The Legacy of Greece Part 3

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, which frankly accepted the existence of s.p.a.ce, and a.s.serted that it was just as real as body. The first hint of such a solution was given by Melissus (_c._ 444 B. C.), who was a Samian but a member of the Eleatic school. He said, 'If things are a many, then each of them must be such as I have shown the One to be.' That was meant as a _reductio ad absurdum_; but, when Leucippus of Miletus (_c._ 440 B. C.), who had also studied in the school of Elea, ventured to a.s.sert the existence of the Void, there was no longer any reason for s.h.i.+rking the conclusion which Melissus had stated only to show its impossibility. The atoms are, in fact, just the continuous indivisible One of Parmenides multiplied _ad infinitum_ in an infinite empty s.p.a.ce. On that side at least, the theory of body was now complete, and the question asked by Thales was answered, and it is of great interest to observe that this was brought about by the renewal of intercourse between the Ionians of Italy and those of the Aegean, a renewal which was made possible by the establishment of the Athenian Empire. Nothing makes us feel the historical connexion more vividly than the re-emergence of the names of Miletus and Samos after all these years. There were, however, certain more fundamental problems which Atomism could not solve, and which were first attacked at Athens itself.

So far, it will be noted, Athens has played no part at all in our story, and in fact no more than two Athenians ever became philosophers of the first rank. It is true that they were called Socrates and Plato, so the exception is a considerable one. It was the foundation of the Athenian Empire that made Athens the natural meeting-place of the most diverse philosophical and scientific views. It was here that the east and west of h.e.l.las came together, and that the two streams of tradition became one, with the result that a new tradition was started which, though often interrupted for a time, continues to the present day.

If we wish to understand the development of Greek philosophy, it is of the first importance that we should realize the intellectual ferment which existed at Athens in the great days of the Periclean age. It has been mentioned already that Anaxagoras of Clazomenae had settled there, and it was not long before his example was followed by others. In particular, Zeno of Elea (_c._ 450 B. C.), the favourite disciple of Parmenides, had a considerable following at Athens. He made it his business to champion the doctrine of his master by showing that those who refused to accept it were obliged to give their a.s.sent to views which were at least as repugnant to common sense, and in this way he incidentally did much for mathematics and philosophy by raising the difficulties of infinite divisibility and continuity in an acute form.

All that is something quite apart from the influence of the 'sophists'

at a rather later date, though they too came both from the east and from the west, and though they had been influenced by the more strictly philosophical schools of these regions. It was into this Athens that Socrates was born (470 B. C.) about ten years after the battle of Salamis, and he was naturally exposed to all these conflicting influences, of which Plato has given us a vivid description in the _Phaedo_, from his earliest youth. He cannot, in fact, be understood at all unless this historical background is kept constantly in view. There can be no reasonable doubt that at a very early age he attached himself to Archelaus, an Athenian who had succeeded Anaxagoras, when that philosopher had to leave Athens for Lampsacus. Ion of Chios, a contemporary witness, said that Socrates had visited Asia Minor with Archelaus, and that appears to refer to the siege of Samos, when Socrates was under thirty. There is no reason whatever to doubt the statement, which Plato makes more than once, that he had met Parmenides and Zeno at a still earlier date. At any rate, the influence of Zeno on the dialectic of Socrates is unmistakable. We may also take it that he was familiar with all sorts of Orphic and Pythagorean sectaries.

Aeschines of Sphettos wrote a dialogue ent.i.tled _Telauges_, in which he represented Socrates as rallying the extreme asceticism of the strict followers of Pythagoras. So far, however, as we can form a picture of him for ourselves, he was not the sort of man to become the disciple of any one. He was a genuine Athenian in respect of what is called his 'irony', which implies a certain humorous reserve which kept him from all extravagances, however interested he might be in the extravagances of others. Nevertheless, while still quite a young man, he had somehow acquired a reputation for 'wisdom', though he himself disclaimed anything of the sort. He had also, it appears, gathered round him a circle of 'a.s.sociates' (?ta???? {hetairoi}). The only direct evidence we have for these early days is the _Clouds_ of Aristophanes (423 B. C.), which is of course a comedy and must not be taken too literally. On the other hand, a comic poet who knew his business (and surely Aristophanes did) could hardly present a well-known man to the Athenian public in a manner which had no relation to fact at all. It is fortunate that there is a pa.s.sage in Xenophon's _Memorabilia_ (i. 6) which seems to supply us with the very background we need to make the _Clouds_ intelligible. It represents Socrates in an entirely different light from that in which he appears in the rest of the work, and it can hardly be Xenophon's own invention. It seems to refer to a time when Plato and Xenophon were babies, if not to a time before they were born, and it is probable that it comes from some literary source which we can no longer trace. We are told, then, that Antiphon the sophist was trying to detach his companions (s????s?asta? {synousiastai}) from Socrates, and a conversation followed in which he charged him with teaching his followers to be miserable rather than happy, and added that he was right not to charge a fee for his teaching, since in fact it was of no value.

