Less is Different: Emergence and Reduction Reconciled [Book Review]

Foundations of Physics 41 (6):1065-1135 (2011)

Authors
Jeremy Butterfield
Cambridge University
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→∞ of a parameter N.But on the other hand, this does not show that the N=∞ 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).
Keywords Emergence  Reduction  Asymptotics  Method of arbitrary functions  Fractals  Superselection  Phase transitions  Thermodynamic limit
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Reprint years 2011
DOI 10.1007/s10701-010-9516-1
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References found in this work BETA

The Sciences of the Artificial.Herbert A. Simon - 1969 - [Cambridge, M.I.T. Press.
Evolutionary Theory and the Reality of Macro Probabilities.Elliott Sober - 2010 - In Ellery Eells & James H. Fetzer (eds.), The Place of Probability in Science. Springer. pp. 133--60.

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Citations of this work BETA

Understanding Toy Models.Alexander Reutlinger, Dominik Hangleiter & Stephan Hartmann - 2018 - British Journal for the Philosophy of Science 69 (4):1069-1099.
Emergence in Holographic Scenarios for Gravity.Dennis Dieks, Jeroen van Dongen & Sebastian de Haro - 2015 - Studies in History and Philosophy of Science Part B: Studies in History and Philosophy of Modern Physics 52 (Part B):203-216.
Holography and Emergence.Nicholas J. Teh - 2013 - Studies in History and Philosophy of Science Part B: Studies in History and Philosophy of Modern Physics 44 (3):300-311.

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