The object of this paper is to show that, in the sixth and fifth centuries B.C., two different and radically opposed systems of thought were elaborated within the Pythagorean school. They may be called respectively the mystical system and the scientific. All current accounts of Pythagoreanism known to me attempt to combine the traits of both systems in one composite picture, which naturally fails to hold together. The confusion goes back to Aristotle, who usually speaks indiscriminately of ‘the Pythagoreans,’ though (...) now and then the phrase ‘some Pythagoreans’ indicates that he was aware of different currents within the school. (shrink)

We can now approach the interpretation of the famous symbol called the Tetractys or Tetrad, which is a compendium of Pythagorean mysticism. The tetractys is itself a system of numbers. It symbolizes the ‘elements of number,’ which are the elements of all things. It contains the concordant ratios of the musical harmony. It might well be described in the Pythagorean oath as ‘containing the root and fountain of everflowing Nature.’ In one of the acousmata preserved in Iamblichus it is identified (...) with the cosmic harmony. It was also called κσμος, ορανς, πν. Theon says it was held in honour because it contained the nature of the universe. (shrink)