&gt; A p-value is simply P(X|H). P(X|H) only means something when H is true. If H is false, P(X|H) tells you nothing.<p>If you <i>know</i> H is false, P(X|H) tells you nothing. But then H wouldn&#x27;t be a hypothesis, null or otherwise.<p>If you <i>don&#x27;t</i> know whether H is true, but you do know something about X, P(X|H) tells you something useful about whether the positive hypothesis to which H is the alternative has an effect apparent in the world to explain.<p>&gt; The null hypothesis can never be &#x27;rejected&#x27; (ie. p-value can never reach 0).<p>Rejection of the null hypothesis does not mean p-value = 0. Scientific progress is not based on logical certainty, but rather practical utility.<p>Necessary truths are the domain of pure logic, not empirical science.