Less is Different: Emergence and Reduction Reconciled

TL;DR

This paper argues that emergence and reduction are compatible by showing that novel behaviors in physics can be deduced through limits of parameters, while the physically real phenomena occur at finite values.

Contribution

It demonstrates that emergence can be reconciled with reduction by analyzing limiting processes and emphasizing the reality of behaviors at finite parameters.

Findings

Emergent behaviors can be deduced by taking limits of parameters.

Physically real phenomena occur at finite parameter values, not only at limits.

Examples include fractals, superselection, and phase transitions.

Abstract

This is a companion to another paper. Together they rebut two widespread philosophical 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 rebuttal. 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 comparison 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 limit, N goes to infinity, of a parameter N. But on the other hand, this does not show that that the infinite limit is "physically real", as some authors have alleged. For my second main claim is that in these same examples, there is a weaker, yet still vivid, novel and robust behaviour that occurs before we get to the limit, i.e. for finite N. And it is this weaker behaviour which is physically real. My examples are: the method of arbitrary functions (in probability theory); fractals (in geometry); superselection for infinite systems (in quantum theory); and phase transitions for infinite systems (in statistical mechanics).