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).
Similar content being viewed by others
References
Avnir, D., Biham, O., et al.: Is the geometry of nature fractal? Science 279, 39–40 (1998)
Anderson, P.: More is different. Science 177, 393–396 (1972); reprinted in Bedau and Humphreys (eds.): Emergence: Contemporary Readings in Philosophy and Science. MIT Press/Bradford Books, Cambridge (2008)
Bangu, S.: Understanding thermodynamic singularities: phase transitions, data and phenomena. Philos. Sci. 76, 488–505 (2009)
Barnsley, M.: Fractals Everywhere. Academic Press, Boston (1988)
Barrenblatt, G.: Scaling, Self-similarity and Intermediate Asymptotics. Cambridge University Press, Cambridge (1996)
Batterman, R.: The Devil in the Details. Oxford University Press, London (2002)
Batterman, R.: Critical phenomena and breaking drops: infinite idealizations in physics. Stud. Hist. Philos. Mod. Phys. 36B, 225–244 (2005)
Batterman, R.: Hydrodynamic vs. molecular dynamics: intertheory relations in condensed matters physics. Philos. Sci. 73, 888–904 (2006)
Batterman, R.: Emergence, singularities, and symmetry breaking. Pittsburgh arXive (2009)
Batterman, R.: On the explanatory role of mathematics in empirical science. Br. J. Philos. Sci. 61, 1–25 (2010)
Belot, G.: Whose Devil? Which Details? Philos. Sci. 72, 128–153 (2005); a fuller version is available at: http://philsci-archive.pitt.edu/archive/00001515/
Berry, M.: Asymptotics, singularities and the reduction of theories. In: Prawitz, D., Skyrms, B., Westerdahl, D. (eds.) Logic, Methodology and Philosophy of Science IX: Proceedings of the Ninth International Congress of Logic, Methodology and Philosophy of Science, Uppsala, Sweden 1991, pp. 597–607. Elsevier, Amsterdam (1994)
Bogen, J., Woodward, J.: Saving the phenomena. Philos. Rev. 97, 303–352 (1988)
Bouatta, N., Butterfield, J.: Emergence and reduction combined in phase transitions. In: Kouneiher, J. (ed.) Frontiers of Fundamental Physics, vol. 11, Proceedings of the Conference. American Institute of Physics (2011, forthcoming)
Brady, R., Ball, R.: Fractal growth of copper electrodeposits. Nature 309(5965), 225–229 (1984)
Butterfield, J.: Emergence, reduction and supervenience: a varied landscape. Found. Phys. (2010, this issue)
Callender, C.: Taking thermodynamics too seriously. Stud. Hist. Philos. Mod. Phys. 32B, 539–554 (2001)
Cardy, J.: Scaling and Renormalization in Statistical Physics. Cambridge Lecture Notes in Physics, vol. 5. Cambridge University Press, Cambridge (1997)
Castaing, B., Gunaratne, G., et al.: Scaling of hard thermal turbulence in Rayleigh-Benard convection. J. Fluid Mech. 204, 1–30 (1989)
Cat, J.: The physicists’ debates on unification in physics at the end of the twentieth century. Hist. Stud. Phys. Biol. Sci. 28, 253–300 (1998)
Chaikin, P., Lubensky, T.: Principles of Condensed Matter Physics. Cambridge University Press, Cambridge (2000)
Colyvan, M.: Probability and ecological complexity’: a review of Strevens (2003). Biol. Philos. 20, 869–879 (2005)
Diaconis, P.: Finite forms of de Finetti’s theorem on exchangeability. Synthese 36, 271–281 (1977)
Diaconis, P., Freedman, D.: De Finetti’s generalizations of exchangeability. In: Jeffrey, R. (ed.) Studies in Inductive Logic and Probability, vol. 2, pp. 233–249. University of California Press, Berkeley (1980)
Diaconis, P., Holmes, S., Montgomery, R.: Dynamical bias in the coin toss. SIAM Rev. 49, 211–235 (2007)
Dixon, P., Wu, L., et al.: Scaling in the relaxation of supercooled liquids. Phys. Rev. Lett. 65, 1108–1111 (1990)
Emch, G.: Algebraic Methods in Statistical Mechanics and Quantum Field Theory. Wiley, New York (1972)
