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Viewing-as explanations and ontic dependence

  • William D’AlessandroEmail author
Article
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Abstract

According to a widespread view in metaphysics and philosophy of science (the “Dependence Thesis”), all explanations involve relations of ontic dependence between the items appearing in the explanandum and the items appearing in the explanans. I argue that a family of mathematical cases, which I call “viewing-as explanations”, are incompatible with the Dependence Thesis. These cases, I claim, feature genuine explanations that aren’t supported by ontic dependence relations. Hence the thesis isn’t true in general. The first part of the paper defends this claim and discusses its significance. The second part of the paper considers whether viewing-as explanations occur in the empirical sciences, focusing on the case of so-called fictional models (such as Bohr’s model of the atom). It’s sometimes suggested that fictional models can be explanatory even though they fail to represent actual worldly dependence relations. Whether or not such models explain, I suggest, depends on whether we think scientific explanations necessarily give information relevant to intervention and control. Finally, I argue that counterfactual approaches to explanation also have trouble accommodating viewing-as cases.

Keywords

Explanation Mathematical explanation Ontological dependence Viewing-as Ontic conception Philosophy of mathematics Philosophy of science Counterfactual dependence Counterpossibles Counterfactuals 

Notes

Acknowledgements

This paper started life as a third of my dissertation at the University of Illinois at Chicago; I’m very grateful to my advisor, Daniel Sutherland, and to my other committee members, Mahrad Almotahari, Kenny Easwaran, Dave Hilbert and Marc Lange, for their feedback and support. The comments of an anonymous referee for Philosophical Studies led to some significant additions and (I hope) improvements. I’ve also benefited from conversations about these issues with Liz Camp, Lisa James, Conor Mayo-Wilson, Chris Pincock, Peter Tan, Lauren Woomer, and audience members at the 2018 Philosophy of Science Association meeting in Seattle. Finally, preemptive thanks to Mark Povich and Verónica Gómez for their comments at my upcoming session at the 2019 Eastern Division meeting of the APA.

