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Was there an Eleatic Background to Pre-Euclidean Mathematics?

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

Abstract

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.

Keywords

Deductive System Greek Philosophy Indirect Proof Greek Mathematic Aristotelian Logic 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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Copyright information

© D. Reidel Publishing Company 1980

Authors and Affiliations

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

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