Brandeis
The movement claim that the Declaration of Independence functions as super-constitutional law that overrides statutes and constitutional provisions where they conflict is unsupported
The Declaration is foundational political philosophy, not enforceable law that overrides statutes or constitutional provisions. But the natural-law constitutional tradition (Arkes, Jaffa, Sandefur, Barnett) treats the deeper question — whether constitutional interpretation may draw on Declaration principles — seriously, and the question is not foreclosed at the scholarly level. Engaged in good faith rather than dismissed.
The movement claim that Swift v. Tyson establishes the Constitution as 'predicated upon the common law' and federal courts as applying common law as the foundational basis of federal jurisprudence is unsupported
Swift v. Tyson (1842) once let federal courts apply general federal common law in diversity cases. Erie Railroad v. Tompkins (1938) overruled it explicitly. The movement still cites Swift for the proposition that the Constitution is 'predicated upon the common law,' and treats Swift as live authority. It isn't — it was overruled the better part of a century ago.