Advertisement

Synthese

, Volume 193, Issue 9, pp 2761–2778 | Cite as

On structural accounts of model-explanations

  • Martin KingEmail author
Article

Abstract

The focus in the literature on scientific explanation has shifted in recent years towards model-based approaches. In recent work, Alisa Bokulich has argued that idealization has a central role to play in explanation. Bokulich claims that certain highly-idealized, structural models can be explanatory, even though they are not considered explanatory by causal, mechanistic, or covering law accounts of explanation. This paper focuses on Bokulich’s account in order to make the more general claim that there are problems with maintaining that a structural criterion can capture the way that highly-idealized models explain. This paper examines Bokulich’s claim that the structural model explanation of quantum wavefunction scarring, featuring semiclassical mechanics, is deeper than the explanation provided by the local quantum model. The challenge for Bokulich is to show that the semiclassical model answers a wider range of w-questions (what-if-things-had-been-different-questions), as this is her method of assessing structural information. I look at two reasonable approaches employing w-questions, and I argue that neither approach is ultimately satisfactory. Because structural similarity has preferences for more fundamental models, I argue that the local quantum model provides explanations that at least as deep as the semiclassical ones. The criterion either wrongly identifies all models as explanatory, or prefers models from fundamental theory. Either way, it cannot capture the way that highly-idealized models explain.

Keywords

Explanation Semiclassical Quantum Structural Scientific model Woodward Bokulich Depth 

