标题： 从休谟到杰恩斯：归纳作为似是而非推理的逻辑 显示英文标题

标题： From Hume to Jaynes: Induction as the Logic of Plausible Reasoning

摘要： 归纳问题自休谟揭示重复观察与普遍推论之间的逻辑缺口以来一直存在。 传统解决这一问题的尝试在两个极端之间摇摆：拉普拉斯和杰弗里斯的概率乐观主义，他们试图通过概率来量化信念；以及波普尔的批判怀疑论，他用证伪代替了证实。 然而，这两种方法都假设归纳必须得出确定性或其否定。 在本文中，我认为当用逻辑一致性（理解为更新过程中信念的内部一致性）而不是真理来重新表述时，归纳问题就会消失。 遵循E.T.杰恩斯的观点，概率被解释为演绎逻辑在不完全信息下的延伸，而不是频率或决策规则。 在这种解释下，贝叶斯定理不是一条经验陈述，而是一个约束理性信念更新的一致性条件。 因此，归纳成为演绎推理应用于不确定前提的特殊情况。 证伪表现为当新数据使后验可能性趋近于零时的贝叶斯更新的极限形式，而贝叶斯因子则量化了证据强度的连续谱。 通过分析示例，包括拉普拉斯的日出问题、杰弗里斯的混合先验和基于信心的重新表述，我表明只有合理的推理逻辑能够无矛盾地统一这些观点。 正确理解的归纳并不是从过去到未来的跳跃，而是保持证据、信念和信息之间一致性的纪律。 显示英文摘要

摘要： The problem of induction has persisted since Hume exposed the logical gap between repeated observation and universal inference. Traditional attempts to resolve it have oscillated between two extremes: the probabilistic optimism of Laplace and Jeffreys, who sought to quantify belief through probability, and the critical skepticism of Popper, who replaced confirmation with falsification. Both approaches, however, assume that induction must deliver certainty or its negation. In this paper, I argue that the problem of induction dissolves when recast in terms of logical coherence (understood as internal consistency of credences under updating) rather than truth. Following E. T. Jaynes, probability is interpreted not as frequency or decision rule but as the extension of deductive logic to incomplete information. Under this interpretation, Bayes's theorem is not an empirical statement but a consistency condition that constrains rational belief updating. Induction thus emerges as the special case of deductive reasoning applied to uncertain premises. Falsification appears as the limiting form of Bayesian updating when new data drive posterior plausibility toward zero, while the Bayes Factor quantifies the continuous spectrum of evidential strength. Through analytical examples, including Laplace's sunrise problem, Jeffreys's mixed prior, and confidence-based reformulations, I show that only the logic of plausible reasoning unifies these perspectives without contradiction. Induction, properly understood, is not the leap from past to future but the discipline of maintaining coherence between evidence, belief, and information.