What Is Science?

This work addresses the demarcation problem by proposing an axiomatic approach to distinguishing science from pseudoscience. It builds on three simple and intuitive axioms that characterize a consistent demarcation criterion. Neither Popper's falsification criterion nor the verification criterion of logical positivism is consistent. Fisherian significance testing and Neyman-Pearson hypothesis testing likewise prove inconsistent, as do demarcation criteria based on Popper's confirmation measure, Mayo's principle of severity testing, Bayesian posterior probabilities, and Barnard's normalized likelihood. Instead, a simple generalization of Royall's likelihood criterion is proposed as a consistent alternative. The proposed criterion is based on analytical and empirical evidence. However, it differs fundamentally from hypothesis testing, which suffers from serious shortcomings that extend well beyond common procedural errors and misinterpretations of test results. It is shown that the deductive framework of hypothesis testing is structurally inconsistent and therefore leads to biased conclusions even if all such errors and misconceptions are eliminated. Through illustrative examples from medicine, biology, astronomy, and mathematics, it is argued that contemporary science should adopt an inductive approach to reach unbiased, consistent, and objective conclusions.