Scientific Inference: Second Edition, Sir Harold Jeffreys
1957

This book is a rigorous and influential treatment of the logic of scientific reasoning, focusing on how evidence supports or refutes hypotheses. Sir Harold Jeffreys, a leading statistician and geophysicist, presents a systematic framework for inference grounded in probability theory.

The central argument of the book is that scientific inference should be based on probabilistic reasoning, rather than purely deductive logic or frequentist statistics. Jeffreys develops what is now recognized as an early and foundational form of Bayesian inference, where prior knowledge is updated with new evidence to produce revised probabilities.

Key topics include:

The role of probability in scientific reasoning
The evaluation and comparison of hypotheses
Prior probability and its justification
Likelihood and evidence in experimental data
Decision-making under uncertainty

Jeffreys emphasizes that scientific laws are not proven with certainty but are supported to varying degrees based on available evidence. He introduces methods for comparing competing theories quantitatively, arguing that inference is inherently a process of weighing probabilities.

The book also addresses philosophical questions about the nature of scientific knowledge, including:

The distinction between induction and deduction
The problem of uncertainty in empirical science
How general laws are inferred from limited observations

Mathematical formulations are used throughout, but Jeffreys also provides conceptual explanations to clarify the reasoning behind the methods.