The pythagoreans (stanford encyclopedia)

Pythagoreanism can be defined in a number of ways.

(1) Pythagoreanism is the philosophy of the ancient Greek philosopher Pythagoras (ca. 570 – ca. 490 BCE), which prescribed a highly structured way of life and espoused the doctrine of metempsychosis (transmigration of the soul after death into a new body, human or animal).

(2) Pythagoreanism is the philosophy of a group of philosophers active in the fifth and the first half of the fourth century BCE, whom Aristotle refers to as “the so-called Pythagoreans” and to whom Plato also refers. Aristotle’s expression, “so-called Pythagoreans,” suggests both that at his time this group of thinkers was commonly called Pythagoreans and, at the same time, calls into question the actual connection between these thinkers and Pythagoras himself. Aristotle ascribes no specific names to these Pythagoreans, but the philosophy which he assigns to them is very similar to what is found in the fragments of Philolaus of Croton (ca. 470-ca. 390 BCE). Thus, Philolaus and his successor Eurytus are likely to have been the most prominent of these Pythagoreans. Philolaus posits limiters and unlimiteds as first principles and emphasizes the role of number in understanding the cosmos. Aristotle also identifies a distinct group of these so-called Pythagoreans who formulated a set of basic principles known as the table of opposites. Plato’s sole reference to Pythagoreans cites their search for the numerical structure of contemporary music and is probably an allusion to Archytas (ca. 420-ca. 350 BCE), who is the first great mathematician in the Pythagorean tradition. Starting from the system of Philolaus he developed his own sophisticated account of the world in terms of mathematical proportion.

(3) Many other sixth-, fifth- and fourth-century thinkers are labeled Pythagoreans in the Greek tradition after the fourth century BCE. By the late fourth century CE many of the most prominent Greek philosophers including Parmenides, Plato and Aristotle come to be called Pythagoreans, with no historical justification. There are nonetheless a number of thinkers of the fifth and fourth century BCE, who can legitimately be called Pythagoreans, although often little is known about them except their names. The most important of these figures is Hippasus.

(4) The last manifestation of Pythagoreanism, Neopythagoreanism, has been the most influential. Neopythagoreanism is not a unified school of thought but rather a tendency, stretching over many centuries, to view Pythagoras, with no historical justification, as the central and original figure in the whole Greek philosophical tradition. This Pythagoras is often thought to have received his philosophy as a divine revelation, which had been given even earlier to wise men of the ancient Near East such as the Persian Magi, the Hebrews (Moses in particular), and the Egyptian priests. All Greek philosophy after Pythagoras, insofar as it may be true, is seen as derived from this revelation. Thus, Plato’s and Aristotle’s ideas are viewed as derived from Pythagoras (with the mediation of other early Pythagoreans). Many pseudepigrapha are produced in later times in order to provide the Pythagorean “originals” on which Plato and Aristotle drew. Some strands of the Neopythagorean tradition emphasize Pythagoras as master metaphysician, who supposedly originated what are, in fact, the principles of Plato’s later metaphysics, the one and the indefinite dyad. Other Neopythagoreans celebrate Pythagoras as the founder of the quadrivium of mathematical sciences (arithmetic, geometry, astronomy and music), while still others portray him as a magician or as a religious expert and sage, upon whom we should model our lives. Neopythagoreanism began already in the second half of the fourth century BCE among Plato’s first successors in the Academy, but particularly flourished from the first century BCE until the end of antiquity. Neopythagoreanism has close connections to Middle and Neoplatonism and from the time of Iamblichus (4th c. CE) is largely absorbed into Neoplatonism. It was the Neopythagorean version of Pythagoreanism that dominated in the Middle Ages and Renaissance.

About the concept of “Nemesis”

This retribution, which has a geometrical rigor, which operates automatically to penalize the abuse of force, was the main subject of Greek thought. It is the soul of the epic. Under the name of Nemesis, it functions as the mainspring of Aeschylus’ tragedies. To the Pythagoreans, to Socrates and Plato, it was the jumping-on point of speculation upon the nature of man and the universe. Wherever Hellenism has penetrated, we find the idea of it familiar. In Oriental countries which are steeped in Buddhism, it is perhaps this Greek idea that has lived on under the name of Karma. The Occident, however, has lost it, and no longer even has a word to express it in any of its languages: conceptions of limit, measure, equilibrium, which ought to determine the conduct of life, are in the West, restricted to a servile function in the vocabulary of technics. We are only geometricians of matter; the Greeks were, first of all, geometricians in their apprenticeship to virtue.

