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had contented themselves with idle speculation, they would not have been massacred or forced to take refuge in flight, a fate which overtook them before the middle of the fifth century.

      It soon proved, however, that the Pythagorean doctrine in its entirety was too high a one for its adherents, and a rift between Pythagorean religion and Pythagorean science was inevitable. Those who were capable of appreciating the scientific side of the movement would tend more and more to neglect the religious rule which it prescribed, and we find accordingly that before the end of the fifth century the leading Pythagoreans, the men whose names we know, are first of all men of science, and more and more inclined to drop what they doubtless regarded as the superstitious side of the doctrine. In the end they were absorbed in the new philosophical schools which arose at Athens. The mass of the faithful, on the other hand, took no interest in arithmetic, geometry, music, and astronomy, and with them to follow Pythagoras meant to go barefoot and to abstain from animal flesh and beans. These continued the tradition even after scientific Pythagoreanism had become extinct as such, and they were a favourite subject of ridicule with the comic poets of the fourth century BC

      It is easy for us to see now that all this indicates a real weakness in Pythagoreanism. Science and religion are not to be brought into union by a simple process of juxtaposition. We do not know how far Pythagoras himself was conscious of the ambiguity of his position; it would not be surprising if he came to feel it towards the end of his life, and we know for certain that he lived long enough to witness the beginnings of the revolt against his society in Croton and elsewhere. It is for this reason that he removed to Metapontum where he died, and where Cicero was able to visit his tomb long afterwards. We shall see later what the weak point in his system was, and we shall have to consider how the discord he had left unresolved was ultimately overcome. For the present, it is more important to note that he was the real founder both of science, and of philosophy as we understand them now. It is specially true of science that it is the first steps which are the most difficult, and Pythagoras left a sufficient achievement in mathematics behind him for others to elaborate. The Greeks took less than three centuries to complete the edifice, and that was chiefly due to Pythagoras, who had laid the foundations truly and well.

      We have now seen how the two great conceptions of Matter and Form were reached; the next problem Greek philosophy had to face was that of Motion. At first the fact of movement had simply been taken for granted. The Ionian tendency was to see motion everywhere; it was rest that had to be explained, or rather the appearance of it. However, when the new conception of an eternal matter began to be taken seriously, difficulties made themselves felt at once. If reality was regarded as continuous, it appeared that there was no room for anything else, not even for empty space, which could only be identified with the unreal, and it was easy to show that the unreal could not exist. But, if there is no empty space, it seems impossible that there should be any motion, and the world of which we suppose ourselves to be aware must be an illusion. Such, briefly stated, was the position taken up by another Ionian of southern Italy, Parmenides of Elea (c. 475 BC), who had begun as a Pythagorean, but had been led to apply the rigorous method of reasoning introduced into geometry with such success by the Pythagoreans to the old question of the nature of the world which had occupied the Milesians. The remarkable thing about the earliest geometers is, in fact, that they did not formulate the conception of Space, which seems to us at the present day fundamental. They were able to avoid it because they possessed the conception of Matter, and regarded Air as the normal state of the material substratum. The confusion of air with empty space is, of course, a natural one, though it may be considered surprising that it should not have been detected by the founders of geometrical science. Such failures to draw all the consequences from a new discovery are common enough, however, in the history of scientific thought.

      Parmenides cleared up this ambiguity, not by affirming the existence of empty space, but by denying the possibility of such a thing, even before it had been asserted by any one. He saw that the Pythagoreans really implied it, though they were quite unconscious of the fact. He is interesting to us as the first philosopher who thought of expounding his system in verse. It was not a very happy thought, as the arguments in which he deals do not readily lend themselves to this mode of expression, and we may be thankful that none of his successors except Empedocles followed his example. It has the very great inconvenience of making it necessary to use different words for the same thing to suit the exigencies of metre. And if there ever was an argument that demanded precise statement, it was that of Parmenides. As it is, his poem has the faults we should look for in a metrical version of Euclid. On the other hand, Parmenides is the first philosopher of whom we have sufficient remains to enable us to follow a continuous argument; for we have nothing of Pythagoras at all, and only detached fragments of the rest. We can see that he was ready to follow the argument wherever it might lead. He took the conception of matter which had been elaborated by his predecessors and he showed that, if it is to be taken seriously, it must lead to the conclusion that reality is continuous, finite, and spherical, with nothing outside it and no empty space within it. For such a reality motion is impossible, and the world of the senses is therefore an illusion. Of course that was not a result in which it was possible for men to acquiesce for long, and historically speaking, the Eleatic doctrine must be regarded as a reductio ad absurdum of earlier speculation. There is no reason to believe, however, that Parmenides himself meant it to be understood in this way. He believed firmly that he had found the truth.

      Several attempts were made to escape the conclusions of Parmenides, and they all start by abandoning the assumption of the homogeneity and continuity of matter which had been implicit in the earlier systems, though it was first brought to the light of day by Parmenides. Here again the influence of contemporary science on philosophic thought is clearly marked. Empedocles of Agrigentum (c. 460 BC), the only citizen of a Dorian state who finds a place in the early history of science and philosophy, was the founder of the Sicilian school of medicine, and it was probably his pre-occupation with that science that led him to revive the old doctrine of Fire, Air, Earth, and Water, which the Milesians had cast aside, but which lent itself readily to the physiological theories of the day. He did not use the word afterwards translated ‘elements’ (στοιχεια) for these. It means literally ‘letters of the alphabet’, and appears to have been first employed in this connexion by the Pythagoreans at a later date, when they found it necessary to take account of the new theory. Empedocles spoke of the ‘four roots’ of things, and by this he meant to imply that these four forms of matter were equally original and altogether disparate. That furnished at least a partial answer to the arguments of Parmenides, which depended on the assumption that matter was homogeneous. He also found it necessary to assume two sources of motion or forces, as we might call them, though Empedocles thought of them as substances, one of which tended to separate the ‘four roots’ and the other to combine them. These he called Love and Strife, and he supposed the life of the world to take the form of alternate cycles, in which one or the other prevailed in turn. In all this he was plainly influenced by his physiological studies. He thinks of the world as an animal organism subject to what are now called anabolism and catabolism. The details of the theory make this quite clear. A similar doctrine was taught by Anaxagoras (c. 460 BC), who came from Clazomenae in Asia Minor to Athens after the Persian Wars, and was one of the teachers of Pericles. His doctrine of ‘seeds’, in which the traditional ‘opposites’—wet and dry, cold and hot—were combined in different proportions, is rather more subtle than that of Empedocles, and it is possible to see in it a curious anticipation of certain features in modern chemistry. Anaxagoras too felt it necessary to assume a force or source of motion, but he thought that one would suffice to account for the rotation (περιχωρησις) to which he attributed the formation of the world. He called that force Mind (νους), but his own description of it shows that he regarded it as corporeal, though he thought it was something more tenuous and unmixed than other bodies. There is little doubt that he selected the term in order to mark the identity of the source of motion in the world with that in the animal organism. That again is in accordance with the scientific interests of the time. In his astronomical theories, however, Anaxagoras showed himself a true eastern Ionian, and lagged far behind the Pythagoreans. For him, as for the Ionians of the Aegean down to and including Democritus, the earth was flat, and the eddy or vortex which gave rise to the world was still rotation in a plane. A more satisfying answer to Parmenides was the doctrine of Atomism,

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