Resolving the Induction Problem: Can We State With Complete Confidence That the Sun Rises Forever?

Abstract

Summary Induction is a form of reasoning that starts with particular examples and generalizes them into a rule, namely, a hypothesis. However, establishing the truth of a hypothesis is problematic because conflicting events may occur, a difficulty known as the induction problem. The sunrise problem is a quintessential example of probability‐based induction. It shows that zero probability must be assigned to the hypothesis that the sun rises forever, regardless of the number of observations. This reveals a fundamental deficiency of probability‐based induction: A hypothesis can never be accepted through the Bayes–Laplace approach. Although alternative approaches have been proposed to address this issue, none has fully resolved the deficiency. In this paper, we investigate how this deficiency arises and demonstrate that confidence can overcome it. Confidence not only reconciles the epistemic and the aleatory interpretations of uncertainty but also aligns with the evidence by allowing the hypothesis to be accepted with complete confidence in rational decision‐making, while remaining falsifiable if conflicting evidence arises.