5. Pythagoras
From Pre-Socratic Philosophers (1958)

What is known as "the school of Miletus" ends with Anaximenes. That these particular Ionian Greeks pro-ceeded for the time being no further with their speculations and discoveries may be associated with the fact that before the death of Anaximenes the Persians had occupied the Greek Asiatic coast.

The next "schools" of philosophy appear in the Greek cities of southern Italy and the next philosophers are also Ionians. Of them one of the most important, and elusive, is Pythagoras, who came from the island of Samos, probably about 531 B.C., settled in southern Italy and there founded what amounted to a religious order. His society appears to have had political as well as religious and philosophical aims. It was certainty suppressed at some date between 460 and 400 B.C., though survivors of the society carried on their teaching in mainland Greece. With some of these Socrates was acquainted and their doctrines undoubtedly influenced Plato. It is impossible to say what precisely Pythagoras believed himself and very difficult to be sure of what his followers believed. One certain fact seems to be that he, for the first time, made philosophy into something which we would call a religion or a way of life. Thus his attitude was a completely different one from that of the thinkers of Miletus who were great exemplars rather of curiosity than of any feeling that they needed in any way to be "saved." They spoke, certainly, about "gods" and, as we have seen, Thales is said to have pronounced that "all things are full of gods." Put, however this statement may be understood, it cannot be presumed to mean any-thing mystical. We translate the Greek word theos as "god," and there are some Greeks (Aeschylus and Plato for example) who sometimes use the word in a sense not unlike that which we attach to it. As a rule, however, theos means either some "force" or the personification in mythology of some force. It would be quite natural for an early cosmologist, looking objectively at the sun or at the moon or at the stars, and having come to some speculative conclusions about their substance, to pronounce that they were "divine." This would not mean that he acknowledged any personal feeling other than scientific curiosity for these heavenly bodies. As for the particular gods (Zeus, Hera, Aphrodite and so on) the early Ionian philosophers do not seem to have speculated upon their existence or their functions. One may suppose that they presumed them to exist, though it is difficult to see what part they could have played in a universe composed entirely of water, air or the unlimited. Later, as we shall see, it was regarded as reasonable to suppose that "the gods" exist, but have nothing whatever to do with mankind.

However in the seventh and sixth centuries B.C. there seems to have taken place, particularly in Attica and in the Greek cities of Italy and Sicily, something that can be described as a religious revival. We find that "the gods" themselves (and in particular Apollo and Dionysus) are taken much more seriously than they were by the adventurous scientists of Ionia. We find also a different outlook on man. A real distinction is now made between the soul and the body. "Ecstasy" — "the stepping out of oneself" — is acknowledged as a fact and investigated as a hint of some "divine" origin of the soul. There is speculation about life after death, and rules are laid down for pure living which may ensure benefits both here and hereafter.

We are not concerned here with the origin of this religious revival or with what exactly is meant by "Orphism" or with what "the mysteries" were. It is sufficient to point out that this religious movement had its effect on Pythagoras and, through him, on the subsequent history of philosophy. With him philosophy enters, as it were, another sphere. Instead of being simply "curiosity" or "`science" it becomes "a way of life," a religion itself or a substitute for one. Yet it remains concerned with the problem first raised by Thales. The underlying substance or principle is still sought for.

In discussing Pythagoras it will be convenient to distinguish between what we know of him as a religious teacher and what we know of him as a philosopher; but again we must remember that he and his followers did not make this distinction. They simply regarded philosophy and mathematics as "good for the soul," as, in fact, the best and highest form of purification. It seems to have been Pythagoras who first defined "the three lives" by comparing all men to those who attend the Olympic Games. The lowest class are those who come there simply to buy and sell; next are the actual competitors; and the highest class is that of those who are simply there to watch ( theõrein, from which our "theory" and "theoretical" are derived). This idea of the dignity, even the sanctity, of the contemplative or philosophical life is a new idea and was to be further developed. It is a moral idea and implies the consideration of man's duty with regard to his soul and the souls of others. This was not a consideration that had occurred to the inquirers of Miletus, but it was to play a most important part in the discussions of Socrates and in the later semi-religious systems of Stoicism and Epicureanism.

Of the actual religious doctrine of Pythagoras we do not know very much. It seems certain that he believed in the transmigration of souls or in "being born again." It is likely that he taught his followers to abstain from animal flesh on the grounds that there was a kinship between men and animals, though it is impossible to say whether this belief derived from primitive notions of taboo or from the rational reflection that the soul of one of one's deceased friends might be inhabiting the body of some animal killed for the table. We hear too of a number of rather curious prohibitions and injunctions, such as:

Do not eat beans.
Do not touch a white cock.
Do not stir the fire with iron.
When you get out of bed, roll up the bedclothes and smooth out the impress of the body.

These are curiosities. The higher discipline of the school was connected with music and mathematics. Either Pythagoras himself or one of his followers certainly discovered the proof of the theorem which bears his name (the discovery is said to have been celebrated by the sacrifice of an ox) and laid the foundations both of arithmetic and geometry. It is impossible to discuss here the strictly mathematical side of the doctrine. (An excellent account will be found in Samuel Sambursky's The Physical World of the Greeks.) Here we are chiefly interested in how the Pythagoreans attempted to answer the question propounded first by Thales; and it seems certain, from the following account given of them by Aristotle, that they really did hold the view that "things are made of numbers." It was a view which influenced Plato and which, in its more mystical form, has had a long history. It is pos-sible also to maintain that the Pythagoreans laid the foundations of modern mathematical physics. Yet to say that "things are made of numbers" is, of course, to go much further than to say that there are numerical relations between things or even that the laws of the universe can he expressed in mathematical terms. To the Pythagoreans, excited, as was natural enough, by their discoveries, there was something sacred in numbers themselves. Numbers and their arrangements expressed quality as well as quantity. This will become clear from the words of Aristotle ( Metaphysics I). It should be noted that Aristotle in writing about "the so-called Pythagoreans who led the field in mathematics and whose studies convinced them that the principles of that science were of universal application," is writing of an already developed school. Pythagoras himself has become a legendary figure.

So far we have been discussing material and efficient causes as understood by the early philosophers. Contemporary with and even prior to them were the so-called Pythagoreans, who led the field in mathematics and whose studies convinced them that the principles of that science were of universal application.

Numbers, of course, are of their very nature the first of those principles; and the Pythagoreans thought they saw in numbers, rather than in fire or earth or water, many re-semblances to things which exist and which come into being. They also realized that the properties and ratios of musical scales depend on numbers. In a word, they saw that other things, in respect of the whole of their natures, resemble numbers, and that numbers are the primary elements of the whole of nature. Hence they considered the principles of numbers as the principles of all things, and the whole universe as a harmony or number. Moreover, they collected and systematized all the instances they could find of correspondence between (1) numbers or harmonies and (2) the properties and relations of the heavens and the whole universal order. If anything was lacking to complete their theories, they quickly supplied it. They held, for instance, that ten is a perfect number and embraces all the powers of number. On this view they asserted that there must be ten heavenly bodies; and as only nine were visible they invented the "counter-earth" to make a tenth.

I have discussed these theories in greater detail elsewhere. My purpose in referring to them now is only to discover what causes were recognized by the Pythagoreans and how they compare with my own list. Well, the Pythagoreans evidently treated numbers both as the material principle and as that which makes things what they are temporarily or permanently. They also held (1) that the principles of number are the Even (or Unlimited or Indefinite) and the Odd (or Limited or Definite); (2) that Unity (because it is both even and odd) is produced out of these two and number out of Unity; and (3) that number, as I have said, constitutes the whole sensible world.
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