Should Christians be Structural Realists? *

1. Should Christians be Structural Realists?* Christian Perspectives in Science Seminar Calvin College, October 3 2008 Elise Crull History and Philosophy of Science University of Notre Dame *A work in progress. Portions of this talk concerning SR and Poincaré have been adapted from collaborative work with Dr. Katherine Brading (Philosophy Department, Univ. Notre Dame)

2. Overview Sketching the Terrain • What is structural realism (SR)? • Common objections Incorporating Faith • Motivations for SR from Christianity • Objections to SR overcome by faith? Poincaré’s Structuralism • What it looks like • What it might mean for faith-based SR Conclusions

3. Sketching the Terrain • Worrall (1989): “Structural Realism: The Best of Both Worlds?” • No Miracles argument (realism) • Pessimistic Meta-induction (anti-realism) • Case Study: Fresnel to Maxwell

4. Sketching the Terrain • Worrall (1989): “There was an important element of continuity in the shift from Fresnel to Maxwell—and this was much more than a simple question of carrying over the successful empirical content into the new theory. At the same time it was rather less than a carrying over of the full theoretical content or full theoretical mechanisms (even in “approximate” form) … There was continuity or accumulation in the shift, but the continuity is one of form or structure, not of content.” (117)

5. Sketching the Terrain Structural Realism (SR): • Science aims to give an accurate representation of the structure of the world • We’ve good reason to believe science is successful with respect to this aim Ontic Structural Realism (OSR): (iii) this structure is all there is Epistemic Structural Realism (ESR): (iii) this structure is all we can know

6. Sketching the Terrain Structural Realism (SR): • Science aims to give an accurate representation of the structure of the world • We’ve good reason to believe science is successful with respect to this aim Structural Empiricism: • Science aims to give an empirically adequate representation of the structure of the world • Acceptance of this representation of the structure of the world commits one only to belief in the empirical adequacy of the structure

7. Sketching the Terrain Structural Realism: • Science aims to give an accurate representation of the structure of the world • We’ve good reason to believe science is successful with respect to this aim Structural Empiricism: • Science aims to give an empirically adequate representation of the structure of the world • Acceptance of this representation of the structure of the world commits one only to belief in the empirical adequacy of the structure Structural Idealism: • Science aims to give accurate representation of the structure of the world as we experience it • We’ve good reason to believe science is successful with respect to this aim

8. Objections to Structural Realism • “Structure all the way down” • Ambiguity of term structure • Mathematical structure not always continuous/ trivially continuous (Chakravartty) • Form/content distinction not principled (Psillos) • Realist enough ? • Historically contingent on badly done history • From logic: non-categoricity corollary of Gödel’s 1st incompleteness theorem (Howard)

9. The Scientific Process à la Poincaré “principles” scientific facts (data) 1st structural moment: interpolation 2nd structural moment: equations/laws brute facts eqn X :: eqn Y • inaccessible • brute fact + • language • Reveals intra-theoretic relations • Involves generalization • (drawing lines) • Involves idealism • Contains elements of convention • Enunciates intra-theoretic relations • Involves generalization • (eqns to laws) • Involves idealism • Based on conventions • Reveals inter-theoretic relations • Involves generalization • (some eqns to principles) • Involves idealism • Based on conventions

10. References/Suggestions for Further Reading Chakravarrty, A. (1998), “Semirealism”, Studies in History and Philosophy of Science, Vol. 29, No. 3, pp. 391-408. Chakravartty, A. (2003), "The Structuralist Conception of Objects", Philosophy of Science, Vol.70, No. 5 pp. 867-878. Folina, J. (1992), Poincaré and the Philosophy of Mathematics. New York: St. Martin’s Press. French, S. (1999), “Models and mathematics in physics: the role of group theory”, in J. Butterfield and C. Pagonis (eds.), From Physics to Philosophy. Cambridge: Cambridge University Press, pp. 187-207. French, S. (2006), “Structure as a Weapon of the Realist”, Proceedings of the Aristotelian Society, Vol. 106, No. 1, pp. 170-187. Ladyman, J. (1998), “What is Structural Realism?”, Studies in the History and Philosophy of Science, Vol. 29, No. 3, pp. 409-424. Poincaré, H. (1902), Science and Hypothesis. Repr. New York: Dover, 1952. Poincaré, H. (1905), The Value of Science. Repr. New York: Dover, 1958.

11. References/Suggestions for Further Reading Poincaré, H. (1913), Last Essays. Repr. New York: Dover, 1963. Psillo, S. (1995), “Is Structural Realism the Best of Both Worlds?”, Dialectica, Vol. 49, No. 1, pp. 15-46. Saatsi, J. (2005), “Reconsidering the Fresnel-Maxwell theory shift: how the realist can have her cake and EAT it too”, Studies in History and Philosophy of Science, Vol. 36, pp. 509-538. Torretti, R. (1984), Philosophy of Geometry from Riemann to Poincaré, 2nd ed. Dordrecht: Reidel. van Fraassen, B. (1980), The Scientific Image. Oxford: Oxford University Press. van Fraassen, B. (2006), “Structure: Its Shadow and Substance”, British Journal for the Philosophy of Science, Vol. 57, pp. 275-307. Worrall, J. (1989), “Structural Realism: the Best of Both Worlds?”, Dialectica, Vol. 43, pp. 99-124. Worrall, J. (1994) “How to remain ‘reasonably’ optimistic: scientific realism and the ‘luminiferous ether”, Philosophy of Science Association, pp. 334-342.