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Degrees of Belief

机译：信仰度

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This article surveys various accounts of degrees of belief and the relation between degrees of belief and full belief or absolute certainty. Corresponding to each notion of degree of belief is a conception of evidential support. Three different kinds of degrees of belief and the corresponding notions of evidential support are considered: probability, evidential support in the maximizing sense and in the satisficing sense. It is argued that probability cannot be the degree of belief or evidential support in either the maximizing or satisficing sense. Reconstructions of maximizing and satisficing degree of belief are proposed, which show that they are ways of evaluating potential answers to questions that demand the inductive expansion of a state K of full belief. These reconstructions are based on an account of inductive expansion briefly summarized in the text that understands inductive expansion to be the choice of a potential answer that maximizes a weighted average of the risk of error and the value of the information acquired. Thus, maximizing this weighted average is an index of degree of evidential support in the maximizing sense. It is explained how an index of evidential support in the satisficing sense can be constructed that achieves the same result. Finally, it is argued that several so called 'qualitative' notions of belief other than full belief are deprived of useful application in deliberation and inquiry because they lack the relevance to inductive expansion that maximizing and satisficing evidential support (or degree of belief) has. The discussion should be of interest to students of measures of uncertainty, inductive or non-monotonic reasoning and decision making.
机译：本文调查了各种信念程度的描述以及信念程度与完全信念或绝对确定性之间的关系。与每种信念度概念相对应的是证据支持的概念。考虑了三种不同的信念程度和相应的证据支持概念：概率，最大化意义上的证据支持和令人满意的意义上的证据支持。有人认为，在最大化或令人满意的意义上，概率不可能是信念或证据支持的程度。提出了对信念的最大化和满意程度的重构，这表明它们是评估对需要归纳式扩展完全信念状态K的问题的潜在答案的方法。这些重构基于对归纳扩展的解释，该归纳在正文中作了简要总结，该归纳理解将归纳扩展理解为潜在答案的选择，该潜在答案可以最大程度地提高错误风险和所获取信息价值的加权平均值。因此，最大化此加权平均值是最大化意义上证据支持程度的指标。解释了如何构建令人满意的证据支持指标来达到相同的结果。最后，有人认为，除了完全信仰之外，还有几个所谓的“定性”信仰概念在审议和询问中被剥夺了有用的应用，因为它们与最大化和满足证据支持（或信仰程度）所具有的归纳性扩展不相关。学生应该对讨论的不确定性，归纳或非单调推理和决策方法感兴趣。

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