Most
of us have long heard of the name of Pythagoras even before any
concepts of Presocratic philosophy or ancient Greek history are being
brought up. We probably first met Pythagoras in the maths lesson
rather than the history lesson though – remember the famous theorem
about right-angled triangles and how that led to all the crazy
trigonometric implications (with an extra sprinkling of vectors in
some cases) and another mathematical challenge that took the big
brains centuries to solve? From the following two articles, you will
find that Pythagoras and his followers, collectively known as the
Pythagoreans, were more than a bunch of maths geeks!
Pythagoras
was one of the most important philosophers of the Presocratic era.
Not only having a lot of contributions to mathematics, the
philosopher has also contributed a lot of original ideas to Western
intellectual history. It is curious to note that no writings have
been attributed to Pythagoras – all of his teachings were compiled
by his school of followers and subsequent thinkers who were
influenced by him. Pythagoras has led a number of followers and
formed a community which were very committed to their shared
philosophical outlook – simple living to nurture one's mind,
tolerance and a reasonably egalitarian attitude to all the members.
Since the Pythagoreans have unfortunately rubbed up the wrong way
with political figures of their era for a couple of times, they were
forced into seclusion and hence led an increasingly ascetic
lifestyle. The legacy of Pythagoras sustained long after his death,
for the next few centuries the Pythagorean school was further
developed and their ideas spread throughout Greece. Pythagoras had a
strong influence on philosophers like Parmenides, Plato and the
so-called neo-Pythagoreans of the later centuries.
While
a lot of mathematical achievements have been attributed to the
Pythagorean school, it is important to appreciate that their ultimate
motivation was a philosophical one rather than a mathematical one –
like examples Euclid or Archimedes. Like the other Presocratic
thinkers, the Pythagoreans wished to discover the physis of things –
the nature and origin of the universe. The reason why mathematics,
specifically numbers, were so important for the Pythagoreans was
because they saw perfection in the numbers. To the Pythagoreans,
perfection meant something rational and harmonious. The rationalist
outlook was the most important perspective for this school of
Presocratic thinkers, and to them, numbers (like the Pythagorean
triples), musical chords, and a rational soul were examples of
something in harmony.
Numbers as universals
The
modern readers are likely to be puzzled by such a speculative and
abstract worldview, yet it is the imaginative side typical of these
ancient thinkers. It was widely believed that Pythagoras was the
first thinker to coin the term ‘kosmos’. To the Pythagoreans, the
origin of the universe was known as 'Monad'. It was a kind of 'number
generator' that worked in a rational way to generate everything in
existence in the universe. The Pythagoreans believed that everything
in the universe was related in a rational way. The whole universe was
originated from numbers and everything in it was modelled on numbers.
The cosmo was operated through mathematical relations and these were
manifested in the resulting harmony from the universe.
Such
a theory bore some resemblance to the deism proposed by the
scientists and natural philosophers of Europe from the Enlightenment.
Scientists like Isaac Newton asserted that God created the world and
let the world operate by reason, through mechanical laws of causes
and effects.
As
the Pythagoreans was enthusiastic about the discussion of the cosmos,
they have also engaged in the discussion of physis. Philolaus, a
famous Pythagorean philosopher, suggested the whole world-order was
comprised of two contrasting attributes – the unlimited and the
limiters. Along with other things that came into existence, these
aspects constructed the cosmos as a harmonious order.
by Ed Law
Conatus Classics
