{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,9,9]],"date-time":"2025-09-09T20:39:30Z","timestamp":1757450370672},"reference-count":40,"publisher":"Springer Science and Business Media LLC","issue":"15","license":[{"start":{"date-parts":[[2014,5,3]],"date-time":"2014-05-03T00:00:00Z","timestamp":1399075200000},"content-version":"tdm","delay-in-days":0,"URL":"http:\/\/www.springer.com\/tdm"}],"content-domain":{"domain":["link.springer.com"],"crossmark-restriction":false},"short-container-title":["Synthese"],"published-print":{"date-parts":[[2014,10]]},"DOI":"10.1007\/s11229-014-0458-6","type":"journal-article","created":{"date-parts":[[2014,5,2]],"date-time":"2014-05-02T06:00:52Z","timestamp":1399010452000},"page":"3525-3540","update-policy":"http:\/\/dx.doi.org\/10.1007\/springer_crossmark_policy","source":"Crossref","is-referenced-by-count":6,"title":["Regular probability comparisons imply the Banach\u2013Tarski Paradox"],"prefix":"10.1007","volume":"191","author":[{"given":"Alexander R.","family":"Pruss","sequence":"first","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"297","published-online":{"date-parts":[[2014,5,3]]},"reference":[{"key":"458_CR1","doi-asserted-by":"crossref","DOI":"10.1017\/CBO9780511895975","volume-title":"Assertion and conditionals","author":"KA Appiah","year":"1985","unstructured":"Appiah, K. A. (1985). Assertion and conditionals. Cambridge: Cambridge University Press."},{"key":"458_CR2","doi-asserted-by":"crossref","first-page":"167","DOI":"10.4064\/fm-77-2-167-170","volume":"77","author":"JL Bell","year":"1972","unstructured":"Bell, J. L., & Fremlin, D. H. (1972). A geometric form of the axiom of choice. Fundamenta Mathematicae, 77, 167\u2013170.","journal-title":"Fundamenta Mathematicae"},{"key":"458_CR3","volume-title":"Applications of model theory of algebra, analysis, and probability","author":"AR Bernstein","year":"1969","unstructured":"Bernstein, A. R., & Wattenberg, F. (1969). Non-standard measure theory. In W. A. J. Luxemberg (Ed.), Applications of model theory of algebra, analysis, and probability. New York: Holt, Rinehart and Winston."},{"key":"458_CR4","volume-title":"Les paradoxes de l\u2019infini","author":"E Borel","year":"1946","unstructured":"Borel, E. (1946). Les paradoxes de l\u2019infini. Paris: Gallimard."},{"key":"458_CR5","doi-asserted-by":"crossref","first-page":"298","DOI":"10.4064\/fm-17-1-298-329","volume":"17","author":"B Finetti de","year":"1931","unstructured":"de Finetti, B. (1931). Sul significato soggestivo della probabilit\u00e0. Fundamenta Mathematicae, 17, 298\u2013329.","journal-title":"Fundamenta Mathematicae"},{"key":"458_CR6","unstructured":"de Finetti, B. (1975). Theory of Probability. (A. Machi & A. F. M. Smith, Trans.). New York: Wiley."},{"key":"458_CR7","doi-asserted-by":"crossref","first-page":"1","DOI":"10.1215\/00318108-2366479","volume":"123","author":"K Easwaran","year":"2014","unstructured":"Easwaran, K. (2014). Regularity and hyperreal credences. Philosophical Review, 123, 1\u201341.","journal-title":"Philosophical Review"},{"key":"458_CR8","doi-asserted-by":"crossref","first-page":"199","DOI":"10.2307\/2586759","volume":"64","author":"U Felgner","year":"1999","unstructured":"Felgner, U., & Truss, J. K. (1999). The independence of the prime ideal theorem from the order-extension principle. Journal of Symbolic Logic, 64, 199\u2013215.","journal-title":"Journal of Symbolic Logic"},{"key":"458_CR9","doi-asserted-by":"crossref","first-page":"13","DOI":"10.4064\/fm-138-1-13-19","volume":"138","author":"M Foreman","year":"1991","unstructured":"Foreman, M., & Wehrung, Friedrich. (1991). The Hahn-Banach Theorem implies the existence of a non-Lebesgue measurable set. Fundamenta Mathematicae, 138, 13\u201319.","journal-title":"Fundamenta Mathematicae"},{"key":"458_CR10","doi-asserted-by":"crossref","first-page":"273","DOI":"10.1023\/B:SYNT.0000004904.91112.16","volume":"137","author":"A H\u00e1jek","year":"2003","unstructured":"H\u00e1jek, A. (2003). What conditional probability could not be? Synthese, 137, 273\u2013323.","journal-title":"Synthese"},{"key":"458_CR11","unstructured":"H\u00e1jek, A. (2011). Staying regular? Australasian Association of Philosophy Conference, July 2011."