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.
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Berka, K. (1980). Was there an Eleatic Background to Pre-Euclidean Mathematics?. In: Hintikka, J., Gruender, D., Agazzi, E. (eds) Theory Change, Ancient Axiomatics, and Galileo’s Methodology. Synthese Library, vol 145. Springer, Dordrecht. https://doi.org/10.1007/978-94-009-9045-6_8
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DOI: https://doi.org/10.1007/978-94-009-9045-6_8
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