It will be seen that this implies a regular relation between Socrates and his followers which was sufficiently well known to arouse professional jealousy. Socrates does not attempt to deny the fact. He says that what he and his companions do is to spend their time together in studying the wisdom of the men of old which they have left behind them in books, and that, if they come upon anything which they think is good, they extract it for their own use, and count it great gain if, in doing this, they become friends to one another. It is obvious that this suggests something quite different from the current view of Socrates as a talker at street corners, something much more like a regular school, and that, so far as it goes, it explains the burlesque of Aristophanes.

The Socrates of whom we know most is, however, quite differently engaged. He has devoted his life to a mission to his fellow men, and especially to his fellow citizens. If we may so far trust Plato's _Apology_, the occasion of that was the answer received from the Delphic oracle by Chaerephon, whom we know from Aristophanes as one of the leading disciples of Socrates in the earlier part of his life.

Chaerephon asked the G.o.d of Delphi whether there was any one wiser than Socrates, and this of course implies that Socrates had a reputation for 'wisdom' before his mission began. The oracle declared that there was no one wiser, and Plato makes Socrates say in the _Apology_ that this was the real beginning of that mission. He set out at first to prove that the oracle was wrong, and for that purpose he tried to discover some one wiser than himself, a search in which he was disappointed, since he could only find people who thought they were wise, and no one who really was so. He therefore concluded that what the oracle really meant was that Socrates was wiser than other people in one respect only. Neither he nor any one else was really 'wise', but Socrates was wiser than the rest because he knew he was not wise and they thought they were. It ought to be clear that this is mostly 'irony', and it is not to be supposed that Socrates attached undue importance to the oracle, which he speaks of quite lightly, but he could hardly have told the story at all unless it was generally known that his mission did in fact date roughly from that period of his life. Historically it would probably be truer to say that the outbreak of the Peloponnesian War, in which Socrates served with great distinction as a hoplite, marked the decisive turning-point.

It was in the camp at Potidaea that he once stood in a trance for twenty-four hours (431 B. C.), and that seems to point to some great psychological change, which may very well have been occasioned or accelerated by his experiences in the war. At any rate we now find him entirely devoted to the conversion of his fellow citizens, and we must try to understand what the message he had for them was.

In the _Apology_ Socrates declares that his mission was divinely imposed upon him, so that he dare not neglect it, even if it should lead to his death, as in fact it did. The tone here is quite different from the half-humorous style in which he deals with the Delphic oracle, and even the 'divine sign'. That only warned him not to do things, mostly quite trivial things, which he was about to do, and never told him to do anything; this, on the contrary, was a positive command, laid upon him by G.o.d, and there can be no doubt that Plato means us to understand this to have been the innermost conviction of Socrates. It is hard to believe that Plato could have misrepresented his master's att.i.tude on such a point. He was present at the trial, and the _Apology_ must have been written not very long afterwards, when the memory of it was still fresh in people's minds. Now Plato tells us quite clearly that what Socrates tried to get the Athenians to understand was the duty of 'caring for their souls' (????? ep?e?e?? {psyches epimeleio}). That is confirmed from other sources, and indeed it is generally admitted. The phrase has, however, become so familiar that it does not at once strike us as anything very new or important. To an Athenian of the fifth century B.

C., on the other hand, it must have seemed very strange indeed. The word translated 'soul' (???? {psyche}) occurs often enough, no doubt, in the literature of the period, but it is never used of anything for which we could be called upon to 'care' in the sense evidently intended by Socrates. Its normal use is to denote the breath of life, the 'ghost' a man 'gives up' at the moment of death. It can therefore be rendered by 'life' in all cases where there is a question of risking or losing life or of clinging to it when we ought to be prepared to sacrifice it, but it is not used for the seat of conscious life at all. It is sometimes employed to signify the seat of the dream-consciousness or of what is now called the subconscious or subliminal self, but never of the ordinary waking consciousness which is the seat of knowledge and ignorance, goodness and badness.[2] On the other hand, that use of the word is quite common in the fourth century, and it may be inferred that this change was due to Socrates. More than once Aristophanes ridicules him for holding some strange view of the 'soul', and these jests were made at a time when Plato was only a child. We cannot, of course, expect to get any very definite idea from them as to the real teaching of Socrates on this subject, but it is not impossible to see what it was, if we take into account the views of the soul which had been held by the philosophical schools of eastern and western Ionia.

[2] See my paper on 'The Socratic Doctrine of the Soul'.

_Proceedings of the British Academy_, 1915-16, pp. 235 sqq.

The Ionians of Asia Minor had certainly identified the soul with that in us which is conscious, and which is the seat of goodness and badness, wisdom and folly; but they did not regard it as what we call the self or treat it as an individual. Anaximenes and his school held that the soul was what they called Air, but that was just because they regarded Air as the primary substance of which all things are made. The soul was something, in fact, that comes to us from outside (???a?e? {thyrathen}) by means of respiration. As Diogenes of Apollonia expresses it, it is 'a small portion of the G.o.d', that is, of the primary substance, enclosed in a human body for a time, and returning at death to the larger ma.s.s of the same substance outside. The formula 'Earth to earth and air to air'

was accepted as an adequate description of what takes place at death.

