✶ Likelihood Literacy: Why Compatibility Is Not Confirmation

The Credencing framework evaluates how assigned confidence answers to evidence. Its existing papers distinguish Objective Evidence, E0, Perceived Evidence, EP, Assigned Credence, CA, and Deep Rationality, SD; separate evidence-processing gaps from belief-integrity gaps; defend warranted uncertainty; diagnose rationalization; extend the model to institutions and AI-mediated inquiry; specify when raw gaps become warranted diagnoses; make posterior credence answerable to its evidential history; and show that credence inherits vulnerability from the frames and categories that make propositions assessable. This paper adds a narrower but crucial missing competence: likelihood literacy. Agents routinely notice that a datum is compatible with a favored hypothesis and then treat that compatibility as confirmation. But evidence supports a hypothesis only by being more expected under that hypothesis than under live rivals. The lacuna is therefore not a new global theory of probability. It is the underformalized micro-skill by which agents distinguish fitting from favoring, coherence from diagnosticity, and narrative accommodation from evidential support. This paper formalizes compatibility, likelihood, likelihood ratios, discriminativity, suppressed alternatives, dependence correction, likelihood inflation, and likelihood literacy as a Deep Rationality competence. It argues that many errors in medicine, public debate, conspiracy thinking, historical reasoning, institutional reporting, and AI-output evaluation occur because agents ask whether E can be explained by H, rather than asking how expected E is under H relative to serious alternatives. The practical result is a likelihood-audit protocol: state the evidence, name the live hypotheses, estimate expectedness under each, include an unknown reserve, check dependence, compare likelihoods before updating, and prevent mere compatibility from inflating perceived evidential support. Credencing then gains a sharper account of how evidence becomes EP: not by being narratively usable, but by discriminating among live possibilities.