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

TL;DR

This paper reinterprets the problem of induction through the lens of logical coherence and Bayesian plausibility, showing that induction is about maintaining rational consistency rather than seeking certainty.

Contribution

It introduces a coherence-based view of induction inspired by Jaynes, unifying Bayesian updating, falsification, and evidential strength without contradiction.

Findings

Bayes's theorem as a consistency condition, not an empirical claim

Falsification as a limiting case of Bayesian updating

Bayesian plausibility quantifies evidential strength

Abstract

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.