Bartha P. (2004) Countable additivity and the de Finetti lottery. British Journal for the Philosophy of Science 55: 301–321
Article
Google Scholar
Benci V., Di Nasso M. (2003a) Alpha-theory: An elementary axiomatic for nonstandard analysis. Expositiones Mathematicae 21: 355–386
Article
Google Scholar
Benci V., Di Nasso M. (2003b) Numerosities of labelled sets: A new way of counting. Advances in Mathematics 173: 50–67
Article
Google Scholar
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
Google Scholar
Benci, V., Galatolo, S. & Ghimenti, M. (2008). An elementary approach to stochastic differential equations using infinitesimals. Unpublished manuscript; http://arxiv.org/abs/0807.3477.
Cutland N. (1983) Nonstandard measure theory and its applications. Bulletin of the London Mathematical Society 15: 529–589
Article
Google Scholar
de Finetti B. (1974) Theory of probability, Vols. 1 & 2 (A. Machí. Wiley, New York
Google Scholar
Douven I., Horsten L., Romeijn J.-W. (2010) Probabilist anti-realism. Pacific Philosophical Quarterly 91: 38–63
Article
Google Scholar
Dudley R. M. (2004) Real analysis and probability. Cambridge University Press, Cambridge
Google Scholar
Easwaran, K. (2010). Regularity and infinitesimal credences. Unpublished manuscript.
Elga A. (2004) Infinitesimal chances and the laws of nature. Australasian Journal of Philosophy 82: 67–76
Article
Google Scholar
Hájek, A. (2010). Staying regular. Unpublished manuscript.
Kolmogorov, A. N. (1933). Grundbegriffe der Wahrscheinlichkeitrechnung. (Ergebnisse Der Mathematik.) Foundations of probability. (2nd ed.) (N. Morrison, Trans., 1956). USA: Chelsea Publishing Company.
Komjáth P., Totik V. (2008) Ultrafilters. American Mathematical Monthly 115: 33–44
Google Scholar
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 Working paper, unpublished.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.
Lavine S. (1995) Finite mathematics. Synthese 103: 389–420
Article
Google Scholar
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
Google Scholar
Lewis D. (1986) Philosophical papers. Oxford University Press, Oxford
Google Scholar
Mancosu P. (2009) Measuring the size of infinite collections of natural numbers. The Review of Symbolic Logic 2: 612–646
Article
Google Scholar
McCall S., Armstrong D. M. (1989) God’s lottery. Analysis 49: 223–224
Google Scholar
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
Google Scholar
Robinson A. (1966) Non-standard analysis. North-Holland Publishing Company, New York
Google Scholar
Rubio J. E. (1994) Optimization and nonstandard analysis. Marcel Dekker, New York
Google Scholar
Schurz G., Leitgeb H. (2008) Finitistic and frequentistic approximation of probability measures with or without σ-additivity. Studia Logica 89: 257–283
Article
Google Scholar
Skyrms B. (1980) Causal Necessity. Yale University Press, New Haven
Google Scholar
Tenenbaum G. (1995) Introduction to analytic and probabilistic number theory. Cambridge University Press, Cambridge
Google Scholar
Truss J. (1997) Foundations of mathematical analysis. Clarendon Press, Oxford
Google Scholar
Väth M. (2007) Nonstandard analysis. Springer, Berlin
Google Scholar
Williamson T. (2007) How probable is an infinite sequence of heads?. Analysis 67: 173–180
Google Scholar