, Volume 190, Issue 6, pp 1039–1058 | Cite as

Theory change as dimensional change: conceptual spaces applied to the dynamics of empirical theories

  • Peter Gärdenfors
  • Frank Zenker


This paper offers a novel way of reconstructing conceptual change in empirical theories. Changes occur in terms of the structure of the dimensions—that is to say, the conceptual spaces—underlying the conceptual framework within which a given theory is formulated. Five types of changes are identified: (1) addition or deletion of special laws, (2) change in scale or metric, (3) change in the importance of dimensions, (4) change in the separability of dimensions, and (5) addition or deletion of dimensions. Given this classification, the conceptual development of empirical theories becomes more gradual and rationalizable. Only the most extreme type—replacement of dimensions—comes close to a revolution. The five types are exemplified and applied in a case study on the development within physics from the original Newtonian mechanics to special relativity theory.


Conceptual spaces Dimensional analysis Incommensurability Newtonian mechanics Scientific revolution Special relativity theory Theory change 


Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.


  1. Andersen H., Barker P., Chen X. (2006) The cognitive structure of scientific revolutions. Cambridge University Press, Cambridge, UKCrossRefGoogle Scholar
  2. Balzer W., Moulines C. U., Sneed J. D. (1987) An architectonic for science: The structuralist program. Reidel, DordrechtCrossRefGoogle Scholar
  3. Balzer, W., Moulines, C. U., Sneed, J. D. (eds) (2000) Structuralist knowledge representation: Paradigmatic examples. Rodopi, AmsterdamGoogle Scholar
  4. Balzer W., Pearce D. A., Schmidt H.-J. (1984) Reduction in science: Structure, examples, philosophical problems. Reidel, DordrechtGoogle Scholar
  5. Barker P. (2012) The cognitive structure of scientific revolutions. Erkenntnis 75(3): 445–465CrossRefGoogle Scholar
  6. Blaug M. (1975) Kuhn versus Lakatos, or paradigms versus research programmes in the history of economics. History of Political Economy 7(4): 399–433CrossRefGoogle Scholar
  7. Bridgman P. (1922) Dimensional analysis. Yale University Press, YaleGoogle Scholar
  8. Chandler P. (1975) Clairaut’s critique of Newtonian attraction: Some insights into his philosophy of science. Annals of Science 32: 369–378CrossRefGoogle Scholar
  9. Chang H. (2004) Inventing temperature: Measurement and scientific progress. Oxford University Press, New YorkCrossRefGoogle Scholar
  10. Clarke B. (2002) From thermodynamics to virtuality. In: Clarke B., Hernderson L. D. (eds) From energy to information: Representation in science and technology, art and literature. Stanford University Press, Stanford, CA, pp 17–33Google Scholar
  11. Coopersmith J. (2010) Energy, the subtle concept: The discovery of Feynman’s blocks from Leibniz to Einstein. Oxford University Press, OxfordGoogle Scholar
  12. Coulson J. M., Richardson J. F., Backhurst J. R., Harker J. H. (2007) Chemical engineering. Elsevier, Burlington, MAGoogle Scholar
  13. Czyz J. (1994) Paradoxes of measures and dimensions originating in Felix Hausdorffs’s ideas. World Scientific, River Edge, NJCrossRefGoogle Scholar
  14. Falkenburg B. (2007) Particle metaphysics: A critical account of subatomic reality. Springer, BerlinGoogle Scholar
  15. Fleck, L. (1935/1979). Genesis and development of a scientific fact. T. Trenn & R. Merton (Eds.). Chicago: University of Chicago Press.Google Scholar
  16. Gärdenfors P. (2000) Conceptual spaces: The geometry of thought. The MIT Press, Cambridge, MAGoogle Scholar
