Abstract
Sometimes historians treat science studied in the past as if it was discovered today. They seem to forget that words mean different things in different times, and evaluate definitions and proofs according to the modern standards of rigor. Kenneth O. May assigns this mistake to the beginner: “The amateur historian examines a mathematical paper of the past as if its author were taking an examination in mathematics today and amuses himself by finding ‘errors’. Or he may force the ideas of one period into an inappropriate framework of another.”1
I would like to say thank to Miklós Laczkovich for his help, and to the National Scientific Research Foundation (OTKA) for their promotion.
This is a preview of subscription content, log in via an institution to check access.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
Preview
Unable to display preview. Download preview PDF.
References
Bell, Eric, Temple: The Development of Mathematics. New York - London: McGraw Hill, 1945.
Cantor, Georg: “Beiträge zur Begründung der transfiniten Mengenlehre”. in: Gesammelte Abhandlungen mathematischen und philosophischen Inhalts (Hrsg: Ernst Zermelo) Berlin: Springer, 1932. S.282–356. Originally published in Mathematische Annalen Bd.46 S. 481–512 (1895); Bd.49. S.207–246 (1897) English translation:
Cantor, Georg: Contributions to the Founding of the Theory of Transfinite Numbers. (Transl, intr, notes by Philip E.B. Jourdain) New York: Dover, 1915.
Cauchy, Augustin Louis: Cours d’analyse l’école royale politechnique. 1821. republished in: Oeuvres complétes d’Augustin Cauchy IIe série. tome III. Paris: Gauthier-Villars, 1897 Dauben, Joseph Warren: Georg Cantor. His Mathematics and Philosophy of the Infinite.
Cambridge, Mass: Harvard University Press, 1979
Fisher, Gordon M.: “Cauchy and the Infinitely Small” in: Historia Mathematica 5. (1978) pp.313–331
Gadamer, Hans-Georg: Truth and Method. (transi. rev. by J. Weinsheimer and D.G. Marshall) London: Sheed and Ward, 1993
Garciadiego, Alejandro: Bertrand Russell and the Origins of Set-Theoretic `Paradoxes’. Basel, et al: Birkhäuser, 1992
Grabiner, Judith V.: The Origins of Cauchy’s Rigorous Calculus. MIT Press, 1981
Kuhn, Thomas: The Structure of Scientific Revolutions. Chicago: University of Chicago Press, 1970
Laugwitz, Detlef: “Infinitely Small Quantities in Cauchy’s Textbooks” in: Historia Mathematica 14. (1987), pp.258–274.
Lakatos, Imre: Proofs and Refutations. (eds: John Worrall and Elie Zahar) Cambridge: Cambridge University Press
Lakatos, Imre: “Cauchy and the Continuum: The Significance of Non-standard Analysis for the History and Philosophy of Mathematics.” In: The Mathematical Intelligencer 1. (1978) N. 3. pp. 151–161.
May, Kenneth O.: Bibliography and Research Manual of the History of Mathematics. University of Toronto Press, 1973
Moore, G.H. and A. Garciadiego: “Burali-Forti’s Paradox: A Reappraisal of Its Origins” in.: Historia Mathematica 8. (1981) pp. 319–350.
Russell, Bertrand: The Principles of Mathematics. Cambridge: at the University Press, 1903.
Author information
Authors and Affiliations
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 1999 Springer Science+Business Media Dordrecht
About this chapter
Cite this chapter
Kiss, O. (1999). Meaningful Mistakes. In: Fehér, M., Kiss, O., Ropolyi, L. (eds) Hermeneutics and Science. Boston Studies in the Philosophy of Science, vol 206. Springer, Dordrecht. https://doi.org/10.1007/978-94-015-9293-2_11
Download citation
DOI: https://doi.org/10.1007/978-94-015-9293-2_11
Publisher Name: Springer, Dordrecht
Print ISBN: 978-90-481-5257-5
Online ISBN: 978-94-015-9293-2
eBook Packages: Springer Book Archive