What is the Pythagorean Doctrine of Number (Cosmopolis)?June 27, 2021
Pythagoras was the first to use the word cosmos (everything) in the history of philosophy.
According to him, the cosmos is a logically organized structure. It was arranged mathematically by Pythagoras. According to him, there are two substances in the basis and origin of everything: 1- Peros: limited- limiting “fire” 2- Apeiron: unlimited “air.” He saw them as massive beings. Pythagoras’ picture of the universe consists of boundless air that pervades everything and finite fire at the center.
According to Pythagoras, number consists of the union of the finite and the unlimited, ‘one and many’. So accordingly the number is similar to a physical object. It is made of fire and air. The basis of everything is number, and the basis of number is unlimited and limited. The basis of the number is air and fire. Limited (fire) is the active one. Unlimited (air) represents things that are more passive. It takes this sample from sperm and egg. It’s like a sperm fertilizing an egg. Fire is the active ingredient in them. The limited and the unlimited combine to form 1. But this number has mass, it is an object.
The number 1 forms the point.
The number 2 forms the line.
The number 3 forms a triangle.
The number 4 creates the rhex.
The number 5 creates fire.
The number 6 creates water.
The cube corresponds to earth in Pythagoras. Boundless air and limited fire numbers are formed. Pythagoras attributes quantitative changes to mathematical numbers. In other words, we can explain the universe with mathematical numbers. In Pythagoras:
When the 1st number is mentioned, the number in the symbolic meaning of today is not considered.
2. Instead of mathematics, there is geometric thinking.
3. The numbers are explained in a certain way. Numbers were seen as the basic element to explain the universe string.
a) Numbers are formed from the combination of finite (fire) and unlimited (air). The source of this thought is the fertilization event.
b) Figures from the combination of numbers,
c) Objects are formed from the combination of shapes,
d) Objects are formed from objects one by one.
According to Pythagoras, everything is made up of quantities. The fact that everything consists of numbers means that we can understand the universe in mathematical expressions. This is the basis of modern science. The thought that the universe has a mathematical form leads some to the conclusion that the structure of the soul of man and the structure of the universe are identical.
In the Miletos school, there was no distinction between animate and inanimate, animate and still. Here it is as if it was made. Pythagoras,
1. It says that the soul is made of air, air is passive and fire is active.
2. It is not clear whether the soul is made of numbers or not.
In Pythagoras the overthrow of monism became evident. Distinctions such as active substance, passive substance, substance with thinking feature, and substance without thinking feature started to emerge gradually. In Pythagoras the soul was made of air. We cannot call Pythagoras’ philosophy a complete philosophy. As if he had just woken up from sleep. Pythagoras made two important contributions to the history of philosophy.
1. He introduced the idea of geometry,
2. He made important contributions to astronomy.
According to Pythagoras: If everything consists of numbers, it must have an order. He connected this order to an information that measures the quantities. He met opposites in harmony. Limited-unlimited, good-bad, one-many. If the air is passive, the soul must also be passive. Because the soul is made of air.
Prepared by: Sociologist Ömer YILDIRIM
Source: Omer YILDIRIM’s Personal Lecture Notes. Atatürk University Sociology Department 1st Year “Introduction to Philosophy” and 2nd, 3rd, 4th Grade “History of Philosophy” Lecture Notes (Ömer YILDIRIM); Open Education Philosophy Textbook