Emch, G.: Quantum statistical physics. In: Butterfield, J., Earman, J. (eds.) Philosophy of Physics, Part B. The Handbook of the Philosophy of Science, pp. 1075–1182. North Holland, Amsterdam (2006)
Emch, G., Liu, C.: The Logic of Thermo-statistical Physics. Springer, Berlin (2002)
Engel, E.: A Road to Randomness in Physical Systems. Springer, Berlin (1992)
Falconer, K.: Fractal Geometry. Wiley, New York (2003)
Frigg, R., Hoefer, C.: Determinism and chance from a Humean perspective. In: Dieks, D., Gonzalez, W., Hartmann, S., Stadler, F., Uebel, T., Weber, M. (eds.) The Present Situation in the Philosophy of Science. Springer, Berlin (2010, forthcoming)
Goldenfeld, N., Martin, O., Oono, Y.: Intermediate asymptotics and renormalization group theory. J. Sci. Comput. 4, 355–372 (1989)
Gross, D.: Microcanonical Thermodynamics; Phase Transitions in Small Systems. World Scientific, Singapore (2001)
Hadzibabic, Z., et al.: Berezinskii-Kosterlitz-Thouless crossover in a trapped atomic gas. Nature 441, 1118–1121 (2006)
Hastings, H., Sugihara, G.: Fractals: A User’s Guide for the Natural Sciences. Oxford University Press, London (1993)
Hooker, C.: Asymptotics, reduction and emergence. Br. J. Philos. Sci. 55, 435–479 (2004)
Jeffrey, R.: Conditioning, kinematics and exchangeability. In: Skyrms, B., Harper, W. (eds.) Causation, Chance and Credence, vol. 1, pp. 221–255. Kluwer, Dordrecht (1988)
Kadanoff, L.: More is the same: phase transitions and mean field theories. J. Stat. Phys. 137, 777–797 (2009); available at http://arxiv.org/abs/0906.0653
Kadanoff, L.: Theories of matter: infinities and renormalization. In: Batterman, R. (ed.) The Oxford Handbook of the Philosophy of Physics. Oxford University Press (2010, forthcoming); available at http://arxiv.org/abs/1002.2985; and at http://jfi.uchicago.edu/~leop/AboutPapers/Trans2.pdf
Kadanoff, L.: Relating theories via renormalization (2010a); available at http://jfi.uchicago.edu/~leop/AboutPapers/RenormalizationV4.0.pdf
Keller, J.: The probability of heads. Am. Math. Mon. 93, 191–197 (1986)
Koenig, R., Renner, R.: A de Finetti representation for finite symmetric quantum states. J. Math. Phys. 46, 012105 (2005); available at arXiv:quant-ph/0410229v1
Koenig, R., Mitchison, G.: A most compendious and facile quantum de Finetti theorem. J. Math. Phys. (2007) 50, 012105; available at arXiv:quant-ph/0703210
Kritzer, P.: Sensitivity and Randomness: The Development of the Theory of Arbitrary Functions. Diplom thesis, University of Salzburg (2003)
Landsman, N.: Between classical and quantum. In: Butterfield, J., Earman, J. (eds.) Philosophy of Physics, Part A. The Handbook of the Philosophy of Science, pp. 417–554. North-Holland, Amsterdam (2006); available at arxiv:quant-ph/0506082 and at http://philsci-archive.pitt.edu/archive/00002328
Lavis, D., Bell, G.: Statistical Mechanics of Lattice Systems 1; Closed Forms and Exact Solutions, 2nd enlarged edn. Springer, Berlin (1999)
Lavis, D., Bell, G.: Statistical Mechanics of Lattice Systems. 2. Exact, Series and Renormalization Group Methods. Springer, Berlin (1999a)
Le Bellac, M.: Quantum and Statistical Field Theory. Oxford University Press, London (1991) (translated by G. Barton)
Liu, C.: Infinite systems in SM explanation: thermodynamic limit, renormalization (semi)-groups and irreversibility. Proc. Philos. Sci. 68, S325–S344 (2001)
Liu, C., Emch, G.: Explaining quantum spontaneous symmetry breaking. Stud. Hist. Philos. Mod. Phys. 36, 137–164 (2005)
Mainwood, P.: Is More Different? Emergent Properties in Physics. D. Phil. dissertation, Oxford University (2006). At: http://philsci-archive.pitt.edu/8339/
Mainwood, P.: Phase transitions in finite systems, unpublished MS (corresponds to Chapter 4 of Mainwood (2006)) (2006a). At: http://philsci-archive.pitt.edu/8340/
