PHILOSOPHY AND IDEAS

Pythagoreanism is the philosophy of a group of thinkers active in the fifth and first half of the fourth centuries BCE, whom Aristotle and Plato both refer to as "the so-called Pythagoreans." The phrase "so-called Pythagoreans" used by Aristotle implies that this group of philosophers was known as Pythagoreans at the time while also casting doubt on the actual connection between these thinkers and Pythagoras himself. Aristotle does not give these Pythagoreans any names, but the philosophy he ascribes to them is highly similar to that contained in Philolaus of Croton's fragments (ca. 470-ca. 390 BCE). As a result, Philolaus and his successor Eurytus were most likely the most prominent Pythagoreans. Limiters and unlimited are primary principles for Philolaus, who emphasizes the importance of numbers in understanding the cosmos. Aristotle also recognizes a unique group of these so-called Pythagoreans as the creators of the table of opposites, a collection of fundamental ideas. Plato's only mention of Pythagoreans is regarding their search for the numerical pattern of modern music and is most likely an allusion to Archytas (ca. 420-ca. 350 BCE), the Pythagorean tradition's first great mathematician. He built his complex description of the world in mathematical proportions based on Philolaus' method.

Philolaus and Archytas, Pythagoras' successors in the Pythagorean tradition, pushed Pythagoras' cosmos in a more scientific and mathematical direction. Pythagoras successfully established a new, more positive vision of the soul's fate after death, as well as a style of life that was appealing for its rigor and discipline and brought a large number of committed followers to him.

After the fourth century BCE, many more sixth-, fifth-, and fourth-century thinkers were dubbed Pythagoreans in the Greek tradition. Many of the most important Greek thinkers, including Parmenides, Plato, and Aristotle, were dubbed Pythagoreans without historical justification by the late fourth