Dr Menahem Luz,
Presocratic Philosophers
Summary 7
Pythagoras of Samos

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Contents

1. General remarks on Pythagoras and the Pythagoreans
2. Pythagoras of Samos
   • reincarnation
   • philosophy of number
3. Alcmaeon of Croton
4. Philolaus of Croton
5. Neo-Pythagoreans
6. Conclusions

General Note

• Little is known of the historical Pythagoras although there exist many late fictional biographies of him.Since he wrote no works himself, many later sayings are attributed to him. Plato mentions the secrecy of the Pythagorean school (tadpis p. 18 no. 1)
• More is known of the later Pythagoreans who were the followers and philosophical descendants of the schools that Pythagoras founded in southern Italy (Tarentum, Croton and Metapontum)
• The majority of references in Plato and Aristotle really refer to later Pythagoreans of the 5th century BC (especially Alcmaeon and Philolaus).
• The earliest Pythagorean literary texts date from the Hellenistic period when there was a Neo-Pythagorean. revival.
• The basis for most references to him in modern religious literature stems from the late 3rd-5th century A.D. when Neo-Platonic biographies of Pythagoras, were written. They rebuild Pythagoras' way of life out of Plato's dialogues and later literature.

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Pythagoras of Samos

• Background
  • Pythagoras was born about 570 BC in the Ionian island of Samos. Press to see map of Ionia.

  • Besides the scientific influence of neighbouring Ionia, Samos was famous for engineering works accomplished by means of mathematical precision.
    • Pythagoras could have studied problems of applied mathematics before he left Samos.
    • tradition also relates that he encountered geometrical examples of his famous theorem (Pythagoras' theorem) in Egypt. At any rate, Pythagoras universalized the specific examples of the theorem known to the Egyptians, making it applicable for every example of a right angled triangle.

  • When he was about 30 years old, Pythagoras went into exile in Southern Italy, setting up a school in the towns of Tarentum, and later in Croton and Metapontum.

  • As such, Pythagoras stands as the earliest of what Aristotle calls "the Italian philosophers" -- meaning those Greek thinkers who resided in southern Italy and Sicily (sometimes called: 'Greater Greece').

  • Press to see map of Western Greek thinkers of Southern Italy.

  • It is not surprising that Pythagoras' school had a strong interest in mathematics (especially, arithmetic, geometry and harmonics).

  • Pythagoras died about 520 BC leaving schools in southern Italy who ascribed to the master every new idea -- and justified it by his authority "he himself said it" (Latin: ipse dixit). Lists of his sayings (akousmata) were collected but were mixed with those of his students as well

  Earliest references to him

  • Heraclitus acknowledged Pythagoras' sophia but thought that he practised (too) much human learning learning (cf. K-R-S 255-256). Heraclitus (544-484 BC) made this criticism just before or after Pythagoras' death (520 BC) when his schools still flourished
  • Xenophanes of Colophon (570-475 BC) was a contemporary of Pythagoras and noted his theory of reincarnation (cf. tadpis p 11 no. 2).

  Reincarnation

  • Pythagoras believed that he himself had existed in previous lives - a theory called in Greek metempsychosis and in English, reincarnation or transmigration of the soul.

    • His contemporary, Xenophanes notes Pythagoras' belief in:
      • his previous lives
      • recollection from previous lives
      • reincarnation in animals
      (cf.tadpis p 11 no. 2).

    • Ion of Chios (c. 450 BC) who lived 70 years after his death, mentions his wisdom (sophos) since he had learned the minds of all mankind (K-R-S 258), perhaps referring to knowledge of previous generations

    • a garbled version is also found in the works of the historian Herodotus (c. 425 BC) who reports on Pythagorean teaching that reached the Thracian people. He notes a belief
      • in the after-life
      • life as a punishment
      • a Pythagorean way of life
        (tadpis pp 17-18 no. 1)

    • Plato understands the Pythagorean theory of the soul as implying a belief in the harmony of the universe (Plato, Timaeus)

    • Aristotle criticised the Pythagorean theory of universal reincarnation as if implying a harmony of all life forms
      (cf.tadpis p 18 no. 3)

    • Other sources base Pythagorean vegetarianism on the belief that animals house human souls that are reincarnated as a punishment) -- but there is no clear early evidence for this belief