The western Ionians, and especially the Pythagoreans, held a very different view. For them, the soul was something divine. It was, in fact, a fallen G.o.d, imprisoned in the body as a punishment for antenatal sin, and it deserved our care in this sense, that it was our chief business in life to purify it so as to secure its release from the necessity of reincarnation in another body. But, during this present life, they held that this divine element slumbers, except in prophetic dreams. As Pindar puts it, 'It sleeps when the limbs are active.'

Neither of these views was familiar to the ordinary Athenian, but Socrates of course knew both well, and felt satisfied with neither. When he spoke of the soul he did not mean any mysterious fallen G.o.d which was the temporary tenant of the body, but the conscious self which it lies with us to try to make wise and good. On the other hand, his insistence on our duty to 'care for' it is quite inconsistent with the view that it is merely something extrinsic, as all the eastern Ionians down to Anaxagoras had taught. It is, on the contrary, our very self, the thing in us which is of more importance to us than anything else whatever. It was to this doctrine of the soul and our duty to it that Socrates felt he must convert mankind and especially his fellow-citizens. It was a strange and novel doctrine then; and, if it has become a commonplace since, that only shows that he was successful, if not in persuading his fellowmen to act on this knowledge, at least in making them aware of it. It was in this way that Socrates healed the rift between science and religion which had proved fatal to the Pythagorean society, and it may be suggested that the significance of his teaching is not exhausted yet. As has been indicated above it is to be found clearly stated in Plato's _Apology of Socrates_, and it furnishes the only clue to a right understanding of the great series of Platonic dialogues down to and including the _Republic_ in which Socrates is represented as the chief speaker. Whether Plato added much or little of his own to the doctrine of his master in these dialogues is an interesting historical problem, but it need not concern the ordinary reader, at least in the first instance. We know from the allusions of Aristophanes that Socrates himself taught a new doctrine of the soul when Plato was a child, and no sympathetic reader can fail to see that the pa.s.sage of the _Apology_ to which we have referred is intended to be a faithful account of that doctrine. All the rest is simply its legitimate development, and it is not of very great importance for us to determine whether that development is due to Socrates or to Plato. The inspiration which has been derived from these writings by many generations will not be lessened by any decision we may come to on this point, so long as we keep clearly in mind that the new doctrine of soul is their princ.i.p.al theme, and that this must be understood in the light of the doctrines which had prepared the way for it. What Socrates did was really this. He deepened the meaning of the Eastern Ionian doctrine by informing it with some of the feeling and emotion which had characterized the Pythagorean teaching on the subject, while on the other hand he rationalized the Pythagorean theory by identifying the soul with our conscious personality.

Now if this is a correct account of what Socrates taught, he must be regarded as inaugurating an entirely new period in the history of philosophy. That is implied in the common term 'Presocratics' generally applied to his predecessors, though the ordinary textbooks are by no means clear as to the grounds for a.s.signing this pre-eminent position to Socrates. We can also see how natural it was for him to lay such emphasis on the conversion of souls as he certainly did. That purpose continued to dominate Greek philosophy to the very end. No doubt successive schools varied in their conception of what conversion meant, but that is the link which binds them all together. In fact, it gave rise to a new literary form, the 'hortatory discourse' (p??t?ept????

????? {protreptikos logos}), which was more and more cultivated as time went on, and was at last taken over by the fathers of the Christian church along with much else of a more fundamental character.

It has been noted already that Socrates had followers among all the leading philosophical schools of the time, and the possibility is not to be excluded that we may still learn more of him from the discovery of new sources. For the present, the recovery of some new and fairly extensive fragments of the _Alcibiades_ of Aeschines of Sphettos is the chief addition to our sources of information. We know that Aeschines was a disciple of Socrates, and the tradition of antiquity was that his dialogues gave the most faithful picture of the man as he really was. If so, that was probably because Aeschines had no philosophy of his own.

For us the chief importance of the new fragments is that, if we read them along with those already known (and it is unfortunate that the old and the new have not yet been printed together), they strongly confirm the impression we get from Plato of the manner of Socrates and his method of argument, and that helps to rea.s.sure us as to the essentially historical character of the Platonic Socrates. The fragments of Aeschines also corroborate Plato by showing that the conversion of Alcibiades (whose life he had saved when a young man) was one of the things that lay nearest his heart.

But the real successor of Socrates was, of course, Plato himself (427-347 B. C.). It is not possible to give even an outline of Plato's philosophy here. Indeed the time has hardly come for that yet, though much admirable work is now being done, especially by a French professor, M. Robin, which promises more certain conclusions than have yet been possible. All that can be attempted here is to indicate the att.i.tude of Plato to some of the problems we have been discussing. His very great contributions to the theory of knowledge will be pa.s.sed over, as they are beginning to be well understood, and the _Theaetetus_ in particular, with its sequel the _Sophist_, is more and more coming to occupy its rightful place as the best introduction to philosophy in general. It is necessary, however, just to notice in pa.s.sing a fundamental question of method which the Platonic dialogues themselves suggest. It is this.

