# What is Pythagorean Number Theory?

June 27, 2021 Off By Felso

The Pythagoreans conducted studies on the reality of form and relationship in the world.

They introduce the idea of ​​a measure, order, proportion and formation of a shape that can be expressed in numbers. They claim that in the absence of these numbers, there would be no relationship, order or law in the world. For this reason, numbers should be the basis of everything. Numbers should be real facts. Everything should be expressed in numbers.

According to the Pythagoreans, numbers are the fundamental principles of things. They consider this as a more formal or relational structure, not with the sense of matter or matter as in the Miletus School. Objects are copies or imitations of numbers. The distinction between matter and form, which is the central point of Plato and Aristotle systems, of metaphysics is made between numbers and objects in Pythagoreans. The Pythagoreans, instead of today’s laws of nature, reveal the existence of numbers similar to them. In their view, there is a numerical relationship in everything. For example, there is a numerical correlation between the length of a string and the decrease in tone of voice.

If numbers are the fundamental principle of objects, it is necessary to investigate what exactly these numbers are. The Pythagoreans devoted themselves to discovering the properties found in numbers. Their relevance to the universe also forms part of their work. Numbers can be distinguished as odd and even; Even numbers are divisible by two, and odd numbers are not. Even numbers are unlimited. Nature itself is a unity of opposites, the single and the double, the limited and the unlimited. Numerous similar oppositions can be counted: limited and unlimited; single and double; one and many; right and left; male and female; stasis and motion; straight and curved; light and darkness; good and bad; square and rectangular. The traces of Pythagoras’ dualism (duality) of limited and unlimited and their harmony are seen in Anaximandros and Anaximenes. The doctrine of the conflict of opposites has already been put forward by Anaximander. The Pythagoreans put the unlimited before the limited; individual things are posited through the delimitation of unlimited space by means of forms in space.

The corporeal world is also numerical and based on a unit. Point one, line two, figure three, solid four. The earth is a cube; fire is a tetrahedron; water icosa-hedron, etc. In other words, the lines and surfaces of the structures are considered as independent entities; For three, there is no body without lines and surfaces. Lines and surfaces are unthinkable without bodies. Spatial forms are causes of bodies. And so these forms can be expressed with numbers. Arithmetic distinctions are thus carried over to the physical world. The Pythagoreans are guided by this transition to the doctrine of an unlimited space, or they nullify oppositions to finite bodies in space. The number-mystic influence of the Pythagoreans on physics and astronomy can be discerned; For example, there are Pythagorean and Neo-Pythagorean traces in Kepler’s theories.

Although fantastic relations have been established between numbers and objects, the historical view of Pythagorean number-mysteryism emerges as an important structure of thought. This thought is devoted to the finding of stability and order in objects. Meaningful formulas are sought in abstract terms of numbers and numerical relations. From the historical source of natural laws that can be expressed mathematically, it is a subject that contemporary science and contemporary philosophy continue to study.

Prepared by: Sociologist Ömer YILDIRIM
Source: Omer Yıldırım’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