Fascinating article. If you know who Kurt Gödel was and understand what a Constitution represents in regards to the logical axioms (i.e. assumptions) made in the formulation of a rules-set (i.e. legal system) and their theorems (i.e. formal legal consequences) underpinning governance and political power, you already know where this is heading.
While it may never be fully possible to abstract the logical principles from the political context, as may be preferred to ensure dialogue does not rapidly devolve into pointless bickering, the underlying principles and the logic stand, as it were, proven and alone. In potentially identifying serious logical inconsistencies within the US Constitution, Kurt Gödel had not necessarily isolated implicit or enduring weakness or failure so much as opportunity. An interesting consequence of the Incompleteness Theorems is that not only is any (sufficiently) complex, formalised and logical system likely to feature or display just such inconsistencies or implicit structural discontinuity, but that it is always possible to creatively (or at the very least – usefully) extend that system to negotiate and account for that inconsistency.
Of course, the indefinitely-extensible nature of these “sufficiently complex” logical, axiomatic systems entails that if you were to identify the specific location and nature of these error-or-authoritarian-catastrophe-inducing theorems, rewording or redefining them would only generate or displace such inconsistencies elsewhere, requiring you to extend the system again. You find yourself, in effect, playing “whack-a-mole” with logical consequences. If sufficiently complex logical systems are indeed indefinitely extensible in this way, perhaps one of the fatal flaws we might make in attempting to generate such constitutional legal frameworks is to assume the plausibility of complete and consistent, fundamentally unchanging rules-sets, assumptions and the consequences derived from them.
Granted, natural language semantics are far removed from the rigid definitions and procedural execution of formal axiomatic systems; I imagine that one interesting aspect of this is the extent to which faith is often placed in Constitutional proclamations as being infallible when such fallibility and consistency (with contextual caveats) has been proven impossible.
I imagine that automated theorem-proving software could be gainfully applied to this topic.