Socrates is considered one of the most important figures in the history of Western philosophy, but he is not a Pre-Socratic philosopher. The Pre-Socratic philosophers were active before Socrates and focused on the natural world and the origins of the universe, while Socrates focused on ethical and political questions.

Empedocles is known for his theory of the four elements, which states that all matter is composed of four basic elements: earth, air, fire, and water. He believed that these elements could combine in different proportions to create different substances.

Democritus is known for his theory of the atom, which states that all matter is composed of tiny, indivisible particles called atoms. He believed that atoms were eternal and unchanging and that they could combine in different ways to create different substances.

Parmenides is known for his theory of the void, which states that there is no such thing as empty space. He believed that the universe is a plenum, or a completely filled space, and that there is no room for anything else to exist.

Xenophanes is known for his theory of the One, which states that there is only one god who is eternal, unchanging, and indivisible. He believed that this god is the source of all things and that everything in the universe is a manifestation of this god.

Heraclitus is known for his theory of the Logos, which states that there is a universal law or principle that governs the universe. He believed that this law is constantly changing and that everything in the universe is in a state of flux. He is also known for his famous saying, "Everything flows.

Anaxagoras is known for his theory of the Nous, which states that there is a universal mind or intelligence that governs the universe. He believed that this mind is separate from the material world and that it is the source of all order and purpose in the universe.

Anaximander is known for his theory of the Apeiron, which states that there is an infinite and eternal substance that is the source of all things. He believed that this substance is not material and that it is the source of all change and motion in the universe.

Thales of Miletus is known for his theory of the Arche, which states that there is a single, underlying substance that is the source of all things. He believed that this substance is water and that everything in the universe is made up of water.

Anaximander is known for his theory of the Physis, which states that there is a natural order or law that governs the universe. He believed that this law is responsible for the birth, growth, and decay of all things.

Anaximenes is known for his theory of the Cosmos, which states that the universe is a single, ordered system. He believed that the universe is made up of air and that everything in the universe is a manifestation of air.

Pythagoras is known for his theory of the Spheres, which states that the universe is made up of a series of concentric spheres. He believed that the Earth is at the center of the universe and that the other planets and stars revolve around it.

Pythagoras is known for his theory of the Harmony of the Spheres, which states that the movement of the planets and stars creates a beautiful and harmonious sound. He believed that this sound is inaudible to humans, but that it is the source of all music and harmony in the universe.

Pythagoras is known for his theory of the Golden Mean, which states that there is a perfect ratio or proportion that is found in nature and art. He believed that this ratio is approximately 1.618 and that it is the source of beauty and harmony in the universe.

Pythagoras is known for his theory of the Transmigration of Souls, which states that the soul is immortal and that it passes from one body to another after death. He believed that the soul is purified through this process and that it eventually reaches a state of perfection.