The Errors of Statistical Hypotheses and Scientific Theories

Abstract

The process of error recognition is explored first in statistics, and then in science. The Type II error found in statistical hypothesis testing is found analogous to Karl Popper’s “logical probability” that is intended to measure the likelihood that a scientific theory can avoid its refutation. Nevertheless, Popper’s reliance on deductive thinking is found detracting from his demarcation that separates science and metaphysics. An improved critical logic for science is presented that permits error recognition more broadly: for induction by Popper’s falsification principle; but also for deduction and emotionality. The reality of induction creates a limitation for a science that has not accommodated a fuller menu of error recognition. The reality of induction places limits of what can be known from empiricism, and this has philosophical implications.