The followers of Aristotle were called the "peripatetics", and often his general "school" of philosophy is called "peripatetic" or "peripateticism." This name comes from the one of two sources. On the one hand, his school in Athens had colonnades in which the instruction perhaps occurred. The Greek for "colonnade" is peripatoi. On the other hand, however, it is also said that Aristotle walked while lecturing. The word for "a walker" in Greek is peripatetikos. Hence, he would walk back and forth with his students, lecturing. From this one little habit (or, perhaps, the aforementioned colonnades), there arose a title that was affixed to philosophers for over two millennia!

It is said that Saul of Tarsus was an early convert to Christianity after having a major conversion experience on the way to Damascus. He was an active persecutor of the early followers of Jesus. Upon his conversion, he changed his name to Paul and was a very active member of the young Christian community. In the course of his many travels throughout the Mediterranean, he penned a number of letters that would have incalculable influence on the future of Western thought. Even to this day, secular thought has changed in the West due to the many influences exerted by Paul's epistles. Not only are the ideals of Catholicism and Orthodoxy influenced by Paul; Protestantism in all of its varied forms has a deep and lasting debt to his epistles, the theology of which was very influential on early Protestant thought. From the Enlightenment onward, it became very normal to see Paul as a kind of "perverter" of the primitive message of Jesus. Even where Paul was rejected, these later thinkers were still working within a framework that was defined by many of his insights—whether or not those thinkers realized it in their reactions. 

Among the epistles that are almost certainly of Pauline origin, the following are generally included: Romans, First and Second Corinthians, First Thessalonians, Galatians, Philippians, and Philemon. Other epistles, traditionally attributed to Paul, are debated among modern scholars, who believe that they may have been written by others who wrote under Paul's name. These letters are Second Thessalonians, Colossians, Ephesians, First and Second Timothy, and Titus.

Even for one who is purely secular in his or her outlook, a surface-level knowledge of Paul's writing is essential for understanding a major and important vein of the Western intellectual heritage.

The probably apocryphal Lao Tze was the author of the book of poetry the Tao Te Ching, which is the foundational text for the philosophy known as Taoism. While many passages are ambiguous and worded in an unusual way, the philosophy largely argues for allowing the "Tao," a spiritual force, to flow through a human's life. The book heavily influenced later Chinese thought, such as Confucianism and Chan Buddhism.

The Poetics were the first comprehensive approach to defining the key elements and requirements of the dramatic form. Tellingly, its author, Aristotle, was a great philosopher, rather than a great playwright or poet. The work features Aristotle's deep, systematic thinking, applied specifically to what is widely considered the "poetic arts," including lyric poetry, epic poetry, tragedy, comedy, and the satyr play.

The great Aristotle was the student of an equally great philosopher, namely Plato. Indeed, Aristotle spent 20 years at Plato's Academy! He didn't do this merely because he was a slouch who didn't want to get a job. Instead, during this many years of learning, Aristotle imbibed much of Plato's thought. His later writings would in many ways temper and limit the excesses of his master. Nevertheless, when one reads Aristotle, one can sense the discussions of the Academy as being directly behind the scenes of Aristotle's own concerns.

Augustine of Hippo (354-430) has probably had more influence on Western society than almost any other person in all of history. This is almost certain when we limit ourselves to authors of Latin texts. After many years as a successful rhetorician (living a dissipate lifestyle), Augustine converted to Christianity. He was soon the Bishop of Hippo and became a prolific writer. His thought would influence Western Christianity throughout all of the Middle Ages and would be an important touch point throughout numerous reformations and revolutions within Western Christendom down to the present day. Indeed, during the Middle Ages, for example, there were two great authorities—the Greek man, Aristotle, and Augustine.

In the Confessions, Augustine tells the tale of his conversion—giving a long history of his life as well as his beliefs. This text is amazing for its personal depth and is a unique testimony of someone's psyche during the period of late antiquity.

Interestingly, one of the great founders of philosophy did not actually write anything that we know of. Almost all that we know of him comes from the reports we have received from Plato as well as the play Clouds by Aristophanes. The bulk of the material, in any case, comes from Plato. In his dialogues, Plato portrays Socrates as discussing philosophical matters with various Athenians. Likely, Plato puts some of his own positions on the lips of Socrates. Nevertheless, if we want to puzzle out just what was the "philosophy of Socrates" our only real source can be found in Plato's dialogues.

The Pre-Socratics are so named merely because of their place in history. They came before Socrates. Socrates is like a "dividing line" for Greek philosophical history! In any case, the Pre-Socratics like Thales and Anaxagoras were interested in the basic elements from which all things were made and how those elements became what we know of in our experience. Other thinkers like Heraclitus and Parmenides were interested in more esoteric questions about being and non-being. In some ways, these thinkers were interested in "metaphysics"—especially Parmenides and Heraclitus. More broadly, the group was interested in cosmology or the way the world is to be understood philosophically. Hence, the best overall category for them is that of "natural philosophy", understanding that all of these terms were coined after the time of the pre-Socratics. With Socrates, philosophy took on a very human-centered and ethical set of concerns.

Origen was one of the early Christian "fathers" in Egypt in the third century AD. He was heavily influenced by Neo-Platonic philosophy, and some of his views ended with him being condemned. He wrote extensively on the Hebrew and Christian scriptures with great critical skills for his times. He remained an influential figure on the Egyptian monastic movement and, today, is held in esteem by contemporary Christians, even if he is not accorded the status of being a "Saint."

This question is referring to the famous paradox of Zeno, often called the "Paradox of Achilles and the Tortoise." The idea is that if the turtle is in front of the runner, there will be an infinite number of points through which the runner will have to pass in order to reach the Tortoise. No matter how fast Achilles runs, this infinite number of points will take an infinite amount of time for him to pass through. Thus, he will never arrive at the Tortoise.

This problem seems strange (and perhaps just idiotic), but it comes down to a confusion that one must be careful not to make. Between two points in space, there are potentially an infinite number of points if we keep dividing that space (considered mathematically, at least). Actually, however, there are not an infinite amount. At least, this is how a follower of Aristotle would answer Zeno. This paradox was just one of many that Zeno used to defend Parmenides.