ARCHYTAS OF TARENTUM (’Αρχυτας)—philosopher, mathematician; physicist, and statesman, b. around 428 BC, d. around 365 BC in Tarentum. He was a disciple of Philolaos. He was the same age as Plato and was his friend.
He was the last great Hellenic Pythagorean. He was elected seven times as commander
in chief in democratic Tarento. Only fragments of Archytas’ original works
have survived. Fragments of the writings Archytas was especially interested in the foundations of sciences and how particular scientific disciplines depend upon each other. Unlike most of the authorities of his time, he treated arithmetic and even logistics (the computational and also the most conceptual part of arithmetic) as a more fundamental and perfect domain of mathematics than geometry, since it has a clearer grasp of its proper object than does geometry (it does not refer to objects accessible to intermediate sense cognition). He treated mathematics in turn as a more fundamental science than astronomy. He accepted and refined the ontology he received from Philolaos. He distinguished two spheres in reality: the primary sphere, and the secondary sphere. The primary sphere of being consists in number and magnitude. The secondary sphere includes everything that appears in number and magnitude, and relations between numbers and magnitudes. Most likely it was Archytas who replaced the inductive model of knowledge discovered by Alcmaion of Croton with a deductive model. According to Archytas, the presence of harmony and number in the cosmos is the source, necessary condition, and cause of the capacity of the cosmos to be known, i.e., knowledge of reality is possible only when the mathematical sciences are applied in the cognitive process (geometry, arithmetic, and harmonics). A. B. L. Van der Waerden, Zenon E. Roskal |

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