Pythagorean thought was dominated by mathematics, and it was profoundly mystical. In the area of cosmology there is less agreement about what Pythagoras himself actually taught, but most scholars believe that the Pythagorean idea of the transmigration of the soul is too central to have been added by a later follower of Pythagoras. The Pythagorean conception of substance, on the other hand, is of unknown origin, partly because various accounts of his teachings are conflicting. The Pythagorean account actually begins with Anaximander's teaching that the ultimate substance of things is "the boundless," or what Anaximander called the "apeiron." The Pythagorean account holds that it is only through the notion of the "limit" that the "boundless" takes form.
Pythagoras wrote nothing down, and relying on the writings of Parmenides, Empedocles, Philolaus and Plato (people either considered Pythagoreans, or whose works are thought deeply indebted to Pythagoreanism) results in a very diverse picture in which it is difficult to ascertain what the common unifying Pythagorean themes were. Relying on Philolaus, whom most scholars agree is highly representative of the Pythagorean school, one has a very intricate picture. Aristotle explains how the Pythagoreans (by which he meant the circle around Philolaus) developed Anaximander's ideas about the apeiron and the peiron, the unlimited and limited, by writing that:
... for they [the Pythagoreans] plainly say that when the one had been constructed, whether out of planes or of surface or of seed or of elements which they cannot express, immediately the nearest part of the unlimited began to be drawn in and limited by the limit.
Continuing with the Pythagoreans:
The Pythagoreans, too, held that void exists, and that it enters the heaven from the unlimited breath – it, so to speak, breathes in void. The void distinguishes the natures of things, since it is the thing that separates and distinguishes the successive terms in a series. This happens in the first case of numbers; for the void distinguishes their nature.
The Pythagoreans are known for their theory of the transmigration of souls, and also for their theory that numbers constitute the true nature of things. They performed purification rites and followed and developed various rules of living which they believed would enable their souls to achieve a higher rank among the gods. Much of their mysticism concerning the soul seems inseparable from the Orphic tradition. The Orphics included various purifactory rites and practices as well as incubatory rites of descent into the underworld. Apart from being linked with this, Pythagoras is also closely linked with Pherecydes of Syros, the man ancient commentators tend to credit as the first Greek to teach a transmigration of souls. Ancient commentators agree that Pherecydes was Pythagoras's most "intimate" teacher. Pherecydes expounded his teaching on the soul in terms of a pentemychos ("five-nooks," or "five hidden cavities") — the most likely origin of the Pythagorean use of the pentagram, used by them as a symbol of recognition among members and as a symbol of inner health (eugieia Eudaimonia).
Wheel of Birth and Scientific Contemplation Edit
The Pythagoreans believed that a release from the "wheel of birth" was possible. They followed the Orphic traditions and practices to purify the soul but at the same time they suggested a deeper idea of what such a purification might be. Aristoxenus said that music was used to purify the soul just like medicine was used to purge the body. But in addition to this, Pythagoreans distinguished three kinds of lives: Theoretic, Practical and Apolaustic. Pythagoras is said to have used the example of Olympic games to distinguish between these three kind of lives. Pythagoras suggests that the lowest class of people who come to the games are the people who come to buy or sell. The next higher class comprises people who come to participate in the games. And the highest class contains people who simply come to look on. Thus Pythagoras suggests that the highest purification of a life is in pure contemplation. It is the philosopher who contemplates about science and mathematics who is released from the "cycle of birth." The pure mathematician's life is, according to Pythagoras, the life at the highest plane of existence.
Thus the root of mathematics and scientific pursuits in Pythagoreanism is also based on a spiritual desire to free oneself from the cycle of birth and death. It is this contemplation about the world that forms the greatest virtue in Pythagorean philosophy.
The Pythagoreans were well known in antiquity for their vegetarianism, which they practised for religious, ethical and ascetic reasons, in particular the idea of metempsychosis – the transmigration of souls into the bodies of other animals. "Pythagorean diet" was a common name for the abstention from eating meat and fish, until the coining of "vegetarian" in the 19th century.
The Pythagorean code further restricted the diet of its followers, prohibiting the consumption or even touching of any sort of bean. It is probable that this is due to their belief in the soul, and the fact that beans obviously showed the potential for life. Some, for example Cicero, say perhaps the flatulence caused by beans is an emergency response system, as protection from potential favism, perhaps because they resemble the kidneys and genitalia, but most likely for magico-religious reasons such as the belief that beans and human beings were created from the same material. Most stories of Pythagoras' murder revolve around his aversion to beans. According to legend, enemies of the Pythagoreans set fire to Pythagoras' house, sending the elderly man running toward a bean field, where he halted, declaring that he would rather die than enter the field – whereupon his pursuers slit his throat. Susceptible persons may develop a hemolytic anemia by eating the beans, or even by walking through a field where the plants are in flower.
Views on Women Edit
Women were given equal opportunity to study as Pythagoreans, and learned practical domestic skills in addition to philosophy. Women were held to be different from men, but sometimes in good ways. The priestess, philosopher and mathematician Themistoclea is regarded as Pythagoras' teacher; Theano, Damo and Melissa as female disciples. Pythagoras is also said to have preached that men and women ought not to have sex during the summer, holding that winter was the appropriate time.