In a previous post of abstracts, I mentioned philosopher Josh Rosaler’s attempt to clarify the distinction between empirical and formal notions of “theoretical reduction”. Reduction is just the idea that one theory reduces to another in some limit, like Galilean kinematics reduces to special relativity in the limit of small velocities.^{ a } Formal reduction is when this takes the form of some mathematical limiting procedure (e.g., ), whereas empirical reduction is an explanatory statement about observations (e.g., “special relativity can explains the empirical usefulness of Galilean kinematics”).
Rosaler’s criticism, which I mostly agree with, is that folks often conflate these two. Usually this isn’t a serious problem since the holes can be patched up on the fly by a competent physicist, but sometimes it leads to serious trouble. The most egregious case, and the one that got me interested in all this, is the quantum-classical transition, and in particular the serious insufficiency of existing limits to explain the appearance of macroscopic classicality. In particular, even though this limiting procedure recovers the classical equations of motion, it fails spectacularly to recover the state space.… [continue reading]