Comparing Relativistic and Newtonian Dynamics in First-Order Logic

  • Judit X. Madarász
  • Gergely Székely
Part of the Veröffentlichungen des Instituts Wiener Kreis book series (WIENER KREIS, volume 16)


In this paper we introduce and compare Newtonian and relativistic dynamics as two theories of first-order logic (FOL). To illustrate the similarities between Newtonian and relativistic dynamics, we axiomatize them such that they differ in one axiom only. This one axiom difference, however, leads to radical differences in the predictions of the two theories. One of their major differences manifests itself in the relation between relativistic and rest masses, see Thms. 5 and 6.


  1. [1]
    H. Andréka, P. Burmeister, and I. Németi. Quasivarieties of partial algebras — a unifying approach towards a two-valued model theory for partial algebras. Studia Sci. Math. Hungar. 16, 1981, pp. 325–372.Google Scholar
  2. [2]
    H. Andréka, J. X. Madarász, and I. Németi. “Logical analysis of special relativity theory,” in: J. Gerbrandy, M. Marx, M. de Rijke, and Y. Venema (Eds.), Essays dedicated to Johan van Benthem on the occasion of his 50th birthday. Vossiuspers, Ams-terdam University Press, 1999. CD-ROM, ISBN: 90 5629 104 1, Scholar
  3. [3]
    H. Andréka, J. X. Madarász, and I. Németi. “Logical axiomatizations of space-time. Samples from the literature,” in: Non-Euclidean geometries, volume 581 of Mathematics and Its Applications. New York: Springer, 2006, pp. 155–185.CrossRefGoogle Scholar
  4. [4]
    H. Andréka, J. X. Madarász, and I. Németi, “Logic of space-time and relativity theory,” in: M. Aiello, I. Pratt-Hartmann and J. van Benthem (Eds.), Handbook of Spatial Logics. Dordrecht: Springer, 2007, pp. 607–711.CrossRefGoogle Scholar
  5. [5]
    H. Andréka, J. X. Madarász, and I. Németi, “On the logical structure of relativity theories.” Research report, Alfréd Rényi Institute of Mathematics, Budapest, 2002. With contributions from A. Andai, G. Sági, I. Sain and Cs. Tőke. 1312 pp.Google Scholar
  6. [6]
    H. Andréka, J. X. Madarász, I. Németi, and G. Székely, “Axiomatizing relativistic dynamics without conservation postulates,” in: Studia Logica 89, 2, 2008, pp. 163–186.CrossRefGoogle Scholar
  7. [7]
    J. Ax, “The elementary foundations of spacetime,” in: Foundations of Physics 8, 7–8, 1978, pp. 507–546.CrossRefGoogle Scholar
  8. [8]
    S. A. Basri, A Deductive Theory of Space and Time. Amsterdam: North-Holland 1966.Google Scholar
  9. [9]
    T. Benda, “A Formal Construction of the Spacetime Manifold,” in: Journal of Philosophical Logic 37, 5, 2008, pp. 441–478.CrossRefGoogle Scholar
  10. [10]
    C. C. Chang and H. J. Keisler, Model theory. Amsterdam: North-Holland 1973, 1977, 1990.Google Scholar
  11. [11]
    H. D. Ebbinghaus, J. Flum and W. Thomas, Mathematical logic. New York: Springer-Verlag 1994.Google Scholar
  12. [12]
    R. Goldblatt, Orthogonality and spacetime geometry. New York: Springer-Verlag 1987.Google Scholar
  13. [13]
    J. X. Madarász. Logic and Relativity (in the light of definability theory). PhD thesis, Eötvös Loránd Univ., Budapest, 2002.Google Scholar
  14. [14]
    J. X. Madarász, I. Németi, and G. Székely, “Twin paradox and the logical foundation of relativity theory,” in: Foundations of Physics 36, 5, 2006, pp. 681–714.CrossRefGoogle Scholar
  15. [15]
    J. X. Madarász, I. Németi, and G. Székely, “First-order logic foundation of relativity theories,” D. Gabbay, S. Goncharov and M. Zakharyaschev (Eds.), in: Mathematical problems from applied logic II. New York: Springer, 2007, pp. 217–252.CrossRefGoogle Scholar
  16. [16]
    J. X. Madarász, I. Németi, and Cs. Tőke. On generalizing the logic-approach to space-time towards general relativity: first steps. in: V. F. Hendricks, F. Neuhaus, S. A Pedersen, U. Scheffler and H. Wansing (Eds.), First-Order Logic Revisited, Logos Verlag, Berlin, 2004, pp. 225–268.Google Scholar
  17. [17]
    V. Pambuccian, “Alexandrov-Zeeman type theorems expressed in terms of definability,” in: Aequationes Mathematicae 74, 3, 2007, pp. 249–261.CrossRefGoogle Scholar
  18. [18]
    G. Székely, First-Order Logic Investigation of Relativity Theory with an Emphasis on Accelerated Observers. PhD thesis, Eötvös Loránd Univ., Budapest, 2009.Google Scholar
  19. [19]
    J. Vaänänen, “Second-order logic and foundations of mathematics,” in: Bulletin of Symbolic Logic 7, 4, 2001, pp. 504–520.CrossRefGoogle Scholar
  20. [20]
    J. Woleński “First-order logic: (philosophical) pro and contra,” in: V. F. Hendricks, F. Neuhaus, S. A. Pedersen, U. Scheffler and H. Wansing (Eds.), First-Order Logic Revisited. Berlin: Logos Verlag 2004, pp. 369–398.Google Scholar

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Authors and Affiliations

  • Judit X. Madarász
  • Gergely Székely

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