Simone Weil

Anaximander

Anaximander was the author of the first surviving lines of Western philosophy. He speculated and argued about “the Boundless” as the origin of all that is. He also worked on the fields of what we now call geography and biology. Moreover, Anaximander was the first speculative astronomer. He originated the world-picture of the open universe, which replaced the closed universe of the celestial vault.

Anaximenes

According to the surviving sources on his life, Anaximenes flourished in the mid 6th century BCE and died around 528. He is the third philosopher of the Milesian School of philosophy, so named because like Thales and Anaximander, Anaximenes was an inhabitant of Miletus, in Ionia (ancient Greece). Theophrastusnotes that Anaximenes was an associate, and possibly a student, of Anaximander’s.

Anaximenes is best known for his doctrine that air is the source of all things. In this way, he differed with his predecessors like Thales, who held that water is the source of all things, and Anaximander, who thought that all things came from an unspecified boundless stuff.

Thales

The ancient Greek philosopher Thales was born in Miletus in Greek Ionia. Aristotle, the major source for Thales’s philosophy and science, identified Thales as the first person to investigate the basic principles, the question of the originating substances of matter and, therefore, as the founder of the school of natural philosophy. Thales was interested in almost everything, investigating almost all areas of knowledge, philosophy, history, science, mathematics, engineering, geography, and politics. He proposed theories to explain many of the events of nature, the primary substance, the support of the earth, and the cause of change. Thales was much involved in the problems of astronomy and provided a number of explanations of cosmological events which traditionally involved supernatural entities. His questioning approach to the understanding of heavenly phenomena was the beginning of Greek astronomy. Thales’ hypotheses were new and bold, and in freeing phenomena from godly intervention, he paved the way towards scientific endeavor. He founded the Milesian school of natural philosophy, developed the scientific method, and initiated the first western enlightenment. A number of anecdotes is closely connected to Thales’ investigations of the cosmos. When considered in association with his hypotheses they take on added meaning and are most enlightening. Thales was highly esteemed in ancient times, and a letter cited by Diogenes Laertius, and purporting to be from Anaximenes to Pythagoras, advised that all our discourse should begin with a reference to Thales (D.L. II.4).

From the Heraclitus Seminar of Martin Heidegger and Eugen Fink

I open the seminar with hearty thanks to Professor Heidegger for his readiness to assume spiritual leadership in our common attempt to advance into the area of the great and historically important thinker Heraclitus. Heraclitus’ voice, like that of Python, reaches us over a thousand years. Although this thinker lived at the origin of the West, and to that extent is longest past, we have not overtaken him even now.
From Martin Heidegger’s dialogue with the Greeks, in many of his writings, we can learn how the furthest becomes near and the most familiar becomes strange, and how we remain restless and are unable to rely on a sure interpretation of the Greeks. For us, the Greeks signify an enormous challenge. Our seminar should be an exercise in thinking, that is, in reflection on the thoughts anticipated by Heraclitus. Confronted with his texts, left to us only as fragments, we are not so much concerned with the philological problematic, as important as it might be,’ as with advancing into the matter itself, that is, toward the matter that must have stood before Heraclitus’ spiritual view. This matter is not simply on hand like a result or like some spoken tradition; rather, it can be opened up or blocked from view precisely through the spoken tradition. It is not correct to view the matter of philosophy, particularly the matter of thinking as Martin Heidegger has formulated it, as a product lying before us. The matter of thinking does not lie somewhere before us like a land of truth into which one can advance; it is not a thing that we can discover and uncover. The reality of, and the appropriate manner of access to, the matter of thinking is still dark for us. We are still seeking the matter of thinking of the thinker Heraclitus, and we are therefore a little like the poor man who has forgotten where the road leads. Our seminar is not concerned with a spectacular business. It is concerned, however, with serious minded work. Our common attempt at reflection will not be free from certain disappointments and defeats. Nevertheless, reading the text of the ancient thinker, we make the attempt to come into the spiritual movement that releases us to the matter that merits being named the matter of thinking.