Category: Persons

Pythagoreans (and Plato)

The Pythagorean world-view was at the onset shaped as a religious practice, and progressively evolved into a kind of mathematical philosophy. Some of Plato’s key philosophical points bear the sign of Pythagorean theories (the immortality of the soul, the doctrine of reincarnation, the significance of the mathematical sciences, and the ontological supremacy of numbers).

Pythagoras and early Pythagorism

Pythagoras (6th century B.C.) was born in Samos, but lived in South Italy. He was a religious leader, and a proponent of a new way of life. We are not aware of the exact content of his teachings. In examining the Pythagoreans of the classical times, we discern two characteristics of the Pythagorean School: the conviction that numbers are the principles of beings; and the doctrine of reincarnation. In all probability the two postulates had not been on an equal par in the beginning of the Pythagorean tradition. It is plausible that at the onset, Pythagorism was a religious movement that, at some point, integrated the belief in the importance of numbers.

The new element that Pythagoras introduced in Greek thought was the understanding of philosophy as a way of life. The initiation into philosophy is not simply the indoctrination in a theoretical system; even more, it consists in a thorough conversion; an engagement in a new way of life. Pythagoras’ teaching places the weight in the experiential, and not the cognitive side. For that reason, philosophy cannot develop in solitude: it requires the participation in a group of men of like mind; a community organized by strict hierarchy and joint ownership, where the predominant figure is that of the teacher and initiator.

It was a common conviction among the ancient writers that Pythagoras pronounced the doctrine of reincarnation. This doctrine propounds that life continues after the death of the body. It also includes the feature of the post mortem punishment or reward. The submission to a new, ascetic way of life is, for the Pythagorean, the only way for beginning his circle of reincarnations propitiously. This way of life involves the practices of distressing the body, and purifying the soul. Consequently, the human soul is considered as something totally different than the body; it is an immortal entity in its own right, which can also live in different bodies. This is the crucial point of Pythagoras’ theoretical revolution.

The role of mathematics

The Pythagoreans had already established their position in the spiritual life of the time of Plato and Aristotle. The most advanced achievements in the fields of mathematics and astronomy were induced by Pythagoreans: the Pythagorean theorem, the discovery of the incommensurable quantities, the roundness of the universe, the proposition regarding the motion of the earth. The theory of music, an advantageous discipline for the Pythagoreans, was brought forward as an autonomous branch of mathematics. Lastly, appreciable was the idiosyncrasy of the Pythagorean tradition in philosophy; a tradition defined by the primordial significance it ascribed to numbers. In accounting collectively about the “so-called Pythagoreans”, Aristotle acknowledges their contribution in philosophical thought, and appraises that they “applied themselves to mathematics, and were the first to develop this science; and through studying it they came to believe that its principles are the principles of everything” (Metaphysics I 985b24-26). A substantial element of the Pythagorean philosophy is the comprehension of the universe as “proportion and number”, an assumption that Aristotle traces to the discovery “that the properties and ratios of the musical scales are based on numbers” (ibid., 985b32-986a4).

The oldest texts from the Pythagorean tradition we draw from Philolaus, a contemporary of Socrates. In Philolaus’ fragments the emphasis is put on the primordial significance of the number, which is promoted to the principle of understanding everything. If existing beings did not bear upon a mathematical structure, we wouldn’t be able to know them (frag. 4). The same goes for the whole universe; even for nature. The universe is composed of limiting and unlimited elements (frag. 1), which are constituents of the numbers. The harmonic order of nature allows for its essential understanding.

These texts bear out the reconciliation of the Pythagorean philosophy with the physiocratic tradition of the Ionian Presocratics. The new element is the connection of the cosmic order with numbers and harmony. Numbers determine the accordance of the notes that produce the harmonious musical result. Numbers lie behind the harmonic motions of the stellar bodies; behind the entrenched structure of the universe. Thus, in the Pythagorean philosophy, mathematics, music, and astronomy are closely related; they are “sciences closely akin” (Plato, Republic 530d), for number defines them all.

The impact of Pythagorean theories on Plato

It is generally assumed that Plato was influenced by the Pythagorean world-view: he affirms the immortality of the soul and the doctrine of reincarnation; he introduces the "hypothetical method" of mathematics into philosophy; he submits the prospective governors of his ideal city to a ten-year study of mathematics; and, via Timaeus, a philosopher from South Italy, he proffers a fascinating -and Pythagorean in origin- mathematical cosmology. Moreover, Plato establishes the Academy in the same way that the closed Pythagorean communities were organized. Therefore, it has been said, and not without good reason, that Plato, especially in his late period, was "Pythagorizing".

This assumption finds support in Aristotle. In the First Book of his Metaphysics, the philosopher lays out a historical report on the preceding philosophy. There, he positions Plato right after the Pythagoreans, exactly for the reason that he thinks their theories to be in line. According to Aristotle, Plato follows the Pythagoreans in two respects:

• He considers numbers as the substances of the sensible beings. However, Plato’s formal Numbers are not material, but belong to a higher ontological level because they are identical with the Forms.

• Plato produces reality from two principles of mathematical nature. Pythagoreans spoke of the limited (or the One), and the unlimited; whereas Plato maintains the One, but replaces the Pythagorean unlimited with the “Indefinite Dyad”.

Aristotle’s report about Plato is not corroborated by what is written in Plato’s dialogues. He must have been relying on Plato’s oral teachings instead – that is, on the so-called “unwritten doctrines”. For all that, Aristotle’s report in not poles apart from dialogues such as the Philebus, Timaeus, and the Laws. For the late Plato the world is a realm of order and harmony; a harmonic “mixture of the Limit and the Unlimited” (Philebus); the mathematical creation of a good Demiurge who employs numbers in shaping the pre-cosmic indefinite "space" (Timaeus). Plato turns on numbers and identifies them with the Forms because he thinks that the number yields the organic relation between the One and the Many, the unity and the multiplicity. The Forms-Numbers are not primordial beings; instead, they are produced by two principles: the first should be yielding unity and stability, and the second multiplicity and indeterminacy. Those principles could be named One and Two (or Plurality) as in Plato; or Limit and the Unlimited as in the Pythagoreans.

Author: Vassilis Kalfas
  • Burkert, W, Lore and Science in ancient Pythagoreanism. Καίμπριτζ Μασσ., 1972.
  • Huffman, C.A. "Pythagoreans." Press, G. ed. The Continuum Companion to Plato. Λονδίνο: London, 2012.
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