Advertisement

Mathematics As Objective Knowledge And As Human Practice

  • Eduard Glas
Chapter
Part of the Logic, Epistemology, and the Unity of Science book series (LEUS, volume 5)

Abstract

Popper’s world-3 doctrine is invoked to argue that characterizing mathematical developments as social processes is not incompatible with insisting on the objectivity and partial autonomy of mathematical knowledge. The argument is illustrated and supported by a historical case-study of the interplay between social and conceptual change in and after the French Revolution.

Keywords

Mathematics Popper world-3 objectivity autonomy revolution social and conceptual change 

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. Boyer, C. B., 1968, A History of Mathematics (New York: Wiley)Google Scholar
  2. Bradley, M., 1975, ‘Scientific Education versus Military Training: The Influence of Napoleon Bonaparte on the Ecole Polytechnique’, Annals of Science 32, 415-449.CrossRefGoogle Scholar
  3. Carnot, L. N. M., 1783, Essai sur les machines en général (Dijon: no publisher)Google Scholar
  4. Dhombres, J. & Dhombres, N., 1989, Naissance d’un nouveau pouvoir: sciences et savants en France 1793-1824, (Paris: Payot) Google Scholar
  5. Ferraro, G., 2001, ‘Analytical Symbols and Geometrical Figures in Eighteenth-Century Calculus’, Studies in History and Philosophy of Science 32, 535-555CrossRefGoogle Scholar
  6. Gillispie, C. C., 1971, Lazare Carnot Savant (Princeton: Princeton University Press)Google Scholar
  7. Glas, E., 1986, ‘On the Dynamics of Mathematical Change in the Case of Monge and the French Revolution’, Studies in History and Philosophy of Science 17, 249-268CrossRefGoogle Scholar
  8. Glas, E., 2001, ‘The Popperian Programme and Mathematics’, Studies in History and Philosophy of Science 32, 119-137, 355-376CrossRefGoogle Scholar
  9. Glas,E., 2002, ‘Socially Conditioned Mathematical Change: The Case of the French Revolution’, Studies in History and Philosophy of Science 33, 709-728CrossRefGoogle Scholar
  10. Grattan-Guinness, I., 1993, ‘The ingénieur-savant, 1800-1830: A Neglected Figure in the History of French Mathematics and Science’, Science in Context 6, 405-433CrossRefGoogle Scholar
  11. Lagrange, J. L., 1811, Mécanique analytique, nouvelle édition, orig. 1788 (Paris: Courcier)Google Scholar
  12. Lakatos, I., 1976, Proofs and Refutations: The Logic of Mathematical Discovery, ed. J. Worrall and G. Currie (Cambridge: Cambridge University Press)Google Scholar
  13. Lakatos, I., 1978, The Methodology of Scientific Research Programmes (Philosophical Papers Vol.1), ed. J. Worrall and G. Currie (Cambridge: Cambridge University Press)Google Scholar
  14. Monge, G., 1811, Géométrie descriptive, nouvelle édition, orig. 1799 (Paris: Klostermann)Google Scholar
  15. Niiniluoto, I., 1992, ‘Reality, Truth, and Confirmation in Mathematics – Reflections on the Quasi-Empiricist Programme’, pp. 60-77 in Echeverria, J., Ibarra, A. and Mormann, T. (eds.), The Space of Mathematics (Berlin, New York: De Gruyter)Google Scholar
  16. O’Hear, A., 1980, Karl Popper (London: Routledge & Kegan Paul)Google Scholar
  17. Popper, K. R., 1969, Conjectures and Refutations: The Growth of Scientific Knowledge, third edition (London: Routledge)Google Scholar
  18. Popper, K.R., 1972, The Logic of Scientific Discovery, sixth edition (London: Hutchinson)Google Scholar
  19. Popper, K. R., 1981, Objective Knowledge: An Evolutionary Approach, revised edition (Oxford: Clarendon)Google Scholar
  20. Popper, K. R., 1983, Realism and the Aim of Science, ed. W. W. Bartley (Totowa: Rowen and Littlefield)Google Scholar
  21. Popper, K. R., 1984, Auf der Suche nach einer besseren Welt (München: Piper)Google Scholar

Copyright information

© Springer 2007

Authors and Affiliations

  • Eduard Glas
    • 1
  1. 1.Delft University of TechnologyThe Netherlands

Personalised recommendations