Emergence and Reduction Combined in Phase Transitions

Abstract

In another paper, one of us argued that emergence and reduction are compatible, and presented four examples illustrating both. The main purpose of this paper is to develop this position for the example of phase transitions. We take it that emergence involves behaviour that is novel compared with what is expected: often, what is expected from a theory of the system's microscopic constituents. We take reduction as deduction, aided by appropriate definitions. Then the main idea of our reconciliation of emergence and reduction is that one makes the deduction after taking a limit of an appropriate parameter $N$. Thus our first main claim will be that in some situations, one can deduce a novel behaviour, by taking a limit $N\to\infty$. Our main illustration of this will be Lee-Yang theory. But on the other hand, this does not show that the $N=\infty$ limit is physically real. For our second main claim will be that in such situations, there is a logically weaker, yet still vivid, novel behaviour that occurs before the limit, i.e. for finite $N$. And it is this weaker behaviour which is physically real. Our main illustration of this will be the renormalization group description of cross-over phenomena.

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Jeremy Butterfield
Cambridge University

References found in this work

The Structure of Science.Ernest Nagel - 1961 - Les Etudes Philosophiques 17 (2):275-275.
More is Different.P. W. Anderson - 1994 - In H. Gutfreund & G. Toulouse (eds.), Biology and Computation: A Physicist's Choice. World Scientific. pp. 3--21.
Taking Thermodynamics Too Seriously.Craig Callender - 2001 - Studies in History and Philosophy of Science Part B: Studies in History and Philosophy of Modern Physics 32 (4):539-553.

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Citations of this work

Smaller Than a Breadbox: Scale and Natural Kinds.Julia R. Bursten - 2018 - British Journal for Philosophy of Science 69 (1):1-23.
Emergence Without Limits: The Case of Phonons.Alexander Franklin & Eleanor Knox - 2018 - Studies in History and Philosophy of Science Part B: Studies in History and Philosophy of Modern Physics 64:68-78.

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