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Some Remarks on the Controversy Between Prof. Knorr And Prof. Szabó

  • Filippo Franciosi
Chapter
Part of the Synthese Library book series (SYLI, volume 145)

Abstract

As a premise to his theory of the origin of the axiomatic method, Szabó puts forward the abstractness of the Greek mathematics, which distinguishes it from the practical nature of Egyptian and Babylonian science. Moreover he maintains that Greek mathematics was abstractive and antiempirical right from the beginning, without any gradual process leading to these features. There was, on the contrary, Szabó supposes, a sudden revolution which affected only the Greek way of thinking, so that in consequence of this revolution, we have, not a transformation of earlier scientifical thought, but the birth of science itself.

Keywords

Abstract Entity Distinguished Place Axiomatic Method Practical Nature Dialectical Thinking 
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Notes

  1. 1.
    Knorr, W. R.: ‘On the Early History of Axiomatics’, this volume pp. 145–186.Google Scholar
  2. 2.
    See note 1 above, especially pp. 149, 165–167.Google Scholar
  3. 3.
    See for instance Ž. Marković, ‘Les mathematiques chez Platon et Aristote’, Bulletin International de l’ Academie Yougoslave des Science et des Beaux-Arts 32 (1939), p. 1–21; A. Frajese, Platone e la matematica nel mondo antico, Roma 1963; Attraverso la storia della matematica, Firenze 1969, pp. 64–86.Google Scholar
  4. 4.
    See for instance Procl. In I Eucl. p. 75 Friedlein.Google Scholar
  5. 5.
    Knorr, ‘On the early History of Axiomatics’. Cf. A. Szabó, Anfänge der griechischen Mathematik, Budapest 1969, p. 252.Google Scholar
  6. 6.
    Plato himself thinks so: See Rep. 526a.Google Scholar
  7. 7.
    See note 1.Google Scholar
  8. 8.
    Plato, Rep. 510d-e; Phaedon 73a.Google Scholar
  9. 9.
    Reidemeister, K.: 1949, Das exakte Denken der Antike, Hamburg, p. 10–c.Google Scholar
  10. 10.
    See note 1.Google Scholar
  11. 11.
    Szabó, Anfänge, p. 263–287; O. Becher, ‘Die Lehre vom Geraden und Ungeraden im Neunten Buch der Euklidischen Elemente’ in , Zur Geschichte der griechischen Mathematik ( Wege der Forschung XXXIII ), Darmstadt 1965, p. 136–7.Google Scholar
  12. 12.
    See note 1.Google Scholar
  13. 13.
    Plato, Phaedo 100c; Theaet. 162e.Google Scholar
  14. 14.
    Plato, Rep. 510c.Google Scholar
  15. 15.
    Plato, Rep. 527b.Google Scholar
  16. 16.
    Euclid, Elem. I, Post. I; prop. 10. Szabó, Anfänge, p. 405–407.Google Scholar
  17. 17.
    Szabó, A. ‘Anfänge des euklidischen Axiomensystems,’ in Zur Gesch. d. gr. Math., p. 394; Frajese A., Maccioni L.: Gli Elementi di Euclide, Torino 1970, p. 65 ff.Google Scholar
  18. 18.
    Procl. In I Eucl. p. 66–67 Fr.Google Scholar
  19. 19.
    Diano, C.: Studi e saggi di filosofia antica, Padova 1973, p. 278.Google Scholar

Copyright information

© D. Reidel Publishing Company 1980

Authors and Affiliations

  • Filippo Franciosi
    • 1
  1. 1.University of PaduaItaly

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