Philosopher Profile – Pythagoras May 23, 2010
Pythagoras
Philosopher Profile
Pythagoras ( c.550 – c.500 B.C.) – The My stic
and the Mathematician
~ Eternity in an Hour
Ee Suen Zheng
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Pythagoreanism
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The term ‘Pythagoreanism’ refers to the way of life and doctrines
that are attributed to Pythagoras. According to Aristotle, many of
these philosophical doctrines were in relation to numbers.
Pythagoreans believed that numbers are ‘the first things in the
whole of nature’, and that ‘the elements of numbers are the
elements of all things’ (Honderich, 2005).
‘Pythagoreans knew that concordant musical intervals (octave,
fourth, and fifth) could be expressed by arithmetical ratios
(Honderich, 2005).’ This probably led to their belief that the
universe as a whole could be explained and understood in
terms of mathematics.
According to Philolaus (born c.470 B.C.), Pythagoras held that
human knowledge was possible only of things that can be
numbered because anything that can be known must have limits
(spatial or temporal) to be distinguishable from one another
(Honderich, 2005). Therefore, the universe as we know it must
consist of things that can be counted.
Details
Full Name
Born
Location
Era
School
Main
Interest
Notable
Ideas
Pythagoras
c.550 – c.500 B.C.
Croton, Italy
Ancient
Philosophy
Pythagoreanism
Mathematics,
Metaphysics,
Ethics, Politics,
Music
Pythagorean
Theorem,
Pythagorean
Tuning, Golden
Ratio, Musica
Universalis
Ee Suen Zheng |Pythagoras
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Philosopher Profile – Pythagoras May 23, 2010
Historical Background
Pythagoras was a native of the island of Samos, and flourished
about 532 B.C. Little is known about his life (some say he was the
Pythagoras
c.550 – c.500 B.C.
son of the god Apollo) and he remains to this very day an elusive
figure. Coincidentally, Samos was a commercial rival of Miletus,
the city where the philosopher Thales flourished. Disappointed
with the government of the island Samos he to emigrated to
Croton in Southern Italy and founded a society of disciples there.
Notable Ideas and Achievements
Known as a polymath and a charismatic figure, Pythagoras has
immense influence both in ancient and modern times. According
to Bertrand Russell (Russell, 1972), mathematics in the sense of
being a demonstrative deductive argument begins with him. It
was Pythagoras who was the first in recorded history to blend
Bust of Pythagoras of Samos in the
Capitoline Museums, Rome
mathematics into philosophy.
For Pythagoras, “all things are numbers.” The statement
Chronology
practically sums up his views on metaphysics. ‘He discovered the
importance of numbers in music, and the connection that he
established between music and arithmetic survives in the
mathematical
terms
“harmonic
mean”
and
“harmonic
N/A: Too little is known of
Pythagoras to reconstruct a
chronology of events.
progression” (Russell, 1972).’
Perhaps his most notable achievement was the Pythagorean
Intellectual Setting
Theorem. The Theorem stated that for right-angled triangles, the
sum of the squares on the sides adjoining the right angle is equal
1.
to the square on the remaining side, the hypotenuse.
2.
3.
c
a
Disliked his government,
left Samos
Visited Egypt
Established himself in
Croton, southern Italy
Pythagorean Theorem:
a2 + b2 = c2
b
Although Pythagorean contributions to geometry are reputedly
great, the extent of their influence is very uncertain.
Ee Suen Zheng |Pythagoras
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Philosopher Profile – Pythagoras May 23, 2010
The Mystic
Clouding his reputation as a pure mathematician, Pythagoras was
Rules of the Pythagorean
Order
also famous with his mysticism. Credited with miracles and magic
powers, he founded a religion based on the transmigration of
souls and the sinfulness of eating beans (Russell, 1972)!
According to Pythagoras, the soul is an immortal thing that
transforms into other kinds of living things and whatever that
comes into existence is born again after a certain cycle.
Therefore, nothing is absolutely new and all things born from
the soul are related like kindred to one another. This doctrine of
the repeated incarnation of the souls (metempsychosis) included
the punishments and rewards for the behaviour in previous
lives.
Influence
The original society/religion that Pythagoras founded did not last
long. However, throughout the fifth century B.C. various theorists
in the Western world were called ‘Pythagoreans’ (Honderich,
2005). Many of these, so called ‘Pythagoreans’, were interested in
mathematics and astronomy. Some had apparently tried to
reduce all knowledge to mathematics (justice is the number 4,
for example) (Burkert, 1972).
1.
2.
To abstain from beans.
Not to pick up what has
fallen.
3.
Not to touch a white
cock.
4.
Not to break bread.
5.
Not to step over a
crossbar.
6.
Not to stir the fire with
iron.
7.
Not to eat from a whole
loaf.
8.
Not to pluck a garland.
9.
Not to sit on a quart
measure.
10. Not to ear the heart.
11. Not to walk on highways.
12. Not to let swallows share
one’s roof.
13. When the pot is taken off
the fire, not to leave the
mark of it in the ashes,
but to stir them together.
14. Do not look in a mirror
beside a light.
15. When you rise from the
bedclothes, roll them
together and smooth out
the impress of the body.
Source: (Russell, 1972)
His most profound influence can be seen in the works of
Parmenides, Empedocles, and Plato. Plato’s view on the
immortality of the soul in Phaedo and his exercise of mathematical
cosmology in Timaeus, are similar to the views held by
Pythagoras/Pythagoreans.
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Philosopher Profile – Pythagoras May 23, 2010
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Food for Thought: Religion and Reasoning
Pythagoras was one of the early advocates of the importance of mathematics in
philosophy. The influence of geometry upon philosophy and science, however, has
usually been taken for granted. Geometry, as established by the ancient Greeks, start
with axioms that are self-evident and proceeds through deductive reasoning to arrive
at theorems that are far from being self-evident.
Philosophers like Plato have used the same method in geometry to solve philosophical
questions and metaphysical problems. But geometry, for all its finesse, deals with exact
circles and perfect squares. In a world of imperfections and irregularities, such ‘circles
and squares’ are absent. This led Plato to think that eternal objects can be conceived
only by God’s thoughts. Hence, Plato’s doctrine that God is a geometer that conceives
things eternal and perfect.
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Bibliography
Barnes, J. (1979). The Presocratic Philosophers. London.
Burkert, W. (1972). Lore and Science in Early Pythagoreanism. Cambridge.
G. S. Kirk, J. E. (1990). The Presocratic Philosophers, 2nd Edition. Cambridge.
Honderich, T. (2005). The Oxford Guide: Philosophy. Oxford: Oxford University Press.
Russell, B. (1972). The History of Western Philosophy. New York, United States of America:
Touchstone, Simon and Schuster, INC.
Ee Suen Zheng |Pythagoras
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