Hostname: page-component-745bb68f8f-s22k5 Total loading time: 0 Render date: 2025-01-28T02:06:26.970Z Has data issue: false hasContentIssue false
  • English
  • Français

Conceptual Change in Mathematics and Science: Lakatos’ Stretching Refined

Published online by Cambridge University Press:  31 January 2023

Arthur Fine
Arthur Fine*
Affiliation:
University of Illinois at Chicago Circle
Get access Rights & Permissions [Opens in a new window]

Extract

I once wrote to Imré Lakatos that if he had not already established himself as an accomplished philosopher and provocateur, he could have made a successful career as a Hollywood script writer. I had in mind, at that time, a beautifully written paper he had constructed by pasting together the cuttings from other papers. I had forgotten that his reputation as a dramatist was already established, with the production of his Proofs and Refutations [9]. For that work, it seems to me, is simply a play within a play. The main character, whose part is written in the footnotes, delivers a monologue which is a commentary on the drama, between teacher and students, that occupies center stage. This main character is not named in the play, so for ease of reference I shall call him “Imré”. What Imré points out is that the drama on center stage imitates life, in showing us the essential features of the methodology by virtue of which mathematical science grows.

Type
Part VIII. Lakatos’ Philosophy of Mathematics
Information
PSA: Proceedings of the Biennial Meeting of the Philosophy of Science Association , Volume 1978 , Issue 2: Volume Two: Symposia and Invited Papers 1978 , 1978 , pp. 328 - 341
Copyright
Copyright © 1981 Philosophy of Science Association

Access options

Get access to the full version of this content by using one of the access options below. (Log in options will check for institutional or personal access. Content may require purchase if you do not have access.)

References

[1] Berkson, William. “The Formal and the Informal.” In PSA 1978. Volume 2. Edited by Asquith, P.D. and Hacking, I. East Lansing, Michigan: Philosophy of Science Association, 1981. Pages 297–308.Google Scholar
[2] Brainerd, Charles J. “The Origins of Number Concepts.” Scientific American 228 #3(1973): 101–109.CrossRefGoogle Scholar
[3] Cantor, George. “Grundlagen einer Allgemeinen Mannigfal tigkeitslehre.” Mathematische Annalen. 1883. (As reprinted as “Foundations of a General Theory of Manifolds.” (trans.) Uwe Parpart in The Campaigner 9(1976): 69–96.)Google Scholar
[4] Dauben, J. “The Invariance of Dimension: Problems in the Early Development of Set Theory and Topology.” Historia Mathematica 2 (1975): 273–288.CrossRefGoogle Scholar
[5] Fine, A. “The Young Einstein and the Old Einstein.” In Essays in Memory of Imré Lakatos. (Boston Studies in the Philosophy of Science, Volume XXXIX.) Edited by Cohen, R.S. et al. Dordrecht, Holland: D. Reidel Publishing Co., 1976. Pages 145–159.Google Scholar
[6] Frege, G. Grundlagen der Arithmetik. Breslau: Verlag Wilhelm Koebner, 1884. Pages 67-104, 115-119. (As reprinted as “The Concept of Number.” In Philosophy of Mathematics. Edited by P. Benacerraf and H. Putnam. Englewood Cliffs, NJ: Prentice-Hall, Inc., 1964. Pages 85–112.)Google Scholar
[7] Freud, S. Vorlesungen zur Einführung in die Psychoanalyse. Leipzig und Wien: H. Heller, 1916-1917. (As reprinted as A General Introduction to Psychoanalysis. (trans.). J. Riviere. Garden City: Garden City Publishing Co., 1943.)Google Scholar
[8] Lakatos, I. “Falsification and the Methodology of Scientific Research Programmes.” In Criticism and the Growth of Knowledge. Edited by Lakatos, I. and Musgrave, A. Cambridge: Cambridge University Press, 1970. Pages 91–196.CrossRefGoogle Scholar
[9] Lakatos, I. Proofs and Refutations. Cambridge: Cambridge University Press, 1976.CrossRefGoogle Scholar
[10] Peano, G. Formulaire de Mathématiques. Turin: Bocca Frères, 1894.Google Scholar
[11] Russell, B. Principles of Mathematics. Cambridge: Cambridge University Press, 1903.Google Scholar
[12] Salomé, L.A. The Freud Journal of Lou Andreas Salomé. New York: Basic Books, Inc., 1964.Google Scholar