Again, natural law is a specific, historically rooted branch of philosophy, and so is this. But what's happening here is not a debate between two schools of philosophy, but an argument against certain schools of legal thought. Conservative constitutional legal thought (embodied most famously by Scalia but also by much of the right wing of the current SCOTUS) is originalist. Originalism opposes the idea of "novel rights" and the "living Constitution," and insists on interpreting the Constitution as people theoretically would have done at the time of its writing.

The takeaway here is the foregoing screed on Progressivism and philosophy is actually a warm-up to an subtextual argument about Constitutional interpretation that is the bedrock of how conservatives view the Judicial Branch.