References

  1. Baker, A. (2005). Are there genuine mathematical explanations of physical phenomena? Mind, 114, 223–238.CrossRefGoogle Scholar
  2. Baron, S., Colyvan, M., & Ripley, D. (2017). How mathematics can make a difference. Philosophers’ Imprint, 17, 1–19.Google Scholar
  3. Batterman, R., & Rice, C. C. (2014). Minimal model explanations. Philosophy of Science, 81, 349–376.CrossRefGoogle Scholar
  4. Beaney, M., Brenda, H., & Dominic, S. (Eds.). (2018). Aspect perception after Wittgenstein: Seeing-as and novelty. New York: Routledge.Google Scholar
  5. Bennett, K. (2017). Making things up. New York: Oxford University Press.CrossRefGoogle Scholar
  6. Berger, R. (1998). Understanding science: Why causes are not enough. Philosophy of Science, 65, 306–332.CrossRefGoogle Scholar
  7. Berto, F., & Jago, M. (2018). Impossible worlds. In E. N. Zalta (Ed.), The Stanford encyclopedia of philosophy (Fall 2018 edition) (forthcoming). https://plato.stanford.edu/archives/fall2018/entries/impossible-worlds/. Accessed 30 Nov 2018.
  8. Bokulich, A. (2011). How scientific models can explain. Synthese, 180, 33–45.CrossRefGoogle Scholar
  9. Bokulich, A. (2012). Distinguishing explanatory from nonexplanatory fictions. Philosophy of Science, 79, 725–737.CrossRefGoogle Scholar
  10. Bokulich, A. (2016). Fiction as a vehicle for truth: Moving beyond the ontic conception. The Monist, 99, 260–279.CrossRefGoogle Scholar
  11. Bokulich, A. (2018). Representing and explaining: The eikonic conception of scientific explanation. Philosophy of Science.  https://doi.org/10.1086/699693.CrossRefGoogle Scholar
  12. Camp, E. (2008). Showing, telling and seeing: Metaphor and ‘poetic’ language. Baltic International Yearbook of Cognition, Logic and Communication, 3, 1–24.Google Scholar
  13. Camp, E. (Forthcoming). Imaginative frames for scientific inquiry: Metaphors, telling facts and just-so stories. In P. Godfrey-Smith, & A. Levy (Eds.), The scientific imagination. Oxford University Press: New York.Google Scholar
  14. Coliva, A. (2012). Human diagrammatic reasoning and seeing-as. Synthese, 186, 121–148.CrossRefGoogle Scholar
  15. Corfield, D. (2005). Mathematical kinds, or being kind to mathematics. Philosophica, 74, 30–54.Google Scholar
  16. Craver, C. F. (2006). When mechanistic models explain. Synthese, 153, 355–376.CrossRefGoogle Scholar
  17. Craver, C. F. (2014). The ontic account of scientific explanation. In M. I. Kaiser, O. R. Scholz, D. Plenge, & A. Hûttemann (Eds.), Explanation in the special sciences: The case of biology and history. Dordrecht: Springer.Google Scholar
  18. D’Alessandro, W. (2017). Arithmetic, set theory, reduction and explanation. Synthese.  https://doi.org/10.1007/s11229-017-1450-8.CrossRefGoogle Scholar
  19. D’Alessandro, W. (2018). Mathematical explanation beyond explanatory proof. British Journal for the Philosophy of Science.  https://doi.org/10.1093/bjps/axy009.CrossRefGoogle Scholar
  20. Day, W., & Krebs, V. J. (Eds.). (2010). Seeing Wittgenstein Anew: New essays on aspect-seeing. New York: Cambridge University Press.Google Scholar
  21. Detlefsen, M. (1988). Fregean hierarchies and mathematical explanation. International Studies in the Philosophy of Science, 3, 97–116.CrossRefGoogle Scholar
  22. Ellenberg, J. (2014). How not to be wrong: The power of mathematical thinking. New York: Penguin Books.Google Scholar
  23. Entman, R. (2007). Framing bias: Media in the distribution of power. Journal of Communication, 57, 163–173.CrossRefGoogle Scholar
  24. Fine, K. (1995). Ontological dependence. Proceedings of the Aristotelian Society, 95, 269–290.CrossRefGoogle Scholar
  25. Fine, K. (2010). Towards a theory of part. Journal of Philosophy, 107, 559–589.CrossRefGoogle Scholar
  26. Floyd, J. (2010). On being surprised: Wittgenstein on aspect-perception, logic, and mathematics. In W. Day & V. J. Krebs (Eds.), Seeing Wittgenstein Anew: New essays on aspect-seeing. New York: Cambridge University Press.Google Scholar
  27. Giaquinto, M. (2007). Visual thinking in mathematics: An epistemological study. New York: Oxford University Press.CrossRefGoogle Scholar
  28. Gowers, T. (2008). \(\pi\). In T. Gowers, J. Barrow-Green, & I. Leader (Eds.), The Princeton companion to mathematics. Princeton: Princeton University Press.Google Scholar
  29. Gullberg, (1997). Mathematics: From the birth of numbers. New York: Norton.Google Scholar
  30. Hafner, J., & Mancosu, P. (2005). The varieties of mathematical explanation. In P. Mancosu, K. F. Jørgensen, & S. A. Pedersen (Eds.), Visualization, explanation and reasoning styles in mathematics (pp. 215–250). Berlin: Springer.CrossRefGoogle Scholar
  31. Hanna, G. (1990). Some pedagogical aspects of proof. Interchange, 21, 6–13.CrossRefGoogle Scholar
  32. Harari, O. (2008). Proclus’ account of explanatory demonstrations in mathematics and its context. Archiv für Geschichte der Philosophie, 90, 137–164.CrossRefGoogle Scholar
  33. Herald, M. (2010). Situations, frames, and stereotypes: Cognitive barriers on the road to nondiscrimination. Michigan Journal of Gender and Law, 17, 39–55.Google Scholar
  34. Kemp, G., & Mras, G. M. (Eds.). (2016). Wollheim, Wittgenstein, and pictorial representation: Seeing-as and seeing-in. New York: Routledge.Google Scholar
  35. Kim, J. (1994). Explanatory knowledge and metaphysical dependence. Philosophical Issues, 5, 51–69.CrossRefGoogle Scholar
  36. Konvisser, M. W. (1986). Elementary linear algebra with applications. New York: Ardsley House.Google Scholar
