Socrates is not a Pre-Socratic philosopher because he lived and taught in the 5th century BCE, while the Pre-Socratic philosophers lived and taught in the 6th and 5th centuries BCE.

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.

Democritus is known for his theory of the atom, which states that all matter is composed of tiny, indivisible particles called atoms.

Heraclitus is known for his theory of the logos, which is a universal principle that governs the universe.

Anaximander is known for his theory of the void, which is an infinite, boundless space that surrounds the universe.

Parmenides is known for his theory of the One, which states that there is only one true reality, which is unchanging and indivisible.

Anaxagoras is known for his theory of the Many, which states that there are an infinite number of different substances, each of which has its own unique properties.

Zeno of Elea is known for his theory of the paradoxes, which are a series of logical arguments that seem to prove that motion is impossible.

Pythagoras is known for his theory of the soul, which states that the soul is immortal and transmigrates from one body to another after death.

Pythagoras is known for his theory of the golden mean, which is a mathematical ratio that is pleasing to the eye and is often used in art and architecture.

Pythagoras is known for his theory of the music of the spheres, which states that the planets and stars move in a harmonious pattern that produces a beautiful sound.

Aristotle is known for his theory of the four causes, which states that there are four different types of causes: the material cause, the formal cause, the efficient cause, and the final cause.

Aristotle is known for his theory of the syllogism, which is a logical argument that consists of two premises and a conclusion.

Aristotle is known for his theory of the categories, which is a system for classifying different types of things into different groups.

Plato is known for his theory of the soul, which states that the soul is immortal and is the true essence of a person.