While Socrates is present in every one of them except the _Laws_, he takes practically no part in some of them, and the dialogues in which this is the case are known on other grounds to belong to the later years of Plato's life. There must be some reason for this, and it is obviously prudent to treat these later dialogues in the first instance as our primary evidence for Plato's own views. Indeed, it is only after his philosophy has been reconstructed from these sources and from the sometimes obscure references to it in Aristotle, that it will be safe to attempt an answer to the question of how much there may be in the dialogues of his early life which is properly to be a.s.signed to Plato himself rather than to Socrates. That is a historical question of great interest; but, as has been said, the solution of it, if that should ever prove possible, would not greatly affect the impression that Athenian philosophy leaves upon us as a whole.

Now, if we consider Plato's later, and presumably therefore most independent writings, we find, just as we should expect from a disciple of Socrates, that the doctrine of soul holds the first place, but that it has certain features of its own which there is no sufficient ground for attributing to Socrates. We are too apt to think of Plato as mainly occupied with what is called the 'theory of Ideas', a theory which is discussed once or twice in his earlier dialogues, and which is there ascribed to Socrates, but which plays no part at all in his mature works. There the chief place is undoubtedly taken by the doctrine of the soul, and we can see that it is of the first importance for Plato. Soul is regarded as the source of all motion in the world, because it is the only thing in the world that moves without being itself moved by anything else. It is this and this alone that enables Plato to account for the existence of the world and of mankind, and to avoid the theory of 'two worlds' into which, as he points out in the _Sophist_, 'the friends of the Ideas', whoever they may have been, were only too apt to fall. In Plato this view of the soul culminates in theology of a kind which he nowhere attributes to Socrates. He represents him, indeed, as a man of a deeply religious nature, but we do not gather that he had felt the need of a formal doctrine of G.o.d. Plato, on the other hand, has left us the first systematic defence of Theism we know of, and it is based entirely on his doctrine of soul as the self-moved mover. But the highest soul, or G.o.d, is not only the ultimate source of motion, but also supremely good. Now, since there are many things in the world which are not good, and since it would be blasphemy to attribute these to G.o.d, there must be other souls in the world which are relatively at least independent. G.o.d is not, directly at least, the cause of all things, but it is not easy to discover the relation in which these other souls are thought of as standing to G.o.d. In the _Timaeus_, the matter is put in this way. The soul of the world, and all other souls human and divine, are the work of the Creator, who is identified with G.o.d, and they are not inherently indestructible, since anything that has been made can be unmade. They are, however, practically indestructible, since G.o.d made all things because He was good and wished them also to be as good as possible. His goodness, therefore, will not suffer Him to destroy what He has once made. That of course is mythically expressed, and Plato is not committed to it as a statement of his own belief, since it is only the account which _Timaeus_ puts into the mouth of the Creator. We can see, however, what was the problem with which he was occupied, and it is not perhaps illegitimate to infer that he approached the question which still baffles speculation from the point of view that G.o.d's omnipotence, as we should call it, is limited by his goodness.

This is a much more important limitation than that imposed by the existence of matter, to which Timaeus also refers. In that, he is simply following the tradition of the Pythagorean society to which he belonged, as is shown by his identification of matter with s.p.a.ce, or rather with 'room'. So far as can be seen at present, we are not ent.i.tled to ascribe this view to Plato without more ado, but that is a point on which the last word has not yet been said.

The description of the creation given by Timaeus is of course to be regarded as mythical in its details, but it has features from which we may learn a good deal as to the direction taken by Plato's thoughts about the world. In particular, while the important part played by geometry is quite intelligible in the mouth of a Pythagorean, he makes use of certain theories which we know to belong to the most recent mathematics of the day, in particular the complete doctrine of the five regular solids, which was due to Theaetetus, who was one of the earliest members of the Academy, and whom Plato represents as having made the acquaintance of Socrates just before the master's death. Theaetetus died young, but we know enough of him to feel sure that he was one of the few great original mathematicians who have appeared in history. In the _Timaeus_ the theory of the regular solids is used to get rid once more of the doctrine of four ultimate 'elements'. These, Timaeus says, are so far from being elements or letters of the alphabet, that they are not even syllables. The way in which the so-called elements are built up out of molecules corresponding in their configuration to the regular solids, and the explanations of their trans.m.u.tation into one another based on the geometrical construction of these figures, is apt to strike the average reader as fantastic, but one of the most distinguished living mathematicians and physicists has stated that he is struck most of all by their resemblance to the scientific theories of the twentieth century. It will be well, therefore, to avoid hasty judgements on this point. It is at any rate easy to understand how the study of mathematics came to hold the preponderating place it did in the Platonic Academy.

