In The Problems of Philosophy, Bertrand Russell presents a justification of induction based on a principle he refers to as “the principle of induction.” Owing to the ambiguity of the notion of probability, the principle of induction may be interpreted in two different ways. If interpreted in terms of the subjective interpretation of probability, the principle of induction may be known a priori to be true. But it is unclear how this should give us any confidence in our use of induction, since induction is applied to the external world outside our minds. If the principle is interpreted in light of the objective interpretation of induction, it cannot be known to be true a priori, since it applies to frequencies that occur in the world outside the mind, and these cannot be known without recourse to experience. Russell’s principle of induction therefore fails to provide a satisfactory justification of induction.

在哲学问题中，伯特兰·罗素根据他称为“归纳原理”的原则提出了归纳证明。由于概率概念的模糊性，归纳原理可以有两种不同的解释。如果用概率的主观解释来解释，归纳原理可能先验地被认为是正确的。但是不清楚这应该如何让我们对我们使用归纳法有信心，因为归纳法适用于我们头脑之外的外部世界。如果根据归纳法的客观解释来解释该原理，则不能先验地知道它为真，因为它适用于发生在心灵之外的世界中的频率，如果不依靠经验就无法知道这些频率。因此，罗素的归纳原理未能提供令人满意的归纳证明。