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.

Leucippus is known for his theory of the void, which states that there is a void or empty space between atoms.

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

Anaximander is known for his theory of the plurality of being, which states that there are many different kinds of beings, each with its own unique properties.

Anaximander is known for his theory of the infinite, which states that the universe is infinite in size and scope.

Pythagoras is known for his theory of the transmigration of souls, which states that the soul passes through a cycle of rebirth after death.

Pythagoras is known for his theory of the golden mean, which is a mathematical ratio that is considered to be aesthetically pleasing.

Aristotle is known for his theory of the four causes, which states that every event has four causes: a material cause, a formal cause, an efficient cause, and a final cause.

Plato is known for his theory of the ideal forms, which states that there is a realm of perfect, unchanging forms that exist independently of the physical world.

Plato is known for his theory of the divided line, which is a diagram that represents the different levels of reality, from the physical world to the realm of the ideal forms.

Plato is known for his theory of the soul, which states that the soul is an immortal, immaterial substance that is distinct from the body.

Aristotle is known for his theory of the Nicomachean Ethics, which is a treatise on moral philosophy that discusses the nature of happiness and the good life.