After Bayes, the oldest Bayesian account of enumerative induction is given by Laplace's so-called rule of succession: if all $n$ observed instances of a phenomenon to date exhibit a given character, the probability that the next instance of that phenomenon will also exhibit the character is $\frac{n+1}{n+2}$. Laplace's rule however has the apparently counterintuitive mathematical consequence that the corresponding "universal generalization" (every future observation of this type will also exhibit that character) has zero probability. In 1932, the British scientist J. B. S. Haldane proposed an alternative rule giving a universal generalization the positive probability $\frac{n+1}{n+2} \times \frac{n+3}{n+2}$. A year later Harold Jeffreys proposed essentially the same rule in the case of a finite population. A related variant rule results in a predictive probability of $\frac{n+1}{n+2} \times \frac{n+4}{n+3}$. These arguably elegant adjustments of the original Laplacean form have the advantage that they give predictions better aligned with intuition and common sense. In this paper we discuss J. B. S. Haldane's rule and its variants, placing them in their historical context, and relating them to subsequent philosophical discussions.

翻译：在贝叶斯之后，最古老的枚举归纳贝叶斯表述是拉普拉斯所谓的递推法则：若迄今观测到的某一现象的所有 $n$ 个实例均展现特定特征，则下一实例亦展现该特征的概率为 $\frac{n+1}{n+2}$。然而，拉普拉斯法则在数学上会导致一个看似反直觉的结果：对应的“全称概括”（即该类型所有未来观测亦将展现该特征）的概率为零。1932年，英国科学家 J. B. S. 霍尔丹提出一种替代法则，使得全称概括具有正概率 $\frac{n+1}{n+2} \times \frac{n+3}{n+2}$。一年后，哈罗德·杰弗里斯在有限总体情形下提出了本质上相同的法则。另一相关变体法则得出预测概率为 $\frac{n+1}{n+2} \times \frac{n+4}{n+3}$。这些对原始拉普拉斯形式进行优雅修正的方案，其优点在于所产生的预测更符合直觉与常识。本文探讨 J. B. S. 霍尔丹法则及其变体，将其置于历史背景中，并关联后续哲学讨论。