Abstract
Are chance zero events possible? David Lewis thought not. He and others have proposed replacing zero chances by nonzero but infinitesimal chances in order that such events might be constructed as possible. I examine the details of a number of models aiming to accomplish this and conclude that they don’t work, ending with a pessimistic assessment of the prospects for this program.
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References
Bartha P, Johns R (2001) Probability and symmetry. Philos Sci 68 (Proceedings)
Bernstein RA, Wattenberg F (1969) Nonstandard measure theory. In: Luxemburg WAJ (ed) Applications of model theory to algebra, analysis, and probability. Holt, Rinehart, and Winston, New York, pp. 171–185
Elga A (Mar 2004) Infinitesimal chances and the laws of nature. Aust J Philos 82(1):67–76
Lewis D (1973) Causation. J Philos 70:556–567
Lindstrom T (1988) An invitation to nonstandard analysis. In: Nigel C (ed) Nonstandard analysis and its applications, number 10 in London Mathematical Society Student Texts. Cambridge University Press, Cambridge
McGee V (1994) Learning the impossible. In: Eells E, Brian S (eds) Probability and conditionals. Cambridge University Press, Cambridge
Nelson E (1987) Radically elementary probability theory. Number 117 in annals of mathematics studies. Princeton University Press, Princeton
Nelson E (2001) Internal set theory, 2001. http://www.math.princeton.edu/~nelson/books.html
Ross D (1997) Loeb measure and probability. In: Nigel Cutland Leif O. Arkeryd, Ward Henson C (eds) Nonstandard analysis, theory and applications. Kluwer, Dordrecht, pp 91–120
Skyrms B (1980) Causal necessity. Yale University Press, New Haven
Schechter E (1997) Handbook of analysis and its foundations. Academic, San Diego
van Fraassen B (1980) The scientific image. Oxford University Press, Oxford
Zaman A (1987) On the impossibility of events of measure zero. Theor Decis 23:157–159
Acknowledgments
I am grateful to Ellery Eells and Alan Macdonald for helpful comments on an earlier draft.
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Barrett, M. (2010). The Possibility of Infinitesimal Chances. In: Eells, E., Fetzer, J. (eds) The Place of Probability in Science. Boston Studies in the Philosophy of Science, vol 284. Springer, Dordrecht. https://doi.org/10.1007/978-90-481-3615-5_3
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DOI: https://doi.org/10.1007/978-90-481-3615-5_3
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