Reduction, Emergence and Renormalization

In previous work, I described several examples combining reduction and emer-gence: where reduction is understood a ̀ la Ernest Nagel, and emergence is un-derstood as behaviour or properties that are novel (by some salient standard). Here, my aim is again to reconcile reduction and emergence, for a case which is apparently more problematic than those I treated before: renormalization. Renormalization is a vast subject. So I confine myself to emphasizing how the modern approach to renormalization (initiated by Wilson and others be-tween 1965 and 1975), when applied to quantum field theories, illustrates both Nagelian reduction and emergence. My main point is that the modern under-standing of how renormalizability is a generic feature of quantum field theories at accessible energies gives us a conceptually unified family of Nagelian reduc-tions. That is worth saying since philosophers tend to think of scientific explana-tion as only explaining an individual event, or perhaps a single law, or at mos