Pythagoras and Gorgias: Ancient Greek Philosophical Currents

Pythagorean Philosophy: Arithmosophy and Transmigration

Pythagoras gathered his disciples into an organized community, where he taught the doctrine of the transmigration of the soul and developed profound mathematical and astronomical studies. According to ancient legend, Pythagoras retained memories of his soul's previous incarnations, which he used to instruct and lecture his followers. Transmigration in Pythagorean doctrine offers a distinctly ethical and religious arithmosophy.

Arithmosophy understands numbers as the root principle of all things. It developed a mathematical symbolism where numbers were identified with dots forming geometrical figures, whose fundamental unit was ten, often represented as an equilateral triangle (the Tetractys). Thus, Pythagoras shifted the problem of the arche (first principle) from matter to form.

Key Domains of Pythagorean Arithmosophy

• Theory of Numbers. Based on the identification of certain numbers with geometric figures, this theory established a highly interesting cross-pollination between arithmetic and geometry.
• Musical Theory. Pythagoras conducted significant research in the field of music, to which he attached great importance.
• Astronomical Theory. By understanding numbers not merely as a formal principle but also as a material aspect of reality, the Pythagoreans viewed mathematics and physics as inseparable.

Gorgias and the Roots of Skepticism

Beyond Pythagorean thought, the art of oratory was also shaped by a teacher's beliefs about right and wrong. One such figure was Gorgias, a disciple of Empedocles the Sicilian. He had written, perhaps to defend his master from the attacks of Eleatic Zeno, a treatise titled On Nature or Non-Existent (also known as On the Non-Existent).

This treatise substantially states the following:

1. That there is no reality.
2. That even if reality existed, it would be unthinkable.
3. That even if it could be known, it could not be explained or communicated to others.

It is very possible that the Sicilian sophist intended to push the Eleatic philosophy to its absurd conclusions. This relativity, which had been present in Protagoras's thought, culminates in Gorgias's profound skepticism.

The Pythagorean Sect: Discipline and Influence

Pythagoras was primarily a religious thinker and the founder of a school governed by a strict disciplinary policy. The Pythagorean sect was not only interested in contact with the divine (achieved through techniques of separation between soul and body, implying severe discipline and a long initiation) but also pursued a reformist political ideal.

They were a closed religious sect, yet also a public organization that sought to influence civic life, praising collective effort and discipline as antidotes to 'softness' (τρυφή, tryphe), which they considered an Ionian vice. Pythagoras was significant as the inspiration for the principles governing this religious sect.

The Pythagoreans were among the first to dedicate themselves to mathematics, significantly advancing this science. Absorbed by their mathematical studies, they came to believe that the principles of numbers were the principles of all beings. This belief stemmed from the observation that numbers, by their very nature, seemed to possess inherent qualities and shared similarities with fundamental elements like fire, earth, and water, as well as with the existence of beings and things in formation.