A philosopher active around 500 BCE, that wrote a book; this gives us a direct path to his thoughts. He felt that wisdom should be earned, he wrote obscurely, so much so that his book was challenging to read.

He developed a cosmology. His cosmos has no beginning or end and is fundamentally made of fire. This fire can transform to become water, earth, and air. It is always in flux but keeps the elements in proportion. This constant change was the way of everything and was needed to keep the world stable. 

He was one of the most influential pre-Socratic thinkers.

Parmenides argued that change was an illusion based on our faulty image of reality. He explained that nothing could be created or destroyed and everything was really “one being." That is, all substances are part of the same larger whole.

As he thought that it was impossible to conceive of “nothingness" he also argued that empty space was an impossibility. This lead him to declare motion to be impossible, as any movement would require empty space to move into.

He was a pioneer of the reductio ad absurdum argument. Aristotle credited him with co-inventing the dialectic method of philosophy.

He is best remembered for his paradoxes. His best-known paradox suggests that movement is impossible. He asks us to imagine a runner on a track. He notes that before the runner can run the whole length, they must first run the first half, then a quarter, then an eighth, and so on.

Several potential solutions have been put forth to his paradoxes and debate continues to this day. The potential answers to his paradoxes have influenced discussions about time, space, and how we perceive reality.

Diogenes founded the Cynical school of philosophy, a school dedicated to simple living and virtue. Advocating a simple, disciplined, self-sufficient life, Diogenes lived in a large jar and owned nothing but a cloak and staff. He begged for food and avoided luxuries like the plague.

He is said to have written a few (lost) essays but is better known for using actions to educate. He would walk down the street backward in an attempt to make people question why they walked forwards and begged from statues to show that he was not concerned with rejection.

The founder of the Stoic school of philosophy, Zeno was heavily influenced by the Cynics.

Initially a wealthy merchant, he became interested in philosophy during a trip to Athens and grew to be a highly regarded teacher. 

Stoicism is a philosophy dedicated to helping its students live the good life. The ancient Stoics believed the universe had a rational, perhaps divine, structure to it and held that while the laws of physics dictated what happened externally, we were still free to choose how we would react to it. They argued that a rational man should strive to live virtuously, and devoted a great deal of time to the question of ethics.