In accordance with the plan of this paper, something must now be said of Plato's att.i.tude to the practical life, a point on which it is very easy to make mistakes. No one has insisted more strongly than he has on the primacy of the Theoretic Life. The philosopher is the man who is in love with the spectacle of all time and all existence and that is what delivers him from petty ambitions and low desires. He has made the toilsome ascent out of the Cave in which the ma.s.s of men dwell, and in which they only behold the shadows of reality. But, even in this enthusiastic description of the philosophic life, an equal stress is laid on the duty of philosopher to descend into the Cave in turn and to rescue as many of their former fellow-prisoners as may be, even against their will, by turning them to the light and dragging them up into the world of truth and reality. It is quite easy to understand, in view of this, that Plato devoted some of the best years of his life to practical affairs and that he relinquished the studies of the Academy for a time in order to direct the education of Dionysius II. The thing appeared well worth doing; for Greek civilization in Sicily, and consequently, as we can now see, the civilization of western Europe, was seriously threatened by the Carthaginians. They had been held at bay by Dionysius I, but after his death everything depended on his successor. Now the education of Dionysius II had been completely neglected, but he had good natural abilities, and his uncle Dion, who was Plato's friend, was ready to answer for his good intentions. Plato could not turn a deaf ear to such a call. Unfortunately Dionysius was vain and obstinate, and he soon became impatient of the serious studies which Plato rightly regarded as necessary to prepare him for his task. The result was a growing estrangement between Plato and his pupil, which made it impossible to hope for a successful issue to the plans of Dion. It is unnecessary to tell the whole story here, but it is right to say that there was nothing at all impracticable in what Plato undertook, and that he was certainly justified in holding that the education of Dionysius must be completed before it would be safe to entrust him with the champions.h.i.+p of the cause of h.e.l.lenism in the west.

His failure to make anything of Dionysius did not lead Plato to abandon his efforts to heal the wounds of h.e.l.lenism. One of the studies most ardently pursued in the Academy was Jurisprudence, of which he is the real founder. It was not uncommon for Greek states to apply to the Academy for legislators to codify existing law or to frame a new code for colonies which had just been founded. That is the real explanation of the remarkable work ent.i.tled the _Laws_, which must have occupied Plato for many years, and which was probably begun while he was still directing the studies of Dionysius. It appears to have been left unfinished; for, while some parts of it are highly elaborated, there are others which make upon us the impression of being a first draft. Even so, it is a great work if we regard it from the proper point of view. It is, in the first place, a codification of Greek, and especially Athenian law, of course with those reforms and improvements which suggest themselves when the subject is systematically treated, and it formed the basis of h.e.l.lenistic, and through that of Roman law, to which the world owes so much. There is no more useful corrective of the popular notion of Plato as an unpractical visionary than the careful study of the dullest and most technical parts of the _Laws_ in the light of the _Inst.i.tutes_.

No attempt has been made here to describe the system of Plato as a whole, and indeed the time has not yet come when such an attempt can profitably be made. We have no direct knowledge of his teaching in the Academy; for we only possess the works which he wrote with a wider public in view. In the case of Aristotle (384-322 B. C.), a similar reservation must be made, though for just the opposite reason. We have only fragments of his published works and what we possess is mainly the groundwork of his lectures in the Lyceum. It will be seen that there is still very much to be done here too. From the nature of the case, notes for lectures take a great deal for granted that would be more fully explained when the lectures were delivered, and some of the most important points are hardly developed at all. Nevertheless there are certain things which come out clearly enough, and it so happens that they are points of great importance from which we can learn something with regard to the philosophical problems of the present day.

In the first place, it is desirable to point out that Aristotle was not an Athenian, but an Ionian from the northern Aegean, and that he was strongly influenced by eastern Ionian science, especially by the system of Democritus (which Plato does not appear to have known) and by the medical theories of the time. That is why he is so unsympathetic to the western schools of philosophy, and especially to the Pythagoreans and the Eleatics. Empedocles alone, who was a biologist like himself, and the founder of a medical school, finds favour in his eyes. He is not, therefore, at home in mathematical matters and his system of Physics can only be regarded as retrograde when we compare it with that of the Academy. He did indeed accept the doctrine of the earth's sphericity, but with that exception his cosmological views must be called reactionary. Where he is really great is in biology, a field of research which was not entirely neglected by the Academy, but which had been treated as secondary in comparison with mathematics and astronomy. The contrast between Plato and Aristotle in this respect seems to repeat on a higher plane that between Pythagoras and Empedocles, and this suggests something like a law of philosophical development which may perhaps throw light on the present situation. It seems as if this alternation of the mathematical and the biological interest was fundamental in the development of scientific thought and that the philosophy of different periods takes its colour from it. The philosophy of the nineteenth century was dominated in the main by biological conceptions, while it seems as if that of the twentieth was to be chiefly mathematical in its outlook on the world. We must not, of course, make too much of such formulas, but it is instructive to study such alternations in the philosophy of the Greeks, where everything is simpler and more easily apprehended.

On the other hand, Aristotle had been a member of the Academy for twenty years, and that could not fail to leave its mark upon him. This no doubt explains the fact, which has often been noted, that there are two opposite and inconsistent strains in all Aristotle's thinking. On the one hand, he is determined to avoid everything 'transcendental', and his dislike of Pythagorean and Platonist mathematics is mainly due to that.

