical Probability, 20(3), 429\u2013441.","journal-title":"Journal of Theoretical Probability"},{"key":"9569_CR36","unstructured":"Shafer, G., & Vovk, V. (2005). Probability and finance: It\u2019s only a game!, Volume 491. John Wiley & Sons."},{"issue":"5","key":"9569_CR37","doi-asserted-by":"publisher","first-page":"959","DOI":"10.1086\/518815","volume":"73","author":"B Skyrms","year":"2006","unstructured":"Skyrms, B. (2006). Diachronic coherence and radical probabilism. Philosophy of Science, 73(5), 959\u2013968.","journal-title":"Philosophy of Science"},{"key":"9569_CR38","first-page":"26","volume":"203","author":"J Ville","year":"1936","unstructured":"Ville, J. (1936). Sur la notion de collectif. Comptes rendus des S\u00e9ances de l\u2019Acad\u00e9,mie des Sciences, 203, 26\u201327.","journal-title":"Comptes rendus des S\u00e9ances de l\u2019Acad\u00e9,mie des Sciences"},{"key":"9569_CR39","unstructured":"Ville, J. (1939). Etude critique de la notion de collectif. Gauthier-Villars Paris."},{"issue":"20","key":"9569_CR40","first-page":"2","volume":"2","author":"B Weatherson","year":"2015","unstructured":"Weatherson, B. (2015). For Bayesians, rational modesty requires imprecision. Ergo, 2(20), 2.","journal-title":"Ergo"},{"issue":"S3","key":"9569_CR41","doi-asserted-by":"publisher","first-page":"S98","DOI":"10.1086\/341837","volume":"69","author":"SL Zabell","year":"2002","unstructured":"Zabell, S.L. (2002). It all adds up: the dynamic coherence of radical probabilism. Philosophy of Science, 69(S3), S98\u2013S103.","journal-title":"Philosophy of Science"}],"container-title":["Journal of Philosophical Logic"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/link.springer.com\/content\/pdf\/10.1007\/s10992-020-09569-2.pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/link.springer.com\/article\/10.1007\/s10992-020-09569-2\/fulltext.html","content-type":"text\/html","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/link.springer.com\/content\/pdf\/10.1007\/s10992-020-09569-2.pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2024,8,12]],"date-time":"2024-08-12T05:30:52Z","timestamp":1723440652000},"score":1,"resource":{"primary":{"URL":"https:\/\/link.springer.com\/10.1007\/s10992-020-09569-2"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2020,8,20]]},"references-count":41,"journal-issue":{"issue":"2","published-print":{"date-parts":[[2021,4]]}},"alternative-id":["9569"],"URL":"https:\/\/doi.org\/10.1007\/s10992-020-09569-2","relation":{},"ISSN":["0022-3611","1573-0433"],"issn-type":[{"type":"print","value":"0022-3611"},{"type":"electronic","value":"1573-0433"}],"subject":[],"published":{"date-parts":[[2020,8,20]]},"assertion":[{"value":"6 June 2019","order":1,"name":"received","label":"Received","group":{"name":"ArticleHistory","label":"Article History"}},{"value":"30 July 2020","order":2,"name":"accepted","label":"Accepted","group":{"name":"ArticleHistory","label":"Article History"}},{"value":"20 August 2020","order":3,"name":"first_online","label":"First Online","group":{"name":"ArticleHistory","label":"Article History"}}]}}