Abstract

This paper attempts to make sense of a notion of ``approximation on certain scales'' in physical theories. I use this notion to understand the classical limit of ordinary quantum mechanics as a kind of scaling limit, showing that the mathematical tools of strict quantization allow one to make the notion of approximation precise. I then compare this example with the scaling limits involved in renormalization procedures for effective field theories. I argue that one does not yet have the mathematical tools to make a notion of ``approximation on certain scales" precise in extant mathematical formulations of effective field theories. This provides guidance on the kind of further work that is needed for an adequate interpretation of quantum field theory.