What is the interpretation of a p-value = 0 then? Empirical science can never reject any theory, it is not powerful enough. At best it can provide a selection of least worst explanations.<p>The H in P(X|H) does not mean &#x27;assumed to be true&#x27;, it means &#x27;is in fact true&#x27;. If H is in fact false, it is counter-factual to assume it is true and therefore any conclusions drawn from the assumption are invalid. This is independent of belief in H.<p>&gt;Necessary truths are the domain of pure logic, not empirical science.<p>Science can never deliver truth, which is why it can never truly reject anything (including null-hypotheses).<p>More generally, this is referred to as the problem of induction.