Erkenntnis

, Volume 81, Issue 5, pp 1073–1091 | Cite as

Are Newtonian Gravitation and Geometrized Newtonian Gravitation Theoretically Equivalent?

Original Article

Abstract

I argue that a criterion of theoretical equivalence due to Glymour (Noûs 11(3):227–251, 1977) does not capture an important sense in which two theories may be equivalent. I then motivate and state an alternative criterion that does capture the sense of equivalence I have in mind. The principal claim of the paper is that relative to this second criterion, the answer to the question posed in the title is “yes”, at least on one natural understanding of Newtonian gravitation.

References

  1. Andréka, H., Madaász, J. X., & Németi, I. (2005). Mutual definability does not imply definitional equivalence, a simple example. Mathematical Logic Quarterly, 51(6), 591–597.CrossRefGoogle Scholar
  2. Andreka, H., & Németi, I. (2014). Definability theory course notes, available at http://www.math-inst.hu/pub/algebraic-logic/DefThNotes0828.pdf. Accessed July 2015.
  3. Barrett, T., & Halvorson, H. (2015a). Glymour and Quine on theoretical equivalence. Journal of Philosophical Logic. doi:10.1007/s10992-015-9382-6.
  4. Barrett, T., & Halvorson, H. (2015b). Morita equivalence, arXiv:1506.04675 [math.LO].
  5. Belot, G. (1998). Understanding electromagnetism. The British Journal for the Philosophy of Science, 49(4), 531–555.CrossRefGoogle Scholar
  6. Borceux, F. (2008). Handbook of Categorical Algebra (Vol. 1). New York: Cambridge University Press.Google Scholar
  7. Cartan, E. (1923). Sur les variétés à connexion affine, et la théorie de la relativité généralisée (première partie). Annales scientifiques de l’École Normale Supérieure, 40, 325–412.Google Scholar
  8. Cartan, E. (1924). Sur les variétés à connexion affine, et la théorie de la relativité généralisée (première partie) (suite). Annales scientifiques de l’École Normale Supérieure, 41, 1–25.Google Scholar
  9. Coffey, K. (2014). Theoretical equivalence as interpretive equivalence. The British Journal for the Philosophy of Science, 65(4), 821–844.CrossRefGoogle Scholar
  10. Craig, W. (1965). Satisfaction for nth order language defined in nth order languages. Journal of Symbolic Logic, 30, 13–25.CrossRefGoogle Scholar
  11. de Bouvere, K. (1965a). Logical synonymity. Indagationes mathematicae, 27, 622–629.CrossRefGoogle Scholar
  12. de Bouvere, K. (1965b). Synonymous theories. In J. W. Addison, L. Henkin, & A. Tarski (Eds.), The theory of models (pp. 402–406). Amsterdam: North-Holland Pub. Co.Google Scholar
  13. DiSalle, R. (2008). Understanding space-time. New York: Cambridge University Press.Google Scholar
  14. Friedrichs, K. O. (1927). Eine invariante Formulierun des Newtonschen Gravitationsgesetzes und der Grenzüberganges vom Einsteinschen zum Newtonschen Gesetz. Mathematische Annalen, 98, 566–575.CrossRefGoogle Scholar
  15. Glymour, C. (1970). Theoretical equivalence and theoretical realism. PSA: Proceedings of the Biennial Meeting of the Philosophy of Science Association, 1970, 275–288.Google Scholar
  16. Glymour, C. (1977). The epistemology of geometry. Noûs, 11(3), 227–251.CrossRefGoogle Scholar
  17. Glymour, C. (1980). Theory and Evidence. Princeton, NJ: Princeton University Press.Google Scholar
  18. Glymour, C. (2013). Theoretical equivalence and the semantic view of theories. Philosophy of Science, 80(2), 286–297.CrossRefGoogle Scholar
  19. Gostanian, R., & Hrbacek, K. (1976). On the failure of the weak Beth property. Proceedings of the American Mathematical Society, 58, 245–249.CrossRefGoogle Scholar
  20. Halvorson, H. (2012). What scientific theories could not be. Philosophy of Science, 79(2), 183–206.CrossRefGoogle Scholar
