cromwell-rule-zero-prior-immune

IN premise — summaries/2026/08/24/wiki-Bayesian_inference-chunk-2.md

Created 2026-08-25T02:58:43+00:00

Cromwell's rule states that if P(M)=0 then P(M|E)=0, and if P(M)=1 and P(E)>0 then P(M|E)=1, meaning hard priors are immune to any evidence.

Summary

If a system locks in a hypothesis as absolutely impossible or absolutely certain, no new evidence can ever change its mind on that point, no matter how strong the evidence is. This matters because it means a reasoning agent that uses hard zero or one probabilities becomes permanently stuck and unable to learn, so the system must avoid encoding any uncertainty as an absolute to stay responsive to new information.