On the other hand, despite his captious and sometimes unfair criticisms of Plato, he evidently admired him greatly and had been much influenced by him. It may be suggested that the tone of his criticisms is partly due to his annoyance at finding that he could not shake off his Platonism, do what he would. This is borne out by the fact that, when he has come to the furthest point to which his own system will take him, he is apt to take refuge in metaphors of a mythical or 'transcendental'

character, for which we are not prepared in any way and of which no explanation is vouchsafed us. That is particularly the case when he is dealing with the soul and the first mover. On the whole his account of the soul is simply a development of eastern Ionian theories, and we feel that we are far removed indeed from the Platonist conception of the soul's priority to everything else. But, when he has told us that the highest and most developed form of soul is Mind, we are suddenly surprised by the statement that Mind in this sense is merely pa.s.sive, while there is another form of it which is separable from matter, and that alone is immortal and everlasting. This has given rise to endless controversy which does not concern us here, but it seems best to interpret it as an involuntary outburst of the Platonism Aristotle could not wholly renounce. Very similar is the pa.s.sage where he tries to explain how the first mover, though itself unmoved, communicates motion to the world. 'It moves it like a thing beloved,' he tells us, and leaves us to make what we can of that. And yet we cannot help feeling that, in pa.s.sages like this, we come far nearer to the beliefs Aristotle really cared about than we do anywhere else. At heart he is a Platonist in spite of himself.

Aristotle's att.i.tude to the practical life is also dependent on Plato's. In the Tenth Book of the _Ethics_ he puts the claims of the Contemplative Life even higher than Plato ever did, so that the practical life appears to be only ancillary to it. He does not feel in the same degree as Plato the call for the philosopher to descend once more into the Cave for the sake of the prisoners there, and altogether he seems far more indifferent to the practical interests of life.

Nevertheless he followed Plato's lead in giving much of his time to the study of Politics and that too with the distinctly practical aim of training legislators. He has often been criticized for his failure to see that the days of the city-state were numbered, and for the way in which he ignores the rise of an imperial monarchy in the person of his own pupil Alexander the Great. That, however, is not quite fair.

Aristotle had a healthy dislike of princes and courts, and the city-state still appealed to him as the normal form of political organization. He could not believe that it would ever be superseded, and he wished to contribute to its better administration. He had, in fact, a much more conservative outlook than Plato, who was inclined to think with Isocrates, that the revival of monarchy was the only thing that could preserve h.e.l.lenism as things were then. We must remember that Aristotle was not himself a citizen of any free state, and that he could hardly be expected to have the same political instincts as Plato, who belonged by birth to the governing cla.s.ses of Athens and had inherited the liberal traditions of the Periclean Age. This comes out best of all perhaps, in the att.i.tude of the two philosophers to the question of slavery. In the _Laws_, which deals with existing conditions, Plato of course recognizes the _de facto_ existence of slavery, though he is very sensible of its dangers and makes many legislative proposals with a view to their mitigation. In the _Republic_, on the other hand, where there is no need to trouble about existing conditions, he makes Socrates picture for us a community in which there are apparently no slaves at all. Aristotle is also anxious to mitigate the worst abuses of slavery, but he justifies the inst.i.tution as a permanent one by the consideration that barbarians are 'slaves by nature' and that it is for their own interest to be 'living tools'. This insistence upon the fundamental distinction between Greeks and barbarians must have seemed an anachronism to many of Aristotle's contemporaries and it had been expressly denounced by Plato as unscientific.

The immediate effect of Aristotle's rejection of Platonist mathematics was one he certainly neither foresaw nor intended. It was to make a breach between philosophy and science. Mathematical science, whether Aristotle realized it or not, was still in the vigour of its first youth, and mathematicians were stirred by the achievements of the last generation to attempt the solution of still higher problems. If the Lyceum turned away from them, they were quite prepared to carry on the Academic tradition by themselves, and they succeeded for a time beyond all expectation. The third century B. C. was, in fact, the Golden Age of Greek mathematics, and it has been suggested that this was due to the emanc.i.p.ation of mathematics from philosophy. If that were true, it would be very important for us to know it; but it can, I think, be shown that it is not true. The great mathematicians of the third century were certainly carrying on the tradition of their predecessors who had been philosophers as well as mathematicians, and it is not to be wondered at that they were able to do so for a time. But the really striking fact is surely that Greek mathematics became sterile in a comparatively short time, and that no further advance was made till the days of Descartes and Leibniz, with whom philosophy and mathematics once more went hand in hand.

Nor was the effect of this divorce on philosophy itself less disastrous. Theophrastus continued Aristotle's work on Aristotle's lines, and founded the science of Botany as his predecessor had founded that of Zoology, but the Peripatetic School practically died out with him and had very little influence till the study of Aristotle was revived long afterwards by the Neoplatonists.

For the present, the divorce of science and philosophy was complete. The Stoics and the Epicureans had both, indeed, a scientific system, but their philosophy was in no sense based upon it. The att.i.tude of Epicurus to science is particularly well marked. He took no interest in it whatever as such, but he used it as an instrument to free men from the religious fear to which he attributed human unhappiness. For that purpose, the science of the Academy, which had led up to a theology, was obviously unsuitable, and, like a true eastern Ionian as he was, Epicurus harked back to the atomic theory of Democritus, adding to it, however, certain things which really made nonsense of it, such, for instance, as the theory of absolute weight and lightness, which Aristotle had unfortunately taught. The Stoics too were corporealists, and found such science as they required in the system of Herac.l.i.tus, though they also adopted for polemical purposes much of Aristotle's Logic, taking pains, however, to alter his terminology. Both these schools, in fact, while remaining faithful to the idea of philosophy as conversion, forgot that it had always been based on science in its best days. It was this, no doubt, which chiefly commended Stoicism and Epicureanism to the Romans, who were never really interested in science.

