This paper addresses the issue of finite versus countable additivity in Bayesian probability and decision theory – in particular, Savage’s theory of subjective expected utility and personal probability. I show that Savage’s reason for not requiring countable additivity in his theory is inconclusive. The assessment leads to an analysis of various highly idealized assumptions commonly adopted in Bayesian theory, where I argue that a healthy dose of, what I call, conceptual realism is often helpful in understanding the interpretational value of sophisticated mathematical structures employed in applied sciences like decision theory. In the last part, I introduce countable additivity into Savage’s theory and explore some technical properties in relation to other axioms of the system.

中文翻译：

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可数可加性、理想化和概念实在论

本文讨论了贝叶斯概率和决策理论中的有限与可加性问题——特别是 Savage 的主观预期效用和个人概率理论。我表明 Savage 在他的理论中不需要可数可加性的原因是不确定的。评估导致对贝叶斯理论中普遍采用的各种高度理想化假设的分析，我认为健康剂量的，我称之为概念现实主义通常有助于理解应用科学中使用的复杂数学结构的解释价值，如决策理论。在最后一部分中，我将可数可加性引入到 Savage 的理论中，并探讨了与系统的其他公理相关的一些技术特性。