What is fundamental?

In an earlier post I mentioned a nice pedagogical article by Bertrand Delamotte on scaling and the renormalisation group. I found the concluding paragraph fascinating and thought provoking.

To conclude, we see that although the renormalization procedure has not evolved much these last thirty years, our interpretation of renormalization has drastically changed:¹² the renormalized theory was assumed to be fundamental, while it is now believed to be only an effective one; [the scaling parameter] was interpreted as an artificial parameter that was only useful in intermediate calculations, while we now believe that it corresponds to a fundamental scale where new physics occurs; nonrenormalizable couplings were thought to be forbidden, while they are now interpreted as the remnants of interaction terms in a more fundamental theory. Renormalization group is now seen as an efficient tool to build effective low energy theories when large fluctuations occur between two very different scales that change the physics qualitatively and quantitatively.

On reflection, I realised that this change in thinking reflects the thinking of quantum field theorists. In contrast, I think the perspective of the concluding sentence has always been the perspective of condensed matter theorists. This can be seen in Haldane's seminal 1978 paper, Scaling theory of the asymmetric Anderson model. It is summarised in the Figure below.