Both Stoicism and Epicureanism made a practical appeal, though of a different kind, and that served to gain credit for them at Rome.

The Academy which Plato had founded still continued to exist, though it was diverted from its original purpose not more than a generation after Plato's death. Mathematics, we have seen, had made itself independent, and the most pressing necessity of the time was certainly the criticism of the new dogmatism which the Stoics had introduced. That was really carrying on one side of Platonism and not the least important. It is true indeed that the Academy appears to us at this distance of time mainly as a school of scepticism, but we must remember that its scepticism was directed entirely to the sensible world, as to which the att.i.tude of Plato himself was not fundamentally different. The real sceptics always refused to admit that the Academics were sceptics in the proper sense of the word, and it is possible that the tradition of Platonism proper was never wholly broken. At any rate, by the first century B. C., we begin to notice that Stoicism tends to become more and more Platonic. The study of Plato's _Timaeus_ came into favour again, and the commentary which Posidonius (_c._ 100 B. C.) wrote upon it had great influence on the development of philosophy down to the end of the Middle Ages. It is this period of eclecticism which is reflected for us in the philosophical writings of Cicero. It had great importance for the history of civilization, but it is far removed from the spirit of genuine Greek philosophy. That was dead for the present, and it did not come to life again till the third century of our era, when Platonism was revived at Rome by Plotinus.

It is only quite recently that historians of Greek philosophy have begun to do justice to 'Neoplatonism'. That is partly due to the contemporary philosophical tendencies noted at the beginning of this paper, and partly to historical investigations into the philosophy of the Middle Ages, which is more and more seen to be dependent mainly on Neoplatonism down to and including the system of St. Thomas Aquinas. It was in fact the most decisive fact in the history of Western European civilization that Plotinus founded his school at Rome rather than at Athens or Alexandria; for that is how Western Europe became the real heir to the philosophy of Greece. Every one knows, of course, that Plotinus was a 'mystic', but the term is apt to suggest quite wrong ideas about him. He is often spoken of still as a man who introduced oriental ideas into Greek philosophy, and he is popularly supposed to have been an Egyptian.

That is most improbable; and, if it were true, it would only make it the more remarkable that, though he certainly studied at Alexandria for eleven years, he never even mentions the religion of Isis, which was so fas.h.i.+onable at Rome in his day, and which had fascinated so genuine a Greek as Plutarch some generations before. There is no doubt that what Plotinus believed himself to be teaching was genuine Platonism, and that he had prepared himself for the task by a careful study of Aristotle and even of Stoicism, so far as that served his purpose. No doubt he was too great a man to make himself the mere mouthpiece of another's thought; but, for all that, he was the legitimate successor of Plato, and it may be added that M. Robin, who has taken upon himself the arduous task of extracting Plato's real philosophy from the writings of Aristotle, has come to the conclusion that there is a great deal more 'Neoplatonism' in Plato than is sometimes supposed.

Plotinus is a mystic, then, though not at all in the sense in which the term is often misused. He sets before his disciples a 'way of life'

which leads by stages to the highest life of all, but that is just what Pythagoras and Plato had done, and it is only the continuation of a tradition which goes back among the Greeks to the sixth century B. C., nearly a thousand years before the time of Plotinus. His aim, like that of his predecessors, is the conversion of souls to this way of life, and he differs from such thinkers as the Stoics and the Epicureans in holding that the 'way of life' to which he calls them must be based once more on a systematic doctrine of G.o.d, the World and Man. The result was that the divorce which had existed for centuries between science and philosophy was once more annulled. We cannot say, indeed, that Plotinus himself made any special study of Mathematics, but there is no doubt at all that his followers did, and it is due to them, and especially to Proclus, that we know as much of Greek Mathematics as we do. Proclus was indeed the systematizer of the doctrine of Plotinus, though he differs from him on certain points, and his influence on later philosophy cannot be overestimated. It can be distinctly traced even in Descartes, whom it reached through a number of channels, the study of which has recently been undertaken by a French scholar, Professor Gilson, of the University of Strasbourg. When his researches are complete, the continuity of Greek and modern philosophy will be plainly seen, and the part played by Platonism in the making of the modern European mind will be made manifest. We shall then understand better than ever why Greek philosophy is a subject of perennial interest.

The history of Greek philosophy is, in fact, the history of our own spiritual past, and it is impossible to understand the present without taking it into account. In particular, the Platonist tradition underlies the whole of western civilization. It was at Rome, as has been pointed out, that Plotinus taught, and it was in certain Latin translations of the writings of his school that St. Augustine found the basis for a Christian philosophy he was seeking. It was Augustine's great authority in the Latin Church that made Platonism its official philosophy for centuries. It is a complete mistake to suppose that the thinking of the Middle Ages was dominated by the authority of Aristotle. It was not till the thirteenth century that Aristotle was known at all, and even then he was studied in the light of Platonism, just as he had been by Plotinus and his followers. It was only at the very close of the Middle Ages that he acquired the predominance which has made so strong an impression on the centuries that followed. It was from the Platonist tradition, too, that the science of the earlier Middle Ages came. A considerable portion of Plato's _Timaeus_ had been translated into Latin in the fourth century by Chalcidius with a very elaborate commentary based on ancient sources, while the _Consolation of Philosophy_, written in prison by the Roman Platonist Boethius in A. D. 525, was easily the most popular book of the Middle Ages. It was translated into English by Alfred the Great and by Chaucer, and into many other European languages. It was on these foundations that the French Platonism of the twelfth century, and especially that of the School of Chartres, was built up, and the influence of that school in England was very great indeed. The names of Grosseteste and Roger Bacon may just be mentioned in this connexion, and it would not be hard to show that the special character of the contribution which English writers have been able to make to science and philosophy is in large measure attributable to this influence.

