Was there an Eleatic Background to Pre-Euclidean Mathematics?

  • Karel Berka
Part of the Synthese Library book series (SYLI, volume 145)


The basic ideas of a recent reconstruction concerned with the origin of deductive mathematics in the 6th and 5th centuries (cp. [9]–[12]) can be summarized briefly as follows: In its very beginning, there existed in Greece only a purely practical, empirical mathematics. The transformation of this empirical mathematics into theoretical mathematics, developed already in the pre-Euclidean period, could be achieved only by means of extra-mathematical reasons. This change, which resulted in the elaboration of Euclid’s Elements, was, in its principal features, determined by the philosophy of two Eleatics: Parmenides and Zeno. Mathematics was, therefore, at least initially, a branch or an inherent part of dialectics.


Deductive System Greek Philosophy Indirect Proof Greek Mathematic Aristotelian Logic 
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  1. [1]
    Burnet, J.: 1930, Early Greek Philosophy, London.Google Scholar
  2. [2]
    Diels, H. and Kranz, W.: 1912, Fragmente der Vorsokratiker, Berlin (Zürich- Dublin, 1971 ).Google Scholar
  3. [3]
    Fritz, K. v.: 1955, Die ARXAI in der griechischen Mathematik, Archiv für Begriffsgeschichte, Bonn, Bd. I, pp. 13–103.Google Scholar
  4. [4]
    Furley, D.J.: 1967 ‘Paramenides of Elea’, The Encyclopedia of Philosophy, Vol. 6, The Macmillan Comp. & The Free Press, New York and London, pp. 47–51.Google Scholar
  5. [5]
    Mueller, I.: 1974, ‘Greek mathematics and Greek logic’, in J. Corcoran (ed.), Ancient Logic and Its Modern Interpretations, D. Reidel, Dordrecht/Boston, pp. 35–70.CrossRefGoogle Scholar
  6. [6]
    Polya, C.: 1957, How to Solve It, Doubleday, Garden City.Google Scholar
  7. [7]
    Reidemeister, K.: 1949, Das exakte Denken der Griechen, Hamburg.Google Scholar
  8. [8]
    Struik, D.J., 1956, A Concise History of Mathematics, London.Google Scholar
  9. [9]
    Szabó, A.: 1954, Zur Geschichte der Dialektik des Denkens’, Acta Antiqua 2, pp. 17–62.Google Scholar
  10. [10]
    Szabó, A.: 1954, ‘Zum Verständniss der Eleaten?’ Acta Antiqua 2, pp. 243–289.Google Scholar
  11. [11]
    Szabó, A.: 1956, ‘Wie ist die Mathematik zu einer deduktiven Wissenschaft geworden?’ Acta Antiqua 4, pp. 109–152.Google Scholar
  12. [12]
    Szabó, A.: 1969, Anfänge der griechischen Mathematik, Akadimiai Kiadó, Budapest.Google Scholar
  13. [13]
    Vlastos, G.: 1967, ‘Zeno of Elea,’ The Encyclopedia of Philosophy, Vol. 8, New York and London, pp. 369–379.Google Scholar

Copyright information

© D. Reidel Publishing Company 1980

Authors and Affiliations

  • Karel Berka
    • 1
  1. 1.Czechoslovak Academy of SciencesCzechoslovakia

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