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from eastern Hellas. Now it has been pointed out that Greek philosophy was based on science, and science originated at Miletus on the mainland of Asia Minor nearly opposite the island of Samos, which was the original home of Pythagoras. The early Milesians were, in fact, men of science rather than philosophers in the strict sense. The two things were not differentiated yet, however, and the traditional account of the matter, according to which Greek philosophy begins with Thales (c. 585 BC), is after all quite justified. The rudimentary mathematical science of which, as explained elsewhere in this volume, he was the originator in fact led him and his successors to ask certain questions about the ultimate nature of reality, and these questions were the beginning of philosophy on its theoretical side. It is true that the Milesians were unable to give any but the crudest answers to these questions, and very likely they did not realise their full importance. These early inquirers only wanted to know what the world was made of and how it worked, but the complete break with mythology and traditional views which they effected cleared the way for everything that followed. It was no small thing that they were able to discard the old doctrine of what were afterwards known as the ‘elements’—Fire, Air, Earth, and Water—and to regard all these as states of a single substance, which presented different appearances according as it was more or less rarefied or condensed. Moreover, Anaximander at least (c. 546 BC), the successor of Thales, shook himself free of the idea that the earth required support of some kind to keep in its place. He held that it swung free in space and that it remained where it was because there was no reason for it to fall in one direction rather than another. In general these early cosmologists saw that weight was not an inherent quality of bodies and that it could not be used to explain anything. On the contrary, weight was itself the thing to be explained. Anaximander also noted the importance of rotary or vortex motion in the cosmical scheme, and he inferred that there might be an indefinite number of rotating systems in addition to that with which we are immediately acquainted. He also made some very important observations of a biological character, and he announced that man must be descended from an animal of a different species. The young of most animals, he said, can find their food at once, while that of the human species requires a prolonged period of nursing. If, then, man had been originally such as he is now, he could never have survived. All this, no doubt, is rudimentary science rather than philosophy, but it was the beginning of philosophy in this sense, that it completely transformed the traditional view of the world, and made the raising of more ultimate problems inevitable.

      This transformation was effected in complete independence of religion. What we may call secularism was, in fact, characteristic of all eastern Ionian science to the end. We must not be misled by the fact that Anaximander called his innumerable worlds ‘gods’ and that his successor Anaximenes spoke of Air as a ‘god’. These were never the gods of any city and were never worshipped by any one, and they did not therefore answer at all to what the ordinary Greek meant by a god. The use of the term by the Milesians means rather that the place once occupied by the gods of religion was now being taken by the great fundamental phenomena of nature, and the later Greeks were quite right, from their own point of view, in calling that atheism. Aristophanes characterizes this way of speaking very accurately indeed in the Clouds when he makes Strepsiades sum up the teaching he has received in the words ‘Vortex has driven out Zeus and reigns in his stead’, and when he makes Socrates swear by ‘Chaos, Respiration and Air’. So too the Milesians spoke of the primary substance as ‘ageless and deathless’, which is a Homeric phrase used to mark the difference between gods and men, but this only means that the emotion formerly attached to the divine was now being transferred to the natural.

       The Milesians, then, had formed the conception of an eternal matter out of which all things are produced and into which all things return, and the conception of Matter belongs to philosophy rather than to science. But besides this they had laid the foundations of geometry, and that led in other hands to the formulation of the correlative conception of Limit or Form. It is needless to enumerate here the Milesian and Pythagorean contributions to plane geometry; it will be sufficient to remind the reader that they covered most of the ground of Euclid, Books I, II, IV, and VI, and probably also of Book III. In addition, Pythagoras founded Arithmetic, that is, the scientific theory of numbers (αριθμητικη), as opposed to the practical art of calculation (λογιστικη). We also know that he discovered the sphericity of the earth, and the numerical ratios of the intervals between the concordant notes of the octave. It is obvious that he was a scientific genius of the first order, and it is also clear that his methods included those of observation and experiment. The discovery of the earth’s spherical shape was due to observation of eclipses, and that of the intervals of the octave can only have been based on experiments with a stretched string, though the actual experiments attributed by tradition to Pythagoras are absurd. It was no doubt this last discovery that led him to formulate his doctrine in the striking saying ‘Things are numbers’, thus definitely giving the priority to the element of form or limit instead of to the indeterminate matter of his predecessors.

      Pythagoras further differed from his predecessors in one respect which proved of vital moment. So far was he from ignoring religion, that he founded a society in southern Italy which was primarily a religious community. It is quite possible that he was influenced by the growth of the Orphic societies which had begun to spread everywhere in the course of the sixth century, but his religion differed from the Orphic in many ways. In particular, Apollo and not Dionysus was the chief god of the Pythagoreans, and all our evidence points to the conclusion that Pythagoras brought his religion, as he had brought his science, from eastern Hellas, though rather from the islands of the Aegean than from mainland Ionia. He was much influenced, we can still see, by certain traditions of the temple of Delos, which had become the religious centre of the Ionic world. There had, of course, been plenty of religious speculation among the Greeks before Pythagoras, and it was of a type not unlike that we find in India, though there are insuperable difficulties in the way of assuming any Aegean influence on India or any Indian influence on the Aegean at this date. It may be that the beginnings of such ideas go back to the time when the Greeks and the Hindus were living together, though it is still more likely that both the Greeks and the Indians were affected by a movement originating in the north, which brought to both of them a new view of the soul. The Delian legend of the Hyperboreans may be thought to point in this direction. However that may be, the main purpose of the religious observances practised by the Orphics and Pythagoreans alike was to secure by means of ‘purifications’ (καθαρμοι) the ransom (λυσις) of the soul, which was regarded as a fallen god, from the punishment of imprisonment in successive bodies. There is no reason to suppose that Pythagoras displayed any particular originality in this part of his teaching. It all depends on the doctrine of transmigration or rebirth (παλιγγενεσια), which is often incorrectly designated by the late and inaccurate term ‘metempsychosis’. There is no doubt that Pythagoras taught this, and also the rule of abstinence from animal flesh which is its natural corollary, but such ideas had been well known in many parts of Greece before his time. The real difficulty is to see the connexion between all this and his scientific work. Here we are of course confined to inferences from what we are told by later writers; but, if the doctrine which Plato makes Socrates expound in the early part of the Phaedo is Pythagorean, as it is generally supposed to be, we may say that what Pythagoras did was to teach that, while the ordinary methods of purification were well enough in their way, the best and truest purification for the soul was just scientific study. It is only in some such way as this that we can explain the religious note which is characteristic of all the best Greek science. It involves the doctrine that the Theoretic Life is the highest way of life for man, a belief still held by Plato and Aristotle, and to which we shall have to return. We may note at once, however, that it is not an ‘intellectualist’ ideal. There is no question of idle contemplation; it is a strenuous way of life, the aim of which is the soul’s salvation, and it gives rise to an eager desire to convert other men. Just for that reason, the Pythagorean philosopher will take part in practical life when the opportunity offers, and he will even rule the state if called upon to do so. The Pythagorean society was a proselytizing body from the first, and it tried to bring in all it could reach, without distinction of nationality, social position, or sex (for women played a great part in it from the first). It was precisely its zeal for the reform of human life, and its attempt to set up a Rule of the Saints in the cities of southern

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