  Philosophy of number

  • Pythagoras, or at least his Pythagorean pupils, seems to have believed that the arche was number (arithmos) and his school took a special interest in mathematical, harmonic and musical theories. Because his teaching was oral, the details are uncertain although there are many late anecdotal stories describing them.
  • Clear early evidence is found in Plato and Aristotle (tadpis p. 18 nos. 1-2) who draw on the works of later Pythagoreans (especially Philolaus). It is dangerous to ascribe their theories to Pythagoras himself
  • By positing number as the arche, the Pythagoreans fall into the pluralist camp -- and are criticised for this by the Eleatic monist, Parmenides.
  • In fact, while Heraclitus explained all change by the concept of logos, the proportional formula that explains change between a substance and its opposite, the Pythagoreans made this idea more precise by working out the proportional and mathematical formulae to explain all objects.
  • Pythagoreans who postdate Parmenides try to offer a dualist system in reply to Parmenides (Aristotle Metaphysics A 986a p. 51). This is often based on the division of number into even and odd
  • At any rate, in ancient mathematics, all number is a plurality but one is not a number, i.e. a plurality, but a unity and the arche of all numbers since they are compounded out of unities.
  • The Pythagoreans made all sensibles based on numerical ratios and geometrical forms, but did not explain how sensible solids are derived from geometrical unities. This was done by Democritus and the atomists who posited solid atomic unities which though non-sensible are the arche of sensible objects.

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Alcmaeon of Croton (early 5th century BC)

Alcmaeon was a major source for Plato and Aristotle. He was not an actual Pythagorean but a doctor, who wrote about them and whose medical theory was influenced by the Pythagorean medical tradition of Croton (Aristotle Metaphysics A 986a (Roth-Shkolnikov, p. 52). He was contemporary with Parmenides, but it is uncertain whose ideas preceded whom.

• Cosmic Principles
  • He developed a theory of health as a constitutional balance (isonomia) whereby no elemental humour overcomes another
  • sickness results from imbalance among the elemental humours whereby one element has 'monarchy' over the others (K-R-S 310)
  • there is a dualistic principle governing all things just like all bodily parts (Metaphysics A 986a p. 52).This should be contrasted to his contemporary, Parmenides.

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Philolaus of Croton

Life
• On the exile of the Pythagoreans from Italy, Philolaus moved to Thebae (see map) and taught there in the year that Socrates was excecuted (see tadpis p 18 no. 1)
• He was perhaps also connected with the Pythagorean exiles at Phlius mentioned in Plato's Phaedo
• after his death, Plato was supposed to have travelled to Italy to buy Philolaus' works (see tadpis p 18 no. 2. It is questionable how much Plato consciously borrowed from him.‡

  Beliefs

  Reincarnation

  • Philolaus taught that life is a punishment for sins in previous reincarnations
  • suicide is thus forbidden as only the god may release us from the prison of life
    (see tadpis p 18 no. 1)

  Harmony

  • Similar to Alcmaeon, Philolaus believed that there are dualistic principles in nature that resemble those of the cosmos (see tadpis p 18 no. 2
  • the same harmony is present in both our minds that grasp the universe and the universe itself (see tadpis p 19 no. 1)
  • every object has a mathematical number or ratio - and only through that ratio can it be known to our minds (see tadpis p 18 no. 6-8
  • Simlar to this is Aristotle Metaphysics A 986a (p 51 (= tadpis p 19 no. 5), although this passage is ascribed to the Pythagoreans in general (see tadpis p 18 no. 1

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Neo-Pythagoreans

These were groups of semi-mystical, semi-scientific thinkers who worked in the Mediterranean area during the Hellenistic and Roman periods (3rd cent. BC-2nd cent. AD). Some of their texts are attempts to Pythagorize earlier works:

• e.g., Timaeus Locrus is a Hellenistic Pythagorean copy of Plato's Timaeus
• or Pseudo-Architas' Categories is a late copy of Aristotle's Categories

Besides anecdotal stories concerning Pythagoras and his pupils, they also wrote more serious introductions to arithmetic and geometry in the 1st-2nd centuries AD.

Pythagorean work was later reabsorbed into Iamblichus' Neo-Platonic revival of Pythagoreanism in the 3rd century AD.
Neo-Platonic Pythagoreanism and its understanding of Pythagoras' way of life left a influence on various relgions both in the west and the east.

With the revival of Neo-Platonic texts in the Renaissance, there was also a revival of interest in Pythagoreanism, especially in the idea of the harmony of the cosmos and astrology (the belief that there is a harmony between the stars and the life of man).

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Conclusions

• Although ostensibly a school, Pythagoreanism is really a movement -- developing different interests at different times
• In one sense, its influence is more important than what it itself propounded and believed since so little of genuinely early Pythagoreanism survives
• As a movement, the members showed an interest in two divergent fields:
  • mysticism and the continuation of the soul
  • scientific research (especially mathematics, harmonics and medicine)
• in Neo-Pythagoreanism, there were attempts to combine both fields as a mystical theory of science.

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