&gt; So a program that “validates itself” simply doesn&#x27;t make sense.<p>The language comes from Gödel&#x27;s incompleteness theorems, in which there exist true statements that cannot be proven true, i.e. validated.<p>A given non-trivial computer program can be relied on to produce results consistent with its definition (its <i>specification</i>), but <i>this cannot be proven</i> in all cases.<p>It&#x27;s not very complicated.<p>&gt; This is precisely the rôle of the foundations of mathematics (or perhaps I should say a foundation, because there exist many competing ones): to provide a system whose consistency need not be questioned, and on top of which the rest of mathematics can be built.<p>This is what Russell and Whitehead had in mind when they wrote their magnum opus &quot;Principia Mathematica&quot; in the early 20th century. Gödel proved that their program was flawed. Surely you knew this?<p>&gt; Also, it seems you misunderstand Gödel&#x2F;Turing&#x2F;etc.&#x27;s result.<p>The misunderstanding is not mine.