Pythagorejská matematika vo svetle karteziánskej fyziky / Journal Article

[Pythagorean Mathematics in the Light of Cartesian Physics]

Kvasz, L. Filosofický časopis. Vol. 65, N° 4 (2017), pp. 513–541. ISSN 0015-1831

This paper is the second part in a series of articles aimed at reconstructing the emergence of mathematics as a deductive discipline in ancient Greece in the period between Thales and Euclid. We understand the emergence of mathematics as the birth of a language which enables the undertaking of deductive proofs. While in the preceding part we focused on the beginnings of Greek mathematics in Thales, here we concentrate on Pythagorean mathematics. In the literature the significance of Pythagoras as a mathematician is called into doubt. Despite this, the main part of the paper involves a reconstruction of the cognitive style of Pythagorean mathematics and this reconstruction is the basis for a defence of its authenticity.

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The aim of the project is to develop a formalization of epistemology analogous to Frege’s formalization of logic. The core of the project centres upon five theses setting out the path to a truly formal epistemology. These theses are based on the deeply-held belief that the current trend in the formalization of epistemology is insufficiently radical.

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