},{"key":"458_CR12","unstructured":"Hofweber, T. (MS). Cardinality arguments against regular hyperreal-valued probability measures."},{"key":"458_CR13","unstructured":"Hofweber, T. (2014). Infinitesimal chances. Philosophers\u2019 Imprint, 14, 1\u201334."},{"key":"458_CR14","doi-asserted-by":"crossref","DOI":"10.1090\/surv\/059","volume-title":"Consequences of the axiom of choice","author":"P Howard","year":"1998","unstructured":"Howard, P., & Rubin, J. E. (1998). Consequences of the axiom of choice. Providence, RI: American Mathematical Society."},{"key":"458_CR15","volume-title":"Theory of probability","author":"H Jeffreys","year":"1961","unstructured":"Jeffreys, H. (1961). Theory of probability (3rd ed.). Oxford: Oxford University Press.","edition":"3"},{"key":"458_CR16","doi-asserted-by":"crossref","first-page":"281","DOI":"10.1111\/j.1520-8583.2010.00194.x","volume":"24","author":"JM Joyce","year":"2010","unstructured":"Joyce, J. M. (2010). A defense of imprecise credences in inference and decision. Philosophical Perspectives, 24, 281\u2013323.","journal-title":"Philosophical Perspectives"},{"key":"458_CR17","doi-asserted-by":"crossref","first-page":"159","DOI":"10.2178\/jsl\/1080938834","volume":"69","author":"V Kanovei","year":"2004","unstructured":"Kanovei, V., & Shelah, S. (2004). A definable nonstandard model of the reals. Journal of Symbolic Logic, 69, 159\u2013164.","journal-title":"Journal of Symbolic Logic"},{"key":"458_CR18","doi-asserted-by":"crossref","first-page":"263","DOI":"10.2307\/2268222","volume":"20","author":"JG Kemeny","year":"1955","unstructured":"Kemeny, J. G. (1955). Fair bets and inductive probabilities. Journal of Symbolic Logic, 20, 263\u201373.","journal-title":"Journal of Symbolic Logic"},{"key":"458_CR19","doi-asserted-by":"crossref","first-page":"229","DOI":"10.1007\/BF01894506","volume":"19","author":"PH Krauss","year":"1968","unstructured":"Krauss, P. H. (1968). Representation of conditional probability measures on boolean algebras. Acta Mathematica Academiae Scientiarum Hungarica, 19, 229\u2013241.","journal-title":"Acta Mathematica Academiae Scientiarum Hungarica"},{"key":"458_CR20","doi-asserted-by":"crossref","unstructured":"Laugwitz, D. (1968). Eine nichtarchimedische Erweiterung angeordneter K\u00f6rper. Mathematische Nachrichten, 37, 225\u2013236.","DOI":"10.1002\/mana.19680370308"},{"key":"458_CR21","volume-title":"On the plurality of worlds","author":"D Lewis","year":"1986","unstructured":"Lewis, D. (1986). On the plurality of worlds. Oxford: Blackwell."},{"key":"458_CR22","doi-asserted-by":"crossref","unstructured":"Luxemburg, W. (1973). What is nonstandard analysis? American Mathematical Monthly, 80, 38\u201367.","DOI":"10.2307\/3038221"},{"key":"458_CR23","unstructured":"McGee, V. (1994). Learning the impossible. In E. Eells & B. Skyrms (Eds.), Probability and conditionals (pp. 179\u2013199). Cambridge: Cambridge University Press."},{"key":"458_CR24","doi-asserted-by":"crossref","first-page":"180","DOI":"10.1007\/BFb0066012","volume-title":"Victoria symposium on nonstandard analysis","author":"R Parikh","year":"1974","unstructured":"Parikh, R., & Parnes, M. (1974). Conditional probabilities and uniform sets. In A. Hurd & P. Loeb (Eds.), Victoria symposium on nonstandard analysis (pp. 180\u2013194). Berlin: Springer."},{"key":"458_CR25","doi-asserted-by":"crossref","first-page":"21","DOI":"10.4064\/fm-138-1-21-22","volume":"138","author":"J Pawlikowski","year":"1991","unstructured":"Pawlikowski, J. (1991). The Hahn-Banach theorem implies the Banach-Tarski paradox. Fundamenta Mathematicae, 138, 21\u201322.","journal-title":"Fundamenta Mathematicae"},{"key":"458_CR26","unstructured":"Pedersen, A. & Paul, M. S. (2013). Strictly coherent preferences, no holds barred. http:\/\/www.saet.uiowa.edu\/Papers2013\/StrictlyCoherentPreferencesNoHoldsBarred_Pedersen.pdf . Accessed 28 April 2014."},{"key":"458_CR27","unstructured":"Pitowsky, I. (1989). Quantum probability., Lecture Notes in Physics Springer: Heidelberg."