  37. Koslicki, K. (2012). Varieties of ontological dependence. In F. Correia & B. Schnieder (Eds.), Metaphysical grounding: Understanding the structure of reality. New York: Cambridge University Press.Google Scholar
  38. Lange, M. (2009). Why proofs by mathematical induction are generally not explanatory. Analysis, 69, 203–211.CrossRefGoogle Scholar
  39. Lange, M. (2014). Aspects of mathematical explanation: Symmetry, unity, and salience. Philosophical Review, 123, 485–531.CrossRefGoogle Scholar
  40. Lange, M. (2015). Explanation, existence and natural properties in mathematics—A case study: Desargues’ theorem. Dialectica, 69, 435–472.CrossRefGoogle Scholar
  41. Lange, M. (2016). Because without cause: Non-causal explanations in science and mathematics. New York: Oxford University Press.CrossRefGoogle Scholar
  42. Lange, M. (2017). Mathematical explanations that are not proofs. Erkenntnis.  https://doi.org/10.1007/s10670-017-9941-z.CrossRefGoogle Scholar
  43. Laptev, B. L., & Rozenfel’d, B. A. (1996). Geometry. In A. N. Kolmogorov & A. P. Yushkevich (Eds.), Mathematics of the 19th century: Geometry, analytic function theory (trans: R. Cooke). Basel: Birkhäuser Verlag.Google Scholar
  44. Lewis, D. (1973). Causation. Journal of Philosophy, 70, 556–567.CrossRefGoogle Scholar
  45. Linnebo, Ø. (2008). Structuralism and the notion of dependence. Philosophical Quarterly, 58, 59–79.Google Scholar
  46. Maddy, P. (2000). Mathematical progress. In E. Grosholz & H. Breger (Eds.), The growth of mathematical knowledge (pp. 341–352). Dordrecht: Kluwer.CrossRefGoogle Scholar
  47. Mancosu, P. (2008). Mathematical explanation: Why it matters. In P. Mancosu (Ed.), The philosophy of mathematical practice (pp. 134–150). New York: Oxford University Press.CrossRefGoogle Scholar
  48. Nolan, D. (2014). Hyperintensional metaphysics. Philosophical Studies, 171, 149–160.CrossRefGoogle Scholar
  49. Pincock, C. (2015). The unsolvability of the quintic: A case study in abstract mathematical explanation. Philosophers’ Imprint, 15, 1–19.Google Scholar
  50. Povich, M. (2016). Minimal models and the generalized ontic conception of scientific explanation. British Journal for the Philosophy of Science, 69, 117–137.CrossRefGoogle Scholar
  51. Resnik, M. (1981). Mathematics as a science of patterns: Ontology and reference. Noûs, 15, 529–550.CrossRefGoogle Scholar
  52. Resnik, M. D., & Kushner, D. (1987). Explanation, independence and realism in mathematics. British Journal for the Philosophy of Science, 38, 141–158.CrossRefGoogle Scholar
  53. Reutlinger, A. (2016). Is there a monist theory of causal and non-causal explanations? The counterfactual theory of scientific explanation. Philosophy of Science, 83, 733–745.CrossRefGoogle Scholar
  54. Reutlinger, A., & Saatsi, J. (Eds.). (2018). Explanation beyond causation: Philosophical perspectives on non-causal explanations. New York: Oxford University Press.Google Scholar
  55. Rice, C. C. (2015). Moving beyond causes: Optimality models and scientific explanation. Noûs, 49, 589–615.CrossRefGoogle Scholar
  56. Ruben, D.-H. (1990). Explaining Explanation. New York: Routledge.Google Scholar
  57. Saatsi, J., & Pexton, M. (2013). Reassessing Woodward’s account of explanation: Regularities, counterfactuals, and noncausal explanations. Philosophy of Science, 80, 613–624.CrossRefGoogle Scholar
  58. Salmon, W. (1984). Scientific explanation: Three basic conceptions. PSA: Proceedings of the Biennial Meeting of the Philosophy of Science Association, 2, 293–305.Google Scholar
  59. Salmon, W. (1989). Four decades of scientific explanation. Pittsburgh: University of Pittsburgh Press.Google Scholar
  60. Sandborg, D. (1998). Mathematical explanation and the theory of why-questions. British Journal for the Philosophy of Science, 49, 603–624.CrossRefGoogle Scholar
  61. Schaffer, J. (2016). Grounding in the image of causation. Philosophical Studies, 173, 49–100.CrossRefGoogle Scholar
  62. Seymour, P. (2016). Hadwiger’s conjecture. In J. Nash & M. Rassias (Eds.), Open problems in mathematics. Berlin: Springer.Google Scholar
  63. Shapiro, S. (1997). Philosophy of mathematics: Structure and ontology. New York: Oxford University Press.Google Scholar
  64. Steiner, M. (1978). Mathematical explanation. Philosophical Studies, 34, 135–151.CrossRefGoogle Scholar
  65. Tappenden, J. (2008). Mathematical concepts: Fruitfulness and naturalness. In P. Mancosu (Ed.), The philosophy of mathematical practice. New York: Oxford University Press.Google Scholar
  66. Tversky, A., & Kahneman, D. (1981). The framing of decisions and the psychology of choice. Science, 211, 453–458.CrossRefGoogle Scholar
  67. Weber, E., & Frans, J. (2017). Is mathematics a domain for philosophers of explanation? Journal for General Philosophy of Science, 48, 125–142.CrossRefGoogle Scholar
  68. Williamson, T. (2007). The Philosophy of Philosophy. Oxford: Blackwell.CrossRefGoogle Scholar
  69. Wittgenstein, L. (2009). Philosophical investigations (trans: Anscombe, G. E. M., Hacker, P. M. S., Schulte, J.) (4th ed.). Wiley: Oxford.Google Scholar
  70. Zelcer, M. (2013). Against mathematical explanation. Journal for General Philosophy of Science, 44, 173–192.CrossRefGoogle Scholar

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© Springer Nature B.V. 2018

Authors and Affiliations

  1. 1.University of Illinois at ChicagoChicagoUSA

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