We analyze recent criticisms of the use of hyperreal probabilities as expressed by Pruss, Easwaran, Parker, and Williamson. We show that the alleged arbitrariness of hyperreal fields can be avoided by working in the Kanovei-Shelah model or in saturated models. We argue that some of the objections to hyperreal probabilities arise from hidden biases that favor Archimedean models. We discuss the advantage of the hyperreals over transferless fields with infinitesimals. In the second part we will analyze two underdetermination theorems by Pruss and show that they hinge upon parasitic external hyperreal-valued measures, whereas internal hyperfinite measures are not underdetermined.

中文翻译：

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无限彩票、旋转器、Hyperreals 的适用性†

我们分析了 Pruss、Easwaran、Parker 和 Williamson 最近对使用超真实概率的批评。我们表明，通过在 Kanovei-Shelah 模型或饱和模型中工作，可以避免所谓的超现实领域的任意性。我们认为，对超真实概率的一些反对意见源于偏爱阿基米德模型的隐藏偏见。我们讨论了超实数相对于无穷小无转移域的优势。在第二部分中，我们将分析 Pruss 的两个欠定定理，并表明它们取决于寄生的外部超实值测度，而内部超限测度不是欠定的。