  17. Gärdenfors P., Zenker F. (2011) Using conceptual spaces to model the dynamics of empirical theories. In: Olsson E. J., Enqvist S. (eds) Belief revision meets philosophy of science. Springer, Berlin, pp 137–153Google Scholar
  18. Gähde U. (2002) Holism, underdetermination, and the dynamics of empirical theories. Synthese 130: 69–90CrossRefGoogle Scholar
  19. Harman P. M. (1982) Energy, force, and matter: The conceptual development of nineteenth-century physics. Cambridge University Press, Cambridge, UKCrossRefGoogle Scholar
  20. Hausdorff F. (1903) Das Raumproblem. Annalen der Naturphilosophie 3: 1–23Google Scholar
  21. Hickman F. R. (1984) Electrodynamical origins of Einstein’s theory of general relativity. International Journal of Theoretical Physics 23: 535–566CrossRefGoogle Scholar
  22. Hoyningen-Huene P. (1993) Reconstructing scientific revolutions: The philosophy of science of Thomas S. Kuhn. University of Chicago Press, ChicagoGoogle Scholar
  23. Huntley H. E. (1952) Dimensional analysis. McDonald, LondonGoogle Scholar
  24. Jammer M. (1957) Concepts of force: A study in the foundations of dynamics. Harvard University Press, Cambridge, MAGoogle Scholar
  25. Joule, J. P. (1849/1887). On the mechanical equivalent of heat. Reprinted in The Scientific Papers of James Prescott Joule (pp. 298–328). London: Dawsons of Pall Mall.Google Scholar
  26. Krantz, D. H., Luce, R. D., Suppes, P., & Tversky, A. (1971, 1989, 1990). Foundations of measurement (Vol. I–III). New York: Academic Press.Google Scholar
  27. Kuhn T. S. (1961) The function of measurement in modern physical science. Isis 52: 161–193CrossRefGoogle Scholar
  28. Kuhn, T. S. (1962/1970). The structure of scientific revolutions. Chicago: University of Chicago Press.Google Scholar
  29. Kuhn T. S. (1976) Theory-change as structure-change: Comments on the Sneed formalism. Erkenntnis 10: 179–199CrossRefGoogle Scholar
  30. Kuhn T. S. (1977) The essential tension: Selected studies in scientific tradition and change. University of Chicago Press, ChicagoGoogle Scholar
  31. Kuhn, T. S. (1987). What are scientific revolutions? In L. Krüger, L. Daston, & M. Heidelberger (Eds.), The probabilistic revolution (pp. 7–22). Cambridge, UK: Cambridge University Press.Google Scholar
  32. Kuhn, T. S. (2000). The Road since Structure: Philosophical Essays, 1970–1993, with an Autobiographical Interview. In J. Conant & J. Haugeland (Eds.). Chicago: University of Chicago Press.Google Scholar
  33. Kyburg H. E. (1984) Theory and measurement. Cambridge University Press, Cambridge, UKGoogle Scholar
  34. Lakatos I. (1978) The methodology of scientific research programs. Cambridge University Press, Cambridge, UKCrossRefGoogle Scholar
  35. Larvor B. (2003) Why did Kuhn’s Structure of Scientific Revolutions cause a fuss?. Studies in the History and Philosophy of Science 34: 369–390CrossRefGoogle Scholar
  36. Lindsay R. B. (1971) The concept of energy and its early historical development. Foundations of Physics 1: 383–393CrossRefGoogle Scholar
  37. Lorentz H. (1899) Simplified theory of electrical and optical phenomena in moving systems. Proceedings Academy of Science, Amsterdam I: 427–443Google Scholar
  38. Losee J. (2004) Theories of scientific progress: An Introduction. Routledge, New York, NYCrossRefGoogle Scholar
  39. Maddox W. T. (1992) Perceptual and decisional separability. In: Ashby G. F. (eds) Multidimensional models of perception and cognition. Lawrence Erlbaum, Hillsdale, NJ, pp 147–180Google Scholar
  40. McMullin E. (2002) The origins of the field concept in physics. Physics in Perspective 4: 13–39CrossRefGoogle Scholar