But the interest of Greek philosophy is not only historical; it is full of instruction for the future too. Since the time of Locke, philosophy has been apt to limit itself to discussions about the nature of knowledge, and to leave questions about the nature of the world to specialists. The history of Greek philosophy shows the danger of this unnatural division of the province of thought, and the more we study it, the more we shall feel the need of a more comprehensive view. The 'philosophy of things human', as the Greeks called it, is only one department among others, and the theory of knowledge is only one department of that. If studied in isolation from the whole, it must inevitably become one-sided. From Greek philosophy we can also learn that it is fatal to divorce speculation from the service of mankind. The notion that philosophy could be so isolated would have been wholly unintelligible to any of the great Greek thinkers, and most of all perhaps to the Platonists who are often charged with this very heresy.

Above all, we can learn from Greek philosophy the paramount importance of what we call the personality and they called the soul. It was just because the Greeks realized this that the genuinely h.e.l.lenic idea of conversion played so great a part in their thinking and in their lives.

That, above all, is the lesson they have to teach, and that is why the writings of their great philosophers have still the power to convert the souls of all that will receive their teaching with humility.

J. BURNET.

MATHEMATICS AND ASTRONOMY

It has been well said that, if we would study any subject properly, we must study it as something that is alive and growing and consider it with reference to its growth in the past. As most of the vital forces and movements in modern civilization had their origin in Greece, this means that, to study them properly, we must get back to Greece. So it is with the literature of modern countries, or their philosophy, or their art; we cannot study them with the determination to get to the bottom and understand them without the way pointing eventually back to Greece.

When we think of the debt which mankind owes to the Greeks, we are apt to think too exclusively of the masterpieces in literature and art which they have left us. But the Greek genius was many-sided; the Greek, with his insatiable love of knowledge, his determination to see things as they are and to see them whole, his burning desire to be able to give a rational explanation of everything in heaven and earth, was just as irresistibly driven to natural science, mathematics, and exact reasoning in general, or logic.

To quote from a brilliant review of a well-known work: 'To be a Greek was to seek to know, to know the primordial substance of matter, to know the meaning of number, to know the world as a rational whole. In no spirit of paradox one may say that Euclid is the most typical Greek: he would know to the bottom, and know as a rational system, the laws of the measurement of the earth. Plato, too, loved geometry and the wonders of numbers; he was essentially Greek because he was essentially mathematical.... And if one thus finds the Greek genius in Euclid and the _Posterior a.n.a.lytics_, one will understand the motto written over the Academy, ?de?? a?e?et??t?? e?s?t? {medeis ageometretos eisito}. To know what the Greek genius meant you must (if one may speak e? a????at?

{en ainigmati}) begin with geometry.'

Mathematics, indeed, plays an important part in Greek philosophy: there are, for example, many pa.s.sages in Plato and Aristotle for the interpretation of which some knowledge of the technique of Greek mathematics is the first essential. Hence it should be part of the equipment of every cla.s.sical student that he should have read substantial portions of the works of the Greek mathematicians in the original, say, some of the early books of Euclid in full and the definitions (at least) of the other books, as well as selections from other writers. Von Wilamowitz-Moellendorff has included in his _Griechisches Lesebuch_ extracts from Euclid, Archimedes and Heron of Alexandria; and the example should be followed in this country.

Acquaintance with the original works of the Greek mathematicians is no less necessary for any mathematician worthy of the name. Mathematics is a Greek science. So far as pure geometry is concerned, the mathematician's technical equipment is almost wholly Greek. The Greeks laid down the principles, fixed the terminology and invented the methods _ab initio_; moreover, they did this with such certainty that in the centuries which have since elapsed there has been no need to reconstruct, still less to reject as unsound, any essential part of their doctrine.

Consider first the terminology of mathematics. Almost all the standard terms are Greek or Latin translations from the Greek, and, although the mathematician may be taught their meaning without knowing Greek, he will certainly grasp their significance better if he knows them as they arise and as part of the living language of the men who invented them. Take the word _isosceles_; a schoolboy can be shown what an isosceles triangle is, but, if he knows nothing of the derivation, he will wonder why such an apparently outlandish term should be necessary to express so simple an idea. But if the mere appearance of the word shows him that it means a thing _with equal legs_, being compounded of ?s?? {isos}, equal, and s?e??? {skelos}, a leg, he will understand its appropriateness and will have no difficulty in remembering it. _Equilateral_, on the other hand, is borrowed from the Latin, but it is merely the Latin translation of the Greek ?s?p?e???? {isopleuros}, _equal-sided_. _