Pythagorean Influence on Plato's Philosophy

Plato's Philosophical Connection to Pythagorean Thought

The Pythagorean school, due to its significant popularity and the encounters Plato had with its members, exerted various influences on his philosophy.

Shared Philosophical Foundations

Mathematics as a Path to Knowledge

Plato, in some ways, agreed with the importance attributed by the Pythagorean school to numbers, famously encapsulated in the maxim: "Numbers are the essence of all things." He also adopted their division between body and soul.

Plato believed that mathematics serves as a crucial tool for attaining knowledge of the Forms (or Ideas). While the Forms represent the true essence and occupy the highest ontological plane, mathematics, though a notch lower (similar to the Divided Line's intelligible realm), still belongs to the intelligible world. It deals with immaterial concepts and allows the soul to draw closer to the Forms.

The Pythagorean Curriculum and Plato's Adaptation

Therefore, when establishing the curriculum for the education of the future philosopher-ruler, essential for a justly governed State, Plato decreed that mathematics must be a core component. He divided the teaching of mathematics into its fundamental components, which should be cultivated in a way that transcends the material, allowing the soul to approach true essence. These disciplines included:

• Arithmetic
• Plane Geometry
• Geometry of Volumes
• Astronomy
• Harmony

This division was largely inherited from the Pythagoreans, with one significant addition: the geometry of volumes. This field was not fully developed in Plato's time, but he was aware of its potential because one of his students was dedicated to its study. Consequently, Plato believed that the study of volumes (geometry of volumes) should precede the study of volumes in motion (astronomy), following the study of surfaces (plane geometry), and thus added it to the essential doctrines.

Critique of Pythagorean Harmony

While the Pythagorean school was the first to include harmony among the mathematical disciplines, Plato criticized their method of studying it. He observed that although they sought mathematical relationships between chords, they relied on the ear and, by extension, the senses. Plato considered this approach to be an improper way to cultivate a discipline meant to elevate the soul beyond the material.

Soul-Body Dualism and Reincarnation

Regarding the soul-body dualism, the Pythagoreans posited that the body was a prison for the soul, from which it could be liberated through reincarnation and the cultivation of mathematics and philosophy. Plato accepted this anthropological dualism, also viewing the body as a prison for the soul. He believed that the body, through its appeals to the senses, material desires, and appetites, distances the soul from purity. Thus, the soul must be released from this prison and purified through knowledge.

Furthermore, Plato championed the Theory of Reminiscence, which asserts that the soul pre-existed in the World of Forms and then incarnated into a body, retaining innate knowledge. This body, being material and mortal, will eventually die, while the soul, immortal and immaterial, will be reincarnated into another body. In this way, Plato fully embraced the theory of reincarnation.

Enduring Pythagorean Influence on Plato

From these points, we can clearly discern the profound influences the Pythagorean school had on Plato. He skillfully adapted and integrated these concepts, with some modifications, to forge his own comprehensive philosophical doctrine.