  21. Halvorson, H. (2013). The semantic view, if plausible, is syntactic. Philosophy of Science, 80(3), 475–478.CrossRefGoogle Scholar
  22. Halvorson, H. (2015). Scientific theories. In Humphreys, P. (Ed.), The Oxford handbook of the philosophy of science. Oxford: Oxford University Press. http://philsci-archive.pitt.edu/11347/.
  23. Hodges, W. (1993). Model theory. New York: Cambridge University Press.CrossRefGoogle Scholar
  24. Knox, E. (2011). Newton-Cartan theory and teleparallel gravity: The force of a formulation. Studies in History and Philosophy of Modern Physics, 42(4), 264–275.CrossRefGoogle Scholar
  25. Knox, E. (2014). Newtonian spacetime structure in light of the equivalence principle. The British Journal for Philosophy of Science, 65(4), 863–880.CrossRefGoogle Scholar
  26. Leinster, T. (2014). Basic category theory. Cambridge: Cambridge University Press.CrossRefGoogle Scholar
  27. Mac Lane, S. (1998). Categories for the working mathematician (2nd ed.). New York: Springer.Google Scholar
  28. Makowsky, J. A., & Shelah, S. (1979). Theorems of Beth and Craig in abstract model theory. I The abstract setting. Transactions of the American Mathematical Society, 256, 215–239.Google Scholar
  29. Malament, D. (1995). Is Newtonian cosmology really inconsistent? Philosophy of Science, 62(4), 489–510.CrossRefGoogle Scholar
  30. Malament, D.B. (2012). Topics in the Foundations of General Relativity and Newtonian Gravitation Theory. Chicago, IL: University of Chicago Press.Google Scholar
  31. Norton, J. (1992). A paradox in Newtonian gravitation theory. PSA: Proceedings of the Biennial Meeting of the Philosophy of Science Association, 1992, 412–420.Google Scholar
  32. Norton, J. (1995). The force of Newtonian cosmology: Acceleration is relative. Philosophy of Science, 62(4), 511–522.CrossRefGoogle Scholar
  33. Poincaré, H. (1905). Science and hypothesis. New York: Walter Scott Publishing Co.Google Scholar
  34. Reichenbach, H. (1958). The philosophy of space and time. New York, NY: Dover Publications.Google Scholar
  35. Saunders, S. (2013). Rethinking Newton’s Principia. Philosophy of Science, 80(1), 22–48.CrossRefGoogle Scholar
  36. Sklar, L. (1977). Space, time, and spacetime. Berkeley: University of California Press.Google Scholar
  37. Sklar, L. (1982). Saving the noumena. Philosophical Topics, 13, 49–72.CrossRefGoogle Scholar
  38. Spirtes, P., & Glymour, C. (1982). Space-time and synonymy. Philosophy of Science, 49(3), 463–477.CrossRefGoogle Scholar
  39. Trautman, A. (1965). Foundations and current problem of general relativity. In S. Deser & K. W. Ford (Eds.), Lectures on general relativity (pp. 1–248). Englewood Cliffs, NJ: Prentice-Hall.Google Scholar
  40. Weatherall, J.O. (2015a). Categories and the foundations of classical field theories. In E. Landry (Ed.), Categories for the working philosopher, arXiv:1505.07084 [physics.hist-ph].
  41. Weatherall, J.O. (2015b). Maxwell-Huygens, Newton-Cartan, and Saunders-Knox spacetimes. Philosophy of Science. arXiv:1501.00148 [physics.hist-ph].
  42. Weatherall, J.O. (2015c). Understanding “gauge”, arXiv:1505.02229 [physics.hist-ph].
  43. Weatherall, J. O., & Manchak, J. B. (2014). The geometry of conventionality. Philosophy of Science, 81(2), 233–247.CrossRefGoogle Scholar
  44. Zaret, D. (1980). A limited conventionalist critique of Newtonian space-time. Philosophy of Science, 47(3), 474–494.CrossRefGoogle Scholar

Copyright information

© Springer Science+Business Media Dordrecht 2015

Authors and Affiliations

  1. 1.Department of Logic and Philosophy of ScienceUniversity of CaliforniaIrvineUSA

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