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Countable additivity, idealization, and conceptual realism

机译：可数的加性，理想化和概念性现实主义

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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.
机译：本文讨论了贝叶斯概率和决策理论中的有限可加性与可加性的问题，尤其是野人的主观预期效用和个人概率理论。我表明野人的理论中不需要可数相加的原因尚无定论。通过评估，可以对贝叶斯理论中通常采用的各种高度理想化的假设进行分析，我认为健康的概念实在论剂量通常有助于理解诸如决策等应用科学中采用的复杂数学结构的解释价值。理论。在最后一部分中，我将可数加性引入Savage理论中，并探讨了与系统其他公理有关的一些技术特性。

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