Indeterminacy of fair infinite lotteries

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• 作者：Philip Kremer (1)
  
• 关键词：Foundations of probability ; Non ; standard analysis ; Infinite lotteries
• 刊名：Synthese
• 出版年：2014
• 出版时间：May 2014
• 年：2014
• 卷：191
• 期：8
• 页码：1757-1760
• 全文大小：104 KB
• 参考文献：1. Kervliet, T. (2013). / A uniform probability measure on the natural numbers. Master Thesis, Department of Mathematics, University of Amsterdam, Amsterdam.
  2. Wenmackers, S., & Horsten, L. (2013). Fair infinite lotteries. / Synthese, / 190, 37-1. CrossRef
  
• 作者单位：Philip Kremer (1)
  
  1. Department of Philosophy, University of Toronto, Jackman Humanities Building 170 St. George Street, Toronto, ON, M5R 2M8, Canada
  
• ISSN：1573-0964

文摘

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.