Fair infinite lotteries

Synthese

Volumn 190, Issue 1, 2013, Pages 37-61

  Wenmackers, Sylvia ^a   Horsten, Leon ^b  

^a UNIVERSITY OF GRONINGEN   (Netherlands)

^b UNIVERSITY OF BRISTOL   (United Kingdom)

Author keywords

Countable additivity; Foundations of probability; Infinity; Non standard analysis

Indexed keywords

EID: 84870809975     PISSN: 00397857     EISSN: 15730964     Source Type: Journal    
DOI: 10.1007/s11229-010-9836-x     Document Type: Article

References (29)

1. Bartha P. (2004) Countable additivity and the de Finetti lottery. British Journal for the Philosophy of Science 55: 301-321.
2. Benci V., Di Nasso M. (2003a) Alpha-theory: An elementary axiomatic for nonstandard analysis. Expositiones Mathematicae 21: 355-386.
3. Benci V., Di Nasso M. (2003b) Numerosities of labelled sets: A new way of counting. Advances in Mathematics 173: 50-67.
4. Benci V., Di Nasso M., Forti M. (2006) The eightfold path to nonstandard analysis. In: Cutland N. J., Di Nasso M., Ross D. A. (eds) Nonstandard methods and applications in mathematics, Lecture notes in logic. Association for Symbolic Logic, AK Peters, Helsinki, pp 3-44.
5. Benci, V., Galatolo, S. & Ghimenti, M. (2008). An elementary approach to stochastic differential equations using infinitesimals. Unpublished manuscript; http://arxiv. org/abs/0807. 3477.
6. Cutland N. (1983) Nonstandard measure theory and its applications. Bulletin of the London Mathematical Society 15: 529-589.
7. de Finetti B. (1974) Theory of probability, Vols. 1 & 2 (A. Machí. Wiley, New York.
8. Douven I., Horsten L., Romeijn J.-W. (2010) Probabilist anti-realism. Pacific Philosophical Quarterly 91: 38-63.
9. Dudley R. M. (2004) Real analysis and probability. Cambridge University Press, Cambridge.
10. Easwaran, K. (2010). Regularity and infinitesimal credences. Unpublished manuscript.
11. Elga A. (2004) Infinitesimal chances and the laws of nature. Australasian Journal of Philosophy 82: 67-76.
12. Hájek, A. (2010). Staying regular. Unpublished manuscript.
13. Kolmogorov, A. N. (1933). Grundbegriffe der Wahrscheinlichkeitrechnung. (Ergebnisse Der Mathematik.) Foundations of probability. (2nd ed.) (N. Morrison, Trans., 1956). USA: Chelsea Publishing Company.
14. Komjáth P., Totik V. (2008) Ultrafilters. American Mathematical Monthly 115: 33-44.
15. Lauwers, L. (2010). Purely finitely additive measures are non-constructible objects. Working paper, unpublished. Retrieved: May 29, 2010, from http://www. econ. kuleuven. be/ces/discussionpapers/Dps10/DPS1010. pdf.
16. Lavine S. (1995) Finite mathematics. Synthese 103: 389-420.
17. Lewis D. (1980) A subjectivist's guide to objective chance. In: Jeffrey R. (eds) Studies in inductive logic and probability II. University of California Press, California.
18. Lewis D. (1986) Philosophical papers. Oxford University Press, Oxford.
19. Mancosu P. (2009) Measuring the size of infinite collections of natural numbers. The Review of Symbolic Logic 2: 612-646.
20. McCall S., Armstrong D. M. (1989) God's lottery. Analysis 49: 223-224.
21. Ramsey F. P. (1926) Truth and probability. In: Braithwaite R. B. (eds) Foundations of mathematics and other essays. Routledge & P. Kegan, London, pp 156-198.
22. Robinson A. (1966) Non-standard analysis. North-Holland Publishing Company, New York.
23. Rubio J. E. (1994) Optimization and nonstandard analysis. Marcel Dekker, New York.
24. Schurz G., Leitgeb H. (2008) Finitistic and frequentistic approximation of probability measures with or without σ-additivity. Studia Logica 89: 257-283.
25. Skyrms B. (1980) Causal Necessity. Yale University Press, New Haven.
26. Tenenbaum G. (1995) Introduction to analytic and probabilistic number theory. Cambridge University Press, Cambridge.
27. Truss J. (1997) Foundations of mathematical analysis. Clarendon Press, Oxford.
28. Väth M. (2007) Nonstandard analysis. Springer, Berlin.
29. Williamson T. (2007) How probable is an infinite sequence of heads?. Analysis 67: 173-180.