Skip to main content
Log in

On structural accounts of model-explanations

  • Published:
Synthese Aims and scope Submit manuscript

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.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Fig. 1
Fig. 2
Fig. 3
Fig. 4

Similar content being viewed by others

Notes

  1. For more information about the quantum models, simulations of the scarring phenomenon, and ergodic and unique ergodic properties of classical and quantum billiards, see Dettman and Georgiou (2010), Gutzwiller (1990), Heller (1984, 1986), Kaplan and Heller (1999), King (2009), McDonald and Kaufman (1979), Tao (2007), Tomsovic and Heller (1993).

References

  • Batterman, R. W. (1992). Quantum chaos and semiclassical mechanics. Proceedings of the Biennial Meetings of the Philosophy of Science Association, 1992(2), 50–65.

    Article  Google Scholar 

  • Batterman, R. W. (2002a). Asymptotics and the role of minimal models. British Journal for the Philosophy of Science, 53, 21–38.

    Article  Google Scholar 

  • Batterman, R. W. (2002b). The devil in the details. Oxford: Oxford University Press.

    Google Scholar 

  • Batterman, R. W. (2005). Critical phenomena and breaking drops: Infinite idealizations in physics. Studies in History and Philosophy of Modern Physics, 36, 225–244.

    Article  Google Scholar 

  • Batterman, R. W., & Rice, C. C. (2014). Minimal model explanations. Philosophy of Science, 81(3), 349–376. doi:10.1086/676677.

    Article  Google Scholar 

  • 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.

    Article  Google Scholar 

  • Bleher, S., Ott, E., & Grebogi, C. (1989). Routes to chaotic scattering. Physical Review Letters, 63(9), 919–922.

    Article  Google Scholar 

  • Bokulich, A. (2008). Reexamining the quantum–classical relation: Beyond reductionism and pluralism. New York: Cambridge University Press.

    Book  Google Scholar 

  • Bokulich, A. (2011). How scientific models can explain. Synthese, 180(1), 33–45.

    Article  Google Scholar 

  • Bokulich, A. (2012). Distinguishing explanatory from nonexplanatory fictions. Philosophy of Science, 79(5), 725–737.

    Article  Google Scholar 

  • Bunimovich, L. (1974). The ergodic properties of certain billiards. Functional Analysis and its Applications, 8, 73–74.

    Article  Google Scholar 

  • Bunimovich, L. (1979). On the ergodic properties of nowhere dispersing billiards. Communications in Mathematical Physics, 65, 295–312.

    Article  Google Scholar 

  • Cartwright, N. (1983). How the laws of physics lie. Oxford: Oxford University Press.

    Book  Google Scholar 

  • 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.

    Article  Google Scholar 

  • 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.

  • Dettman, C. P., & Georgiou, O. (2011). Open mushrooms: Stickiness revisited. Journal of Physics: Mathematical and Theoretical, 44, 195102.

    Google Scholar 

  • Esfeld, M., & Lam, V. (2008). Moderate structural realism about space–time. Synthese, 160, 27–46.

    Article  Google Scholar 

  • French, S., & Ladyman, J. (2003). Remodelling structural realism: Quantum physics and the metaphysics of structure. Synthese, 136, 31–56.

    Article  Google Scholar 

  • Gutzwiller, M. C. (1990). Chaos in classical and quantum mechanics. New York: Springer.

    Book  Google Scholar 

  • Heller, E. J. (1984). Bound-state eigenfunctions of classically chaotic Hamiltonian systems: Scars of periodic orbits. Physical Review Letters, 53(16), 1515–1518.

    Article  Google Scholar 

  • Heller, E. J. (1986). Qualitative properties of eigenfunctions of classically chaotic Hamiltonian quantum chaos and statistical. Nuclear Physics, 263, 162–181.

    Google Scholar 

  • Hempel, C. G., & Oppenheim, P. (1948). Studies in the logic of explanation. Philosophy of Science, 15(2), 135–175.

    Article  Google Scholar 

  • Kaplan, L., & Heller, E. J. (1999). Measuring scars of periodic orbits. Physical Review E, 59(6), 6609–6628.

    Article  Google Scholar 

  • King, C. (2009). Exploring quantum, classical and semiclassical chaos in the stadium billiard. Quanta, 3(1), 16–31.

    Article  Google Scholar 

  • Ladyman, J. (1998). What is structural realism? Studies in History and Philosophy of Modern Science, 29, 409–424.

    Article  Google Scholar 

  • McDonald, S. W., & Kaufman, A. N. (1979). Spectrum and eigenfunctions for a Hamiltonian with stochastic trajectories. Physical Review Letters, 42(18), 1189–1191.

    Article  Google Scholar 

  • McMullin, E. (1985). Galilean idealization. Studies in History and Philosophy of Science, 16(3), 247–273.

    Article  Google Scholar 

  • 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.

    Chapter  Google Scholar 

  • Rice, C. (2012). Optimality explanations: A plea for an alternative approach. Biology and Philosophy, 27, 685–703.

    Article  Google Scholar 

  • Rice, C. (2013). Moving beyond causes: Optimality models and scientific explanation. Noûs, 49(2), 589–615.

    Google Scholar 

  • Schupbach, J., & Sprenger, J. (2011). The logic of explanatory power. Philosophy of Science, 78(1), 105–127.

    Article  Google Scholar 

  • Stöckmann, H. (2010). Stoe billiards. In stoe\(\_\)billiards.jpeg (Ed.). Sholarpedia.

  • Strevens, M. (2008). Depth: An account of scientific explanation. Harvard, MA: Harvard University Press.

    Google Scholar 

  • 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.

  • Teller, P. (2001). Twilight of the perfect model model. Erkenntnis, 55(3), 393–415.

    Article  Google Scholar 

  • Tomsovic, S., & Heller, E. J. (1993). Long-time semiclassical dynamics of chaos: The stadium billiard. Physical Review E, 47(1), 282–299.

    Article  Google Scholar 

  • Wayne, A. (2011). Extending the scope of explanatory idealization. Philosophy of Science, 78(5), 830–841.

    Article  Google Scholar 

  • Weslake, B. (2010). Explanatory depth. Philosophy of Science, 77(2), 273–294.

    Article  Google Scholar 

  • Woodward, J. (2003). Making things happen: A theory of causal explanation. Oxford: Oxford University Press.

    Google Scholar 

  • Woodward, J., & Hitchcock, C. (2003a). Explanatory generalizations, part I: A counterfactual account. Noûs, 37(1), 1–24.

    Article  Google Scholar 

  • Woodward, J., & Hitchcock, C. (2003b). Explanatory generalizations, part II: Plumbing explanatory depth. Noûs, 37(2), 181–199.

    Article  Google Scholar 

  • Worrall, J. (1989). Structural realism: The best of both worlds? Dialectica, 43(1–2), 99–124.

    Article  Google Scholar 

Download references

Author information

Authors and Affiliations

Authors

Corresponding author

Correspondence to Martin King.

Rights and permissions

Reprints and permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

King, M. On structural accounts of model-explanations. Synthese 193, 2761–2778 (2016). https://doi.org/10.1007/s11229-015-0885-z

Download citation

  • Received:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s11229-015-0885-z

Keywords

Navigation