References

  1. Batterman, R. W. (1992). Quantum chaos and semiclassical mechanics. Proceedings of the Biennial Meetings of the Philosophy of Science Association, 1992(2), 50–65.CrossRefGoogle Scholar
  2. Batterman, R. W. (2002a). Asymptotics and the role of minimal models. British Journal for the Philosophy of Science, 53, 21–38.CrossRefGoogle Scholar
  3. Batterman, R. W. (2002b). The devil in the details. Oxford: Oxford University Press.Google Scholar
  4. Batterman, R. W. (2005). Critical phenomena and breaking drops: Infinite idealizations in physics. Studies in History and Philosophy of Modern Physics, 36, 225–244.CrossRefGoogle Scholar
  5. Batterman, R. W., & Rice, C. C. (2014). Minimal model explanations. Philosophy of Science, 81(3), 349–376. doi: 10.1086/676677.CrossRefGoogle Scholar
  6. Belot, G., & Jansson, L. (2010). Review of reexamining the quantum–classical relation: Beyond reductionism and pluralism, by A. Bokulich. Studies in History and Philosophy of Modern Physics, 41, 81–83.CrossRefGoogle Scholar
  7. Bleher, S., Ott, E., & Grebogi, C. (1989). Routes to chaotic scattering. Physical Review Letters, 63(9), 919–922.CrossRefGoogle Scholar
  8. Bokulich, A. (2008). Reexamining the quantum–classical relation: Beyond reductionism and pluralism. New York: Cambridge University Press.CrossRefGoogle Scholar
  9. Bokulich, A. (2011). How scientific models can explain. Synthese, 180(1), 33–45.CrossRefGoogle Scholar
  10. Bokulich, A. (2012). Distinguishing explanatory from nonexplanatory fictions. Philosophy of Science, 79(5), 725–737.CrossRefGoogle Scholar
  11. Bunimovich, L. (1974). The ergodic properties of certain billiards. Functional Analysis and its Applications, 8, 73–74.CrossRefGoogle Scholar
  12. Bunimovich, L. (1979). On the ergodic properties of nowhere dispersing billiards. Communications in Mathematical Physics, 65, 295–312.CrossRefGoogle Scholar
  13. Cartwright, N. (1983). How the laws of physics lie. Oxford: Oxford University Press.CrossRefGoogle Scholar
  14. Craver, C. (2006). Physical law and mechanistic explanation in the Hodgkin and Huxley model of the action potential. Philosophy of Science, 75(5), 1022–1033.CrossRefGoogle Scholar
  15. Dettman, C. P., & Georgiou, O. (2010). Open intermittent billiards: A dynamical window. Retrieved from http://iopscience.iop.org/1751-8121/labtalk-article/46000. Accessed 3 Jan 2015.
  16. Dettman, C. P., & Georgiou, O. (2011). Open mushrooms: Stickiness revisited. Journal of Physics: Mathematical and Theoretical, 44, 195102.Google Scholar
  17. Esfeld, M., & Lam, V. (2008). Moderate structural realism about space–time. Synthese, 160, 27–46.CrossRefGoogle Scholar
  18. French, S., & Ladyman, J. (2003). Remodelling structural realism: Quantum physics and the metaphysics of structure. Synthese, 136, 31–56.CrossRefGoogle Scholar
  19. Gutzwiller, M. C. (1990). Chaos in classical and quantum mechanics. New York: Springer.CrossRefGoogle Scholar
  20. Heller, E. J. (1984). Bound-state eigenfunctions of classically chaotic Hamiltonian systems: Scars of periodic orbits. Physical Review Letters, 53(16), 1515–1518.CrossRefGoogle Scholar
  21. Heller, E. J. (1986). Qualitative properties of eigenfunctions of classically chaotic Hamiltonian quantum chaos and statistical. Nuclear Physics, 263, 162–181.Google Scholar
  22. Hempel, C. G., & Oppenheim, P. (1948). Studies in the logic of explanation. Philosophy of Science, 15(2), 135–175.CrossRefGoogle Scholar
  23. Kaplan, L., & Heller, E. J. (1999). Measuring scars of periodic orbits. Physical Review E, 59(6), 6609–6628.CrossRefGoogle Scholar
  24. King, C. (2009). Exploring quantum, classical and semiclassical chaos in the stadium billiard. Quanta, 3(1), 16–31.CrossRefGoogle Scholar
  25. Ladyman, J. (1998). What is structural realism? Studies in History and Philosophy of Modern Science, 29, 409–424.CrossRefGoogle Scholar
  26. McDonald, S. W., & Kaufman, A. N. (1979). Spectrum and eigenfunctions for a Hamiltonian with stochastic trajectories. Physical Review Letters, 42(18), 1189–1191.CrossRefGoogle Scholar
  27. McMullin, E. (1985). Galilean idealization. Studies in History and Philosophy of Science, 16(3), 247–273.CrossRefGoogle Scholar
  28. Morrison, M. (1999). Models as autonomous agents. In M. Morrison & M. Morgan (Eds.), Models as mediators: Perspectives on natural and social science (pp. 38–65). Cambridge: Cambridge University Press.CrossRefGoogle Scholar
  29. Rice, C. (2012). Optimality explanations: A plea for an alternative approach. Biology and Philosophy, 27, 685–703.CrossRefGoogle Scholar
  30. Rice, C. (2013). Moving beyond causes: Optimality models and scientific explanation. Noûs, 49(2), 589–615.Google Scholar
  31. Schupbach, J., & Sprenger, J. (2011). The logic of explanatory power. Philosophy of Science, 78(1), 105–127.CrossRefGoogle Scholar
  32. Stöckmann, H. (2010). Stoe billiards. In stoe\(\_\)billiards.jpeg (Ed.). Sholarpedia.Google Scholar
  33. Strevens, M. (2008). Depth: An account of scientific explanation. Harvard, MA: Harvard University Press.Google Scholar
  34. Tao, T. (2007). Open question: Scarring for the Bunimovich stadium. Retrieved from http://terrytao.wordpress.com/2007/03/28/open-question-scarring-for-the-bunimovich-stadium/. Accessed 28 Nov 2014.
  35. Teller, P. (2001). Twilight of the perfect model model. Erkenntnis, 55(3), 393–415.CrossRefGoogle Scholar
  36. Tomsovic, S., & Heller, E. J. (1993). Long-time semiclassical dynamics of chaos: The stadium billiard. Physical Review E, 47(1), 282–299.CrossRefGoogle Scholar
  37. Wayne, A. (2011). Extending the scope of explanatory idealization. Philosophy of Science, 78(5), 830–841.CrossRefGoogle Scholar
  38. Weslake, B. (2010). Explanatory depth. Philosophy of Science, 77(2), 273–294.CrossRefGoogle Scholar
  39. Woodward, J. (2003). Making things happen: A theory of causal explanation. Oxford: Oxford University Press.Google Scholar
  40. Woodward, J., & Hitchcock, C. (2003a). Explanatory generalizations, part I: A counterfactual account. Noûs, 37(1), 1–24.CrossRefGoogle Scholar
  41. Woodward, J., & Hitchcock, C. (2003b). Explanatory generalizations, part II: Plumbing explanatory depth. Noûs, 37(2), 181–199.CrossRefGoogle Scholar
  42. Worrall, J. (1989). Structural realism: The best of both worlds? Dialectica, 43(1–2), 99–124.CrossRefGoogle Scholar

Copyright information

© Springer Science+Business Media Dordrecht 2015

Authors and Affiliations

  1. 1.University of GuelphGuelphCanada

Personalised recommendations