Pythagoras's Mathematical Philosophy
The Pythagorean Theorem is probably Pythagoras's most famous contribution, establishing that in a right triangle, the square of the hypotenuse equals the sum of the squares of the other two sides. Though known to earlier cultures, the Pythagoreans proved it and used it extensively.
Pythagoras and his school believed numbers were the essence of all things and that numerical relationships could explain natural phenomena. They developed a theory of proportions and studied properties of numbers, such as even and odd numbers, perfect numbers, and friendly numbers.
Pythagoras discovered that musical intervals could be expressed as simple numerical proportions. This observation led to the formulation of musical harmony theory, where strings vibrating in specific proportions produce pleasing sounds. The Pythagoreans applied this theory to cosmology, proposing the idea of the "music of the spheres," where celestial bodies moved according to harmonic proportions.
Parmenides of Elea: Being and Non-Being
Parmenides 515−450BCE was a Presocratic Greek philosopher and founder of the Eleatic school of philosophy. Born in Elea, a Greek colony in southern Italy, Parmenides came from a noble family and played an important role in Elea's political life.
Most of what we know about Parmenides comes from fragments of his poem "On Nature" and references in later philosophers' works. The poem divides into two parts: the way of truth (aletheia) and the way of opinion (doxa).
In the way of truth, Parmenides argues that being is, and non-being is not. This radical assertion suggests that only being exists and that change, multiplicity, and becoming are illusions. According to Parmenides, being is eternal, immutable, indivisible, and complete. The poem begins with a goddess revealing truth to Parmenides, stating there is only one path for thought: that being is, since thinking about non-being is impossible and inconceivable.
The way of opinion describes the world of appearance and human opinion, where people believe in multiplicity and change. Parmenides considers these beliefs misleading and not reflecting being's true nature.
Parmenides is known for his contribution to ontology. He maintains that being is a unique, continuous, and homogeneous entity. This idea challenges traditional notions of change and plurality and presents a challenge to sensory perception and common thought.