Foundations of Physics

, Volume 39, Issue 4, pp 397–406 | Cite as

Some Comments on “The Mathematical Universe”

Article

Abstract

I discuss some problems related to extreme mathematical realism, focusing on a recently proposed “shut-up-and-calculate” approach to physics (Tegmark in Found. Phys. 38:101, 2008; New Sci., September 15th, 2007). I offer arguments for a moderate alternative, the essence of which lies in the acceptance that mathematics is (at least in part) a human construction, and discuss concrete consequences of this—at first sight purely philosophical—difference in point of view.

Keywords

Philosophy of science Mathematical realism Theory of everything 

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. 1.
    Tegmark, M.: The mathematical universe. Found. Phys. 38, 101 (2008). arXiv:0704.0646 [gr-qc] MATHCrossRefADSMathSciNetGoogle Scholar
  2. 2.
    Tegmark, M., Reality by numbers. New Sci., September 15th, 2007. See also: Tegmark, M.: Shut up and calculate. arXiv:0709.4024 [physics.pop-ph]
  3. 3.
    French, S., Ladyman, J.: Remodelling structural realism: quantum physics and the metaphysics of structure. Synthese 136(1), 31–56 (2003) MATHCrossRefMathSciNetGoogle Scholar
  4. 4.
    Cao, T.: Can we dissolve physical entities into mathematical structure? Synthese 136(1), 57–71 (2003) MATHCrossRefGoogle Scholar
  5. 5.
    Saunders, S.: Structural realism, again. Synthese 136(1), 127–133 (2003) MATHCrossRefMathSciNetGoogle Scholar
  6. 6.
    Weinberg, S.: Dreams of a Final Theory. Pantheon, New York (1992) Google Scholar
  7. 7.
    Zinkernagel, H.: High-energy physics and reality—some philosophical aspects of a science. PhD thesis, Copenhagen (1998) Google Scholar
  8. 8.
    Wigner, E.: The unreasonable effectiveness of mathematics in the natural sciences. Commun. Pure Appl. Math. 13, I (1960) CrossRefGoogle Scholar
  9. 9.
    Husserl, E.: Die Krisis der europäischen Wissenschaften und die transzendentale Phänomenologie: Eine Einleitung in die phänomenologische Philosophie. Philosophia (Belgrad) 1, 77–176 (1936) Google Scholar
  10. 10.
    Merleau-Ponty, M.: Phénoménologie de la Perception. Gallimard, Paris (1945) Google Scholar
  11. 11.
    Heidegger, M.: Vom Wesen der Wahrheit (1930). In: Wegmarken, Gesamtausgabe, vol. 9. Klostermann, Frankfurt am Main (1967) Google Scholar
  12. 12.
    Wittgenstein, L.: On Certainty. Blackwell, Oxford (1979). Edited by G.E.M. Anscombe and G.H. von Wright, translated by Denis Paul and G.E.M. Anscombe Google Scholar
  13. 13.
    Popper, K.: Quantum Theory and the Schism in Physics. Unwin Hyman, London (1982) Google Scholar
  14. 14.
    Bernal, A.N., Sanchez, M., Soler Gil, F.J.: Physics from scratch. Letter on M. Tegmark’s “The Mathematical Universe”. arXiv:0803.0944 [gr-qc]
  15. 15.
    Dehaene, S.: The Number Sense. Oxford University Press, Oxford (1997) MATHGoogle Scholar
  16. 16.
    Pepperberg, I.M., Gordon, J.D.: Number comprehension by a Grey Parrot (Psittacus erithacus), including a zero-like concept. J. Comp. Psychol. 119(2), 197–209 (2005) CrossRefGoogle Scholar
  17. 17.
    Balaguer, M.: Platonism and Anti-Platonism in Mathematics. Oxford University Press, Oxford (1998) MATHGoogle Scholar
  18. 18.
    Russell, B.: On denoting. Mind 14, 479–493 (1905) CrossRefGoogle Scholar
  19. 19.
    Biermann, K.R.: Kronecker, Leopold. In: Gillispie, C.C. (ed.) Dictionary of Scientific Biography. Scribner, New York (1981) Google Scholar
  20. 20.
    Tait, W.: The Provenance of Pure Reason: Essays in the Philosophy of Mathematics and Its History. Oxford University Press, Oxford (2005) MATHGoogle Scholar
  21. 21.
    Quine, W.V.O.: Two Dogmas of Empiricism. Philos. Rev. 60, 20–43 (1951) CrossRefGoogle Scholar
  22. 22.
    Esfeld, M., Lam, V.: Moderate structural realism about space-time. Synthese 160, 27–46 (2008) CrossRefMathSciNetGoogle Scholar
  23. 23.
    Anderson, P.W.: More is different. Sci. New Ser. 177(4047), 393 (1972) Google Scholar
  24. 24.
    Barcelo, C., Liberati, S., Visser, M.: Analogue gravity. Living Rev. Rel. 8, 12 (2005). arXiv:gr-qc/0505065 Google Scholar
  25. 25.
    Volovik, G.E.: The Universe in a Helium Droplet. Clarendon Press, Oxford (2003) MATHGoogle Scholar
  26. 26.
    Einstein, A.: Address to the Prussian Academy of Sciences, Berlin (1921) Cited in: Shapiro, F.R., Epstein, J. The Yale Book of Quotations. Yale University Press, New Haven (2006) Google Scholar

Copyright information

© Springer Science+Business Media, LLC 2009

Authors and Affiliations

  1. 1.Instituto de Astrofísica de AndalucíaCSICGranadaSpain
  2. 2.Instituto de Estructura de la MateriaCSICMadridSpain

Personalised recommendations