},{"key":"458_CR28","doi-asserted-by":"crossref","first-page":"231","DOI":"10.1086\/670299","volume":"80","author":"AR Pruss","year":"2013","unstructured":"Pruss, A. R. (2013a). Probability, regularity, and cardinality. Philosophy of Science, 80, 231\u2013240.","journal-title":"Philosophy of Science"},{"key":"458_CR29","doi-asserted-by":"crossref","first-page":"682","DOI":"10.1093\/analys\/ant076","volume":"73","author":"AR Pruss","year":"2013","unstructured":"Pruss, A. R. (2013b). Null probability, dominance and rotation. Analysis, 73, 682\u2013685.","journal-title":"Analysis"},{"key":"458_CR30","unstructured":"Pruss, A. R. (2016). Divine creative freedom. In J. Kvanvig (Ed.), Oxford studies in the philosophy of religion. Oxford: Oxford University Press."},{"key":"458_CR31","volume-title":"Real and complex analysis","author":"W Rudin","year":"1987","unstructured":"Rudin, W. (1987). Real and complex analysis (3rd ed.). New York: McGraw Hill.","edition":"3"},{"key":"458_CR32","doi-asserted-by":"crossref","unstructured":"Shimony, A. (1955). Coherence and the axioms of confirmation. Journal of Symbolic Logic, 20, 1\u201328.","DOI":"10.2307\/2268039"},{"key":"458_CR33","first-page":"1","volume":"92","author":"RM Solovay","year":"1970","unstructured":"Solovay, R. M. (1970). A model of set-theory in which every set of rals is Lebesgue measurable. Transactions of the American Mathematical Society, 92, 1\u201356.","journal-title":"Transactions of the American Mathematical Society"},{"key":"458_CR34","volume-title":"Causal necessity: A pragmatic investigation of the necessity of laws","author":"B Skyrms","year":"1980","unstructured":"Skyrms, B. (1980). Causal necessity: A pragmatic investigation of the necessity of laws. New Haven: Yale University Press."},{"key":"458_CR35","doi-asserted-by":"crossref","first-page":"64","DOI":"10.1086\/288280","volume":"37","author":"RC Stalnaker","year":"1970","unstructured":"Stalnaker, R. C. (1970). Probability and conditionals. Philosophy of Science, 37, 64\u201380.","journal-title":"Philosophy of Science"},{"key":"458_CR36","volume-title":"Subjective Probability","author":"P Suppes","year":"1994","unstructured":"Suppes, P. (1994). Qualitative theory of subjective probability. In G. Wright & P. Ayton (Eds.), Subjective Probability. Chichester: Wiley."},{"key":"458_CR37","doi-asserted-by":"crossref","first-page":"386","DOI":"10.4064\/fm-16-1-386-389","volume":"16","author":"E Szpilrajn","year":"1930","unstructured":"Szpilrajn, E. (1930). Sur l\u2019extension de l\u2019ordre partiel. Fundamenta Mathematicae, 16, 386\u2013389.","journal-title":"Fundamenta Mathematicae"},{"key":"458_CR38","doi-asserted-by":"crossref","first-page":"417","DOI":"10.1007\/BF00649400","volume":"5","author":"BC Fraassen van","year":"1976","unstructured":"van Fraassen, B. C. (1976). Representation of conditional probabilities. Journal of Philosophical Logic, 5, 417\u2013430.","journal-title":"Journal of Philosophical Logic"},{"key":"458_CR39","doi-asserted-by":"crossref","first-page":"661","DOI":"10.2307\/2314250","volume":"74","author":"C Villegas","year":"1967","unstructured":"Villegas, C. (1967). On qualitative probability. American Mathematical Monthly, 74, 661\u2013669.","journal-title":"American Mathematical Monthly"},{"key":"458_CR40","volume-title":"The Banach-Tarski paradox","author":"S Wagon","year":"1994","unstructured":"Wagon, S. (1994). The Banach-Tarski paradox. Cambridge: Cambridge University Press."}],"container-title":["Synthese"],"original-title":[],"language":"en","link":[{"URL":"http:\/\/link.springer.com\/content\/pdf\/10.1007\/s11229-014-0458-6.pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"text-mining"},{"URL":"http:\/\/link.springer.com\/article\/10.1007\/s11229-014-0458-6\/fulltext.html","content-type":"text\/html","content-version":"vor","intended-application":"text-mining"},{"URL":"http:\/\/link.springer.com\/content\/pdf\/10.1007\/s11229-014-0458-6","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2019,8,9]],"date-time":"2019-08-09T22:14:43Z","timestamp":1565388883000},"score":1,"resource":{"primary":{"URL":"http:\/\/link.springer.com\/10.1007\/s11229-014-0458-6"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2014,5,3]]},"references-count":40,"journal-issue":{"issue":"15","published-print":{"date-parts":[[2014,10]]}},"alternative-id":["458"],"URL":"https:\/\/doi.org\/10.1007\/s11229-014-0458-6","relation":{},"ISSN":["0039-7857","1573-0964"],"issn-type":[{"value":"0039-7857","type":"print"},{"value":"1573-0964","type":"electronic"}],"subject":[],"published":{"date-parts":[[2014,5,3]]}}}