Abstract
The clarification of the concept of emergence has long been on the agenda of the metaphysics of science; notions such as ‘irreducibility’, ‘novelty’ and ‘unpredictability’ have been invoked in an attempt to better circumscribe this notoriously elusive idea. This paper joins this effort, by examining a class of familiar physical processes, such as boiling and freezing—generically called ‘phase transitions’—since many philosophers and physicists take them to be good candidates of emergent phenomena. While I am broadly sympathetic to this view, in this paper I ask what kind of emergence they instantiate. I am asking this question because I would like to argue that the two kinds of emergence currently identified in the metaphysics literature, ‘weak’ and ‘strong’, do not adequately characterize these phenomena.
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Notes
- 1.
- 2.
- 3.
See O’Connor and Wong (2009) for an inventory.
- 4.
This is, again, a stipulation, as typically the notion is slightly broader than this.
- 5.
- 6.
For an inventory of these problems, see Sklar (1993).
- 7.
Kim breaks it down in three steps, but I collapsed the last two.
- 8.
When presented with this argument, biologists and philosophers of biology alike are skeptical; but the topic of reduction in biology is a large and complex one, and it would certainly require a separate paper to discuss the success of the F-model in that context.
- 9.
Further significant constraints are also imposed on this idealized model (called the Ising model), one of them being that the ratio between the number of particles in it and the volume it occupies is finite. When all these details are considered, it is not clear to what of the three types of idealizations identified by Weisberg (2007) this one belongs.
- 10.
As Kadanoff urges, “the existence of a phase transition requires an infinite system. No phase transitions occur in systems with a finite number of degrees of freedom.” (2000, 238).
- 11.
As Callender memorably suggested, we should not ‘take thermodynamics too seriously’: “After all, the fact that thermodynamics treats phase transitions as singularities does not imply that statistical mechanics must too.” (2001, 550).
- 12.
Slightly more precisely, Franzosi et al. (2000, p. 2774) describe their central idea as follows: “a major topology change (…) is at the origin of the phase transition in the model considered.” Furthermore: “suitable topology changes of equipotential sub-manifolds of configuration space can entail thermodynamic phase transitions(…). The method we use, though applied here to a particular model, is of general validity and it is of prospective interest to the study of phase transitions in those systems that challenge the conventional approaches, as might be the case of finite systems.” Kastner (2008) is another paper discussing this issue, also mentioned by Callender and Menon (2013).
- 13.
The topology change is not the only approach Callender and Menon discuss in their (2013). Two others, the ‘back-bending’ in the microcanonical caloric curve (Sect. 3.1.1) and the perpendicular distribution of zeros (Sect. 3.1.2) are also mentioned, but these approaches too fall under the same disclaimer, that “Probably none of the definitions provide necessary and sufficient conditions for a phase transition that overlaps perfectly with thermodynamic phase transitions”, while also adding, without really explaining the claim, that “That, however, is okay, for thermodynamics itself does not neatly characterize all the ways in which macrostates can change in an ‘abrupt’ way” (2013, 210).
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Acknowledgments
I presented versions of this paper in several places (Urbana IL, Peoria IL, Boston MA, Fort-Wayne IN, and Berlin), and my audiences have been extremely helpful in commenting on, and criticizing previous versions of the paper. I thank a group of mathematical physicists at Bradley University (and my host there, Vlad Niculescu), Rob Cummins, Laura Ruetsche, Jessica Wilson, Peter Bokulich, Alisa Bokulich, John Stachel, Iulian Toader, Ioan Muntean, Mark Zelczer, Alex Manafu, Paul Humphreys, Craig Callender, Bob Batterman, Margie Morrison and Brigitte Falkenburg. I am of course responsible for all remaining philosophical or scientific errors.
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Bangu, S. (2015). Neither Weak, Nor Strong? Emergence and Functional Reduction. In: Falkenburg, B., Morrison, M. (eds) Why More Is Different. The Frontiers Collection. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-662-43911-1_9
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