Skip to main content
Log in

Cauchy and the continuum

The significance of non-standard analysis for the history and philosophy of mathematics

  • Article
  • Published:
The Mathematical Intelligencer Aims and scope Submit manuscript

This is a preview of subscription content, log in via an institution to check access.

Access this article

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

References

  • Abel, N. H. [1826a]: ’Untersuchungen über die Reihe 1 +m/1x +m·m − 1/1 ·2x 2 + ...,Journal für die Reine und Angewandte Mathematik, 1, pp. 311–339.

    Article  MATH  Google Scholar 

  • Agassi, J. [1963]: Towards an Historiography of Science, Wesleyan University Press.

  • Baumann, J. J. [1869]:Die Lehren von Zeit, Raum und Mathematik, volume 2. Berlin: G. Reiner.

    Google Scholar 

  • Beck, L. J. [1952]:The Method of Descartes: A Study of the Regulae. Oxford: Clarendon Press.

    MATH  Google Scholar 

  • Bell, E. T. [1937]:Men of Mathematics. London: Victor Gollancz.

    MATH  Google Scholar 

  • Bell, E. T. [1940]:The Development of Mathematics. New York: McGraw-Hill.

    Google Scholar 

  • Bourbaki, N. [1940b]:Topologie Générale. Paris: Hermann.

    MATH  Google Scholar 

  • Bourbaki, N. [1960]:Eléments ďHistoire des Mathématiques. Paris: Hermann.

    Google Scholar 

  • Bover, C.B. [1949]:The Concepts of the Calculus. New York: Columbia University Press.

    Google Scholar 

  • Cajori, F. [1919]:A History of Mathematics. 2nd edition. New York and London: Macmillan, 1961.

    Google Scholar 

  • Cauchy, A. L. [1821]:Cours ďAnalyse de ľEcole Royale Polytechnique. Paris: de Bure.

    Google Scholar 

  • Cauchy, A. L. [1823]:Résumé des leçons sur le calcul Infinitésimal. Paris: de Bure. InOeuvres Complètes, Séries 2, volume 4, pp. 5–261.

    Google Scholar 

  • Cauchy, A. L. [1853]: ’Note sur les séries convergentes dont les Divers Terms sont des Functions Continues ďune Variable Réelle ou Imaginaire entre des Limites Données’,Comptes Rendus des Séances des ľAcadémie des Sciences, 36, pp. 454–459.

    Google Scholar 

  • Chwistek,L. [1948]:The Limits of Science. London: Kegan Paul.

    Google Scholar 

  • Dirichlet, P. L. [1829]:’Sur la Convergence des Séries Trigonométriques que Servent à Représenter une Function Arbitraire entre des Limites Données’,Journal für die Reine und Angewandte Mathematik, 4, pp. 157–169.

    Article  MATH  Google Scholar 

  • Duhem, P. [1906] :La Théorie Physique; son Objet, sa Structure, English translation of the second (1914) edition:The Aim and Structure of Physical Theory. Princeton University Press, 1954.

  • Fourier, J. [1822]:Théorie analytique de la Chaleur. Translated into English asThe Analytical Theory of Heat. New York: Dover.

    Google Scholar 

  • Frayne, T., Morel, A. C. and Scott, D. S. [1962–3]: ’Reduced Direct Products’,Fundamenta Mathematica, 51, pp. 195–228.

    MathSciNet  Google Scholar 

  • Grattan-Guinness, I. and Ravetz, J. R. [1972]:Joseph Fourier, 1768–1830. Cambridge, Mass.: M.I.T. Press.

    MATH  Google Scholar 

  • Hardy, G. H. [1918]: ’Sir George Stokes and the Concept of Uniform Convergence’,Proceedings of the Cambridge Philosophical Society, 18/19, pp. 148–156.

    Google Scholar 

  • Houel, J. [1878]:Calcul Infinitesimal, volume 1. Paris.

  • Klein, F. [1908]:Elementary Mathematics from an Advanced Standpoint. New York: Dover.

    Google Scholar 

  • Kreisel, G. [1956–7]: ’Some Uses of Metamathematics’,British Journal for the Philosophy of Science, 7, pp. 161–173.

    Article  Google Scholar 

  • Kreisel, G. and Krivine, J. L. [1967]:Elements of Mathematical Logic. Amsterdam: North Holland.

    Book  MATH  Google Scholar 

  • Lakatos, I. [1963–4]: ’Proofs and Refutations’,British Journal for the Philosophy of Science, 14, pp. 1–25, 120–139, 221–243, 296, 342. Republished in revised form as part of Lakatos [1976c].

    Article  MathSciNet  Google Scholar 

  • Lakatos, I. [1976c]:Proofs and Refutations: The Logic of Mathematical Discovery. Edited by J. Worrall and E. G. Zahar. Cambridge University Press.

  • Leibniz, G. W. F. [1678]: ’Letter to Conring, 19 March’, in L. Loemker (ed. ) :Leibniz’s Philosophical Papers and Letters, pp. 186–191. Dordrecht: Reidel, 1967.

  • Lhuilier, S.A.J. [1787]:Exposition Elémentaire des Principes des Calculs Supérieurs. Berlin: G. J. Decker.

    Google Scholar 

  • Pringsheim, A. [1916]: ’Grundlagen der Allgemeinen Functionen lehre’, In M. Burkhardt, W. Wutinger and R. Fricke (eds.):Encyklopädie der Mathematischen Wissenschaften, 2, Erste Teil, Erste Halbband, pp. 1–53. Leipzig: Teubner.

    Google Scholar 

  • Robinson, A. [1966]:Non-Standard Analysis. Amsterdam: North Holland.

    MATH  Google Scholar 

  • Robinson, A. [1967]: ’The Metaphysics of the Calculus’, in I. Lakatos (ed): [1967], pp. 28–40.

  • Russell, B. A. W. [1948]:Human Knowledge: Its Scope and Limits. London: George Allen and Unwin.

    Google Scholar 

  • Rychlik, K. [1962]:Théorie der Reellen Zahlen im Bolzano’s Handschriftlichen Nachlasse. Prague: Verlag der Tschechoslowakischen Akademie der Wissenschaften.

    Google Scholar 

  • Sacks, G. E. [1972]: ’Differential Closure of a Differential Fielď,Bulletin of the American Mathematical Society, 78, pp. 629–634.

    Article  MATH  MathSciNet  Google Scholar 

  • Seidel, P. L. [1847]: ’Note über eine Eigenschaft der Reihen, welche Discontinuirliche Functionen daisteilen’,Abhandlungen der Mathematik -Physikalischen Klasse der Königlich Bayerischen Akademie der Wissenschaften, 5, pp. 381–394.

    Google Scholar 

  • Smith, D. E. [1929]:A Scource Book in Mathematics. New York: Dover, 1959.

    Google Scholar 

  • Whewell, W. [1858]:History of Scientific Ideas, volume 1. (Part One of the third edition ofThe Philosophy of the Inductive Sciences.)

Download references

Authors

Rights and permissions

Reprints and permissions

About this article

Cite this article

Lakatos, I. Cauchy and the continuum. The Mathematical Intelligencer 1, 151–161 (1978). https://doi.org/10.1007/BF03023263

Download citation

  • Issue Date:

  • DOI: https://doi.org/10.1007/BF03023263

Keywords

Navigation