Less is different: Emergence and reduction reconciled

Abstract

This is a companion to another paper. Together they rebut two widespread philo-sophical doctrines about emergence. The first, and main, doctrine is that emergence is incompatible with reduction. The second is that emergence is supervenience; or more exactly, supervenience without reduction. In the other paper, I develop these rebuttals in general terms, emphasising the second rebuttal. Here I discuss the situation in physics, emphasising the first rebut-tal. I focus on limiting relations between theories and illustrate my claims with four examples, each of them a model or a framework for modelling, from well-established mathematics or physics. I take emergence as behaviour that is novel and robust relative to some com-parison class. I take reduction as, essentially, deduction. The main idea of my first rebuttal will be to perform the deduction after taking a limit of some parameter. Thus my first main claim will be that in my four examples (and many others), we can deduce a novel and robust behaviour, by taking the limitN → ∞ of a parameter