PYTHAGORAS (  570 BC - 500 BC)

By T K Jayaraman IRS (Rtd) Teaches Western Philosophy; English and French at Indian Institute of World Culture Bengaluru

You are quite familiar with his name as a geometrical theorem is named after him. Pythagoras was the founder of the Pythagorean School of philosophy. They were not as much concerned with substance as the other Pre-Socratic philosophers. They were concerned with form and the relations of things.They were mathematicians and tried to explain things with the help of numbers.

 

 Pythagoras was born in Samos and immigrated to the Greek colonies in Southern Italy in 529 BC. He fled to escape the tyranny of Polycrates. He settled in Crotona and founded an association whose objectives were ethical, religious and political. He was concerned with virtue and moral life. Individual should have self control. He should subdue his passions to harmonise his soul. One should respect the authority of elders, teachers and State. The members of the association lived in a community as a large family, taking their meals in common, wearing the same kind of dress and applying themselves to arts, crafts, music, medicine and mathematics. The purification of the soul was their objective. The Pythagorean practices did not go well with the ruling class. Pythagoras was forced to seek refuge in Metapontum where he died in 500 BC.His followers were driven from Italy to Greece. His disciples continued to teach his doctrines for hundreds of years.

Pythagoras said, “All things are numbers”.Measure, order, proportion and uniform recurrence can be expressed in numbers. Without numbers, it is reasoned that there can be no such relations and uniformities, no order, no law; hence number must lie at the basis of everything. Numbers must be true realities, the grounds of things, and everything else an expression of numbers. Numbers constitute the formal and relational  structure  of  substances  or  thing.  Things are copies or imitations of numbers. The  distinction between matter  and  form  which  is  central  to Platonic  and  Aristotelian  Metaphysics  was  foreshadowed  by  the Pythagorean  distinction  between  number  and  things. It was discovered that there is a numerical relation between the lengths of strings and the pitches of the corresponding tones. It was simply called number. In other words, Pythagoreans placed number behind the phenomena as their basic principle and ground. 

They devoted themselves to the peculiarities of numbers. Numbers are odd and even. Odd are limited. Even are unlimited. The odd and even, the finite and the infinite constitute the essence of the universe. Nature itself is a union of opposites. We are offered ten such opposites. 1.  limited and unlimited 2. Odd and even 3.one and many 4.  Right and left 5.male and female 6. rest and motion 7. straight and crooked 8. light and darkness 9.good and bad10.square  and rectangle. The Pythagorean doctrine of dualism can be traced back to Anaximander and Anaximenes. The doctrine of the conflict of opposites was foreshadowed by Anaximander; and the concept of unlimited was shared by Anaximander and Anaximenes. The Pythagoreans regarded unlimited as prior to the limited; individual things arise as limitation of the unlimited space by the imposition of forms on space.

The corporeal  world is also numerical, being based on the unit. The point is one, the line is two, the figure is three, the solid four. Earth is a cube; fire, a tetrahedron; water an icosahedrons, and so on.  The spatial forms are the causes of the bodies, and since these forms can be expressed by numbers, the latter are the ultimate causes. The influence of the Pythagorean number mysticism on physics and astronomy has been appreciable; the Keplerian theories marked Pythagorean influences. The conception of a mathematically expressible natural law is at the very core of modern science and philosophy. Perhaps, Pythagoreans were not much off the mark.

 According to the Pythagorean School, there is a central fire at the centre of the universe which is in spherical form. These notions paved the way for the construction of the heliocentric theory, which was propounded by Aristarchus of Samos about 280 BC Pythagorean ethics is rooted in number-mysticism. Love and friendship are expressed by number eight, because love and friendship are harmony and octave is harmony. Pythagoras says, “In this life, there are three kinds of men, just as there are three sorts of people who come to the Olympic Games.  The lowest class is made of those who come to buy and sell, the next above them are those who compete. Best of all, however, are those who come to simply look on. The greatest purification of all is therefore, the disinterested science, and it is the man who devotes himself to that, the true philosopher, who has most effectually released himself from the “wheel of birth”