Another example: Chevron
One general application of The Law of Interpretation is to figure out which purported rules or canons of statutory interpretation are actually valid.
On our view, there are basically two routes to validity: Either a rule is a principle of language, in which case it should accurately track how lawmakers communicate; or it is a principle of law, in which case it should satisfy the tests provided by the rule of recognition for valid legal norms in our system. (You can replace the latter with your own preferred theory of jurisprudence, but I'll leave that as an exercise for the reader.)
So to take one newly controversial example, is the rule of agency deference pronounced in Chevron v. NRDC valid? I am dubious.
As a matter of language, the argument would be that an ambiguous grant of regulatory authority is a way of implicitly communicating a delegation. Through silence or open-endedness, Congress says "fill any relevant gaps (to be exercised subject to procedural safeguards, such as notice-and-comment rulemaking, and so on)." I don't think that's an accurate account of what the text usually communicates on its own, although somebody strongly committed to a certain model of congressional intent might be able to make a case for it.
As a matter of law, Chevron would have to be a certain kind of closure rule: If the agency was generally granted power to regulate a field through certain means, then it's the challenger's burden to show that some particular subfield was excluded from this grant, and this burden can be met only with clear text.
But why this closure rule? As Aditya Bamzai has persuasively shown, the cases from which Chevron purported to derive authority actually described different rules—such as rules of customary or contemporaneous interpretation. And the APA does not appear to have been intended to codify anything like the Chevron principle either. So it seems unlikely that any of our normal sources of law justify the decision in Chevron.
Now even if Chevron is wrongly decided, that still leaves the slightly different question of whether it should be overruled now. But I'll leave that for another project; we've done enough for this post.