  41. Melera R. D. (1992) The concept of perceptual similarity: From psychophysics to cognitive psychology. In: Algom D. (eds) Psychophysical approaches to cognition. Elsevier, Amsterdam, pp 303–388CrossRefGoogle Scholar
  42. Moulines C. U. (2002) Introduction: Structuralism as a program for modeling theoretical science. Synthese 130: 1–11CrossRefGoogle Scholar
  43. Navarro J. (2005) J. J. Thomson on the nature of matter: Corpuscles and the continuum. Centaurus 47: 259–282CrossRefGoogle Scholar
  44. Oberheim, E., & Hoyningen-Huene, P. (2009). The incommensurability of scientific theories. In E.N. Zalta (Ed.), The Stanford encyclopedia of philosophy. Accessed 24 December 2011.
  45. Okun L. B. (1989) The concept of mass. Physics Today 42(6): 31–36CrossRefGoogle Scholar
  46. Palmer A. C. (2008) Dimensional analysis and intelligent experimentation. World Scientific Publishing, Hackensack, NJCrossRefGoogle Scholar
  47. Poincaré H. (1897) Science and method (F. Maitland, Trans.). Thomas Nelson and Sons, LondonGoogle Scholar
  48. Rayleigh L. (1915) The principle of similitude. Nature 95: 66–68CrossRefGoogle Scholar
  49. Rehg W. (2009) Cogent science in context: The science wars, argumentation theory and Habermas. The MIT Press, Cambridge, MAGoogle Scholar
  50. Rivadulla A. (2004) The Newtonian limit of relativity theory and the rationality of theory change. Synthese 141: 417–429CrossRefGoogle Scholar
  51. Roche J. (1998) The mathematics of measurement: A critical history. The Athlone Press, LondonGoogle Scholar
  52. Roseveare N. T. (1982) Mercury’s perihelion from LeVerrier to Einstein. Clarendon Press, OxfordGoogle Scholar
  53. Schofield R. E. (1964) Joseph Priestley, the theory of oxidation and the nature of matter. Journal of the History of Ideas 25: 285–294CrossRefGoogle Scholar
  54. Sneed J. D. (1971) The logical structure of mathematical physics. Reidel, DordrechtCrossRefGoogle Scholar
  55. Soler L., Sankey H., Hoyningen-Huene P. (2009) Rethinking scientific change and theory comparison: Stabilities, ruptures, incommensurabilities? (Boston studies in the philosophy of science, vol. 255). Springer, BerlinGoogle Scholar
  56. Stegmüller W. (1976) The structuralist view of theories. Springer, BerlinGoogle Scholar
  57. Stevens S. S. (1946) On the theory of scales of measurement. Science 103: 677–680CrossRefGoogle Scholar
  58. Sibum H. O. (1995) Reworking the mechanical value of heat: Instruments of precision and gestures of accuracy in early Victorian England. Studies in History and Philosophy of Science 26: 73–106CrossRefGoogle Scholar
  59. Suppes P. (2002) Representation and invariance of scientific structures. CSLI Publications, Stanford, CAGoogle Scholar
  60. Thomson J. J. (1881) On the electric and magnetic effects produced by the motion of electrified bodies. Philosophical Magazine 11: 229–249CrossRefGoogle Scholar
  61. Thomson J. J. (1897) Cathode rays. Philosophical Magazine 44: 293–316CrossRefGoogle Scholar
  62. Thomson J. J. (1899) On the masses of the ions in gases at low pressures. Philosophical Magazine 48: 547–567CrossRefGoogle Scholar
  63. Zenker F. (2009) Ceteris paribus in conservative belief revision. On the role of minimal change in rational theory development. Peter Lang, BerlinGoogle Scholar
  64. Zenker, F. (forthcoming). From features via frames to spaces: Modeling scientific conceptual change without incommensurability or aprioricity. In T. Gamerschlag, D. Gerland, R. Osswald, & W. Petersen (Eds.), Proceedings of CTF09, Duesseldorf, June 2009.Google Scholar

Copyright information

© Springer Science+Business Media B.V. 2012

Authors and Affiliations

  1. 1.Department of PhilosophyLund UniversityLundSweden

Personalised recommendations