Synthese 191 (8):1757-1760 (2014)

Philip Kremer
University of Toronto at Scarborough
In ‘Fair Infinite Lotteries’ (FIL), Wenmackers and Horsten use non-standard analysis to construct a family of nicely-behaved hyperrational-valued probability measures on sets of natural numbers. Each probability measure in FIL is determined by a free ultrafilter on the natural numbers: distinct free ultrafilters determine distinct probability measures. The authors reply to a worry about a consequent ‘arbitrariness’ by remarking, “A different choice of free ultrafilter produces a different ... probability function with the same standard part but infinitesimal differences.” They illustrate this remark with the example of the sets of odd and even numbers. Depending on the ultrafilter, either each of these sets has probability 1/2, or the set of odd numbers has a probability infinitesimally higher than 1/2 and the set of even numbers infinitesimally lower. The point of the current paper is simply that the amount of indeterminacy is much greater than acknowledged in FIL: there are sets of natural numbers whose probability is far more indeterminate than that of the set of odd or the set of even numbers
Keywords Foundations of probability  Non-standard analysis  Infinite lotteries
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DOI 10.1007/s11229-013-0364-3
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References found in this work BETA

Fair Infinite Lotteries.Sylvia Wenmackers & Leon Horsten - 2013 - Synthese 190 (1):37-61.

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Citations of this work BETA

Infinitesimal Probabilities.Vieri Benci, Leon Horsten & Sylvia Wenmackers - 2016 - British Journal for the Philosophy of Science 69 (2):509-552.
Infinitesimal Probabilities.Sylvia Wenmackers - 2016 - In Richard Pettigrew & Jonathan Weisberg (eds.), The Open Handbook of Formal Epistemology. PhilPapers Foundation. pp. 199-265.
Triangulating Non-Archimedean Probability.Hazel Brickhill & Leon Horsten - 2018 - Review of Symbolic Logic 11 (3):519-546.

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