PYTHAGORAS

(c. 570 — 495? B.C.)

 

'DUALISM'

Pythagoras was born on the island of Samos but emigrated to southern Italy about 525. As the charismatic but authoritarian founder of a secret and frequently persecuted society of religious ascetics he is something of a legendary figure. However, it is not easy to distinguish his own contributions to philosophy from the various modifications introduced by his followers in the Pythagorean 'school', particularly as he wrote nothing himself.

 

COSMOLOGY/ PHILOSOPHY OF NATURE

[1] Pythagoras is said to have thought of the cosmos as a plurality [a] in some sense made up of numbers [a]. He seems to have introduced the idea of a Limit (peras) as controlling the Unlimited [b] (manifested as time and space or void). These basic principles are manifested in sets of opposites [c]: the Limit is odd, one, static, right, male, and good; the Unlimited is many, even, in motion, left, female, and bad. The link between oddness and perfection is shown by the fact that the addition of odd numbers always produces perfect squares, for example, 1 + 3 = 4; whereas addition of evens produces (imperfect) oblongs. These are illustrated in the so-called gnomon diagrams of the Pythagoreans: respectively, : : and : : :. From the unit comes the 'indefinite dyad', that is, the group of two; and this together with the unit produces the other numbers. And because for Pythagoras physical objects could be identified with numbers, the unit can be thought of as producing points successively — the single point (the number 1), lines (2), plane figures (3), and solid objects (4). The early Pythagoreans may have regarded some numbers as particularly significant. Number 4, for example, was associated with justice, 5 with marriage, 6 with animation, and 7 with opportunity. The theory of numbers may also be interpreted with reference to musical harmonies [d], as there is an obvious connection between intervals on the musical scale and the lengths of the strings on a lyre.

 

RELIGIOUS PHILOSOPHY/ PSYCHOLOGY

[2] Philosophy for Pythagoras was regarded as the foundation for a whole way of life. The cosmos was understood as a universal divine living organism or 'world-soul'. The individual soul was thought of as a part of this [a], trapped in the body; and this gave rise to the doctrine of the transmigration of souls ('metempsychosis') [b]. This is the belief that after death the soul would be reborn in another body — a human, an animal, or even a plant. One's aim in life must therefore be to escape the wheel of rebirth by attending to the appropriate rites for training and purifying the soul [c] so as to return ultimately to the disembodied state of the cosmos .

 

CRITICAL SUMMARY

There is an intimate connection between the mathematical/rationalist/'scientific' aspects of Pythagorean philosophy and his concern with the mystical, religious and ethical. However, there are problems with both. We know that numbers are used in measurement, but Pythagoras's apparent identification of physical objects with them seems less acceptable. The association of higher numbers with abstract ideas such as justice and opportunity in a quasi-mystical sense is even more philosophically suspect. Likewise, metempsychosis presents difficulties for the concept of personal identity and the relationship of 'soul' to body. But while Pythagorean thought is in some sense 'dualistic', it is probably mistaken to think of it in, say, Platonic or Cartesian terms; at this early stage of Greek philosophy no clear-cut distinction between matter and form had been explicitly articulated. Nevertheless the Pythagorean account of numbers and the doctrine of transmigration were to prove important influences on Plato's early thought and that of many neo-Platonic philosophers.

 

READING

G. S. Kirk, J. E. Raven, & M. Schofield, The Presocratic Philosophers, ch. VII.

R. D. McKirahan, Philosophy before Socrates, ch. 9.

J. A. Philip, Pythagoras and Early Pythagoreanism.

See also essays by C. H. Kahn and F. M. Cornford in Mourelatos; and by W. A. Heidel in Furley and Allen.

 

CONNECTIONS

Pythagoras

Note: also the general rejection of Pythagoreanism as 'superstitious' philosophy by Francis Bacon [1a 2d]. The influence of Pythagoras on Neoplatonism was no doubt mediated by the Neopythagoreans and Plato.

 

[1a]

Unity and multiplicity

→Heraclitus →Parmenides →Zeno →Plotinus

[1c] [1a] [1b] [1g]

 

[1a]

Numbers as basic cosmic principle

→Plato →Philo →Leibniz

[1d 5d] [1h] [2c]

 

[1b]

Limited and unlimited space and time

Anaximander→    Anaximenes→ →Zeno

[1c] [1a] [2a]

 

[1c]

Opposites

Anaximander→ →Heraclitus    Anaxagoras

[1b] [1d] [1c]

 

[1d]

Harmony/ cosmic order

→Heraclitus

[1e]

 

[2a]

World-Soul/ Spirit

→Plato →Plutarch →Plotinus    Bruno    Nicholas of Cusa

[5c] [1c] [1h j] [1d] [2i]

 

[2b]

The soul and transmigration

→Empedocles →Plato →Aristotle →Leibniz

[3a] [9b] [15a] [2f]

 

[2c]

Purification of the soul — escape from polluting material world

→Plato →Plotinus

[4b 9e] [2c]