Mandelbrot, B.: The Fractal Geometry of Nature. Freeman, San Francisco (1982)
Menon, T., Callender, C.: Going through a phase: philosophical questions raised by phase transitions. In: Batterman, R. (ed.) The Oxford Handbook of Philosophy of Physics. Oxford University Press (2011, forthcoming)
Myrvold, W.: Deterministic laws and epistemic chances. Unpublished manuscript (2011)
Nagel, E.: The Structure of Science: Problems in the Logic of Scientific Explanation. Harcourt, New York (1961)
Nelson, E.: Radically Elementary Probability Theory. Annals of Mathematics Studies, vol. 117. Princeton University Press, Princeton (1987)
Peitgen, H.-O., Richter, P.: The Beauty of Fractals. Springer, Heidelberg (1986)
Poincaré, H.: Calcul de Probabilities. Gauthier-Villars, Paris (1896); page reference to 1912 edition
Richardson, L.: The problem of contiguity: an appendix of statistics of deadly quarrels. Gen. Syst. Yearbook 6, 139–187 (1961)
Renner, R.: Symmetry implies independence. Nat. Phys. 3, 645–649 (2007)
Rueger, A.: Physical emergence, diachronic and synchronic. Synthese 124, 297–322 (2000)
Rueger, A.: Functional reduction and emergence in the physical sciences. Synthese 151, 335–346 (2006)
Ruelle, D.: Statistical Mechanics: Rigorous Results. Benjamin, Elmsford (1969)
Sewell, G.: Quantum Theory of Collective Phenomena. Oxford University Press, London (1986)
Sewell, G.: Quantum Mechanics and its Emergent Microphysics. Princeton University Press, Princeton (2002)
Shenker, O.: Fractal geometry is not the geometry of nature. Stud. Hist. Philos. Sci. 25, 967–982 (1994)
Simon, H.: Alternative views of complexity. In: The Sciences of the Artificial, 3rd edn. MIT Press, Cambridge (1996); the Chapter is reprinted in Bedau and Humphreys (2008); page reference to the reprint
Smith, P.: Explaining Chaos. Cambridge University Press, Cambridge (1998)
Sober, E.: Evolutionary theory and the reality of macro-probabilities. In: Eells, E., Fetzer, J. (eds.) The Place of Probability in Science. Boston Studies in the Philosophy of Science, vol. 284, pp. 133–161. Springer, Berlin (2010)
Stoppard, T.: Arcadia. Faber and Faber, London (1993)
Strevens, M.: Bigger than Chaos: Understanding Complexity through Probability. Harvard University Press, Cambridge (2003)
Thompson, C.: Mathematical Statistical Mechanics. Princeton University Press, Princeton (1972)
von Plato, J.: The method of arbitrary functions. Br. J. Philos. Sci. 34, 37–47 (1983)
von Plato, J.: Creating Modern Probability. Cambridge University Press, Cambridge (1994)
Wayne, A.: Emergence and singular limits. Synthese (2009, forthcoming) available at http://philsci-archive.pitt.edu/archive/00004962/
Weinberg, S.: Newtonianism, reductionism and the art of congressional testimony. Nature 330, 433–437 (1987); reprinted in Bedau and Humphreys (2008); page reference to the reprint; also reprinted in Weinberg, S. Facing Up: Science and its Cultural Adversaries, Harvard University Press, pp. 8–25
Werndl, C.: Review of Strevens (2003). Br. J. Philos. Sci. (2010, forthcoming)
Wimsatt, W.: Aggregativity: reductive heuristics for finding emergence. Philos. Sci. 64, S372–S384 (1997); reprinted in Bedau and Humphreys (2008); page reference to the reprint
Yeomans, J.: Statistical Mechanics of Phase Transitions. Oxford University Press, London (1992)
Feynman, R.: The Feynman Lectures on Physics, vol. 2. Addison-Wesley, Reading (1964)
Author information
Authors and Affiliations
Corresponding author
Rights and permissions
About this article
Cite this article
Butterfield, J. Less is Different: Emergence and Reduction Reconciled. Found Phys 41, 1065–1135 (2011). https://doi.org/10.1007/s10701-010-9516-1
Received:
Accepted:
Published:
Issue Date:
DOI: https://doi.org/10.1007/s10701-010-9516-1