论文标题
解决归纳问题：我们可以通过归纳而完全信心陈述太阳永远升起吗？
Resolving the induction problem: Can we state with complete confidence via induction that the sun rises forever?
论文作者
论文摘要
归纳是一种推理形式，从特定的例子开始，并将其推广到规则，即假设。但是，由于发生冲突事件的可能发生，也称为归纳问题，因此建立假设的真相是有问题的。 Laplace（1814）首先引入的日出问题是基于概率的诱导的典型示例。在他的解决方案中，无论观测数量多少，始终将零概率分配给了太阳永远升起的假设。这是基于概率的诱导基本缺乏的症状：永远无法通过贝叶斯 - 宽面条方法接受假设。已经提出了替代先验来解决这个问题，但他们未能完全克服缺陷。我们研究了为什么会发生这种情况，并证明信心不会表现出如此缺陷，因为这不是概率，因此不遵守贝叶斯的规则。信心不仅是允许对概率的认知解释和依恋解释之间的和解的可能性，而且是通过使我们能够完全信心接受假设作为合理决策来实现证据的决议。
Induction is a form of reasoning that starts with a particular example and generalizes to a rule, namely, a hypothesis. However, establishing the truth of a hypothesis is problematic due to the potential occurrence of conflicting events, also known as the induction problem. The sunrise problem, first introduced by Laplace (1814), is a quintessential example of the probability-based induction. In his solution, a zero probability is always assigned to the hypothesis that the sun rises forever, regardless of the number of observations made. This is a symptom of fundamental deficiency of probability-based induction: A hypothesis can never be accepted via the Bayes-Laplace approach. Alternative priors have been proposed to address this issue, but they have failed to fully overcome the deficiency. We investigate why this occurs and demonstrate that the confidence does not exhibit such a deficiency, as it is not a probability and therefore does not adhere to Bayes' rule. The confidence is neither a likelihood to allow not only a reconciliation between epistemic and aleatory interpretations of probability but also a resolution in agreement with the evidence by enabling us to accept a hypothesis with complete confidence as a rational decision.
