Less is Different: Emergence and Reduction Reconciled
By Jeremy Butterfield. 2011
266 citations recorded by the source corpus.
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).
Subfields: Computational Theory and Mathematics, Statistical and Nonlinear Physics
View Paper: https://www.semanticscholar.org/paper/be63ab14a0801e481b3d218d8ec7e679212a3c43
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In Computational Theory and Mathematics
In Statistical and Nonlinear Physics
Citations in the corpus
- The Oxford Handbook of Philosophy of Physics (2013, background): “Some authors, particularly Jeremy Butterfield (2011) and John Norton (2011), have expressed the view that there are no particularly pressing issues here: the use of infinite limits is perfectly straightforwardly justified by appeal to pragmatic considerations.”
- Approximation and Idealization: Why the Difference Matters* (2012, methodology): “For a recent defense of this form of reduction with similar applications intended, see Butterfield (2011a). well behaved.”
- Emergence, Reduction and Supervenience: A Varied Landscape (2011, background): “Such limits will be a topic in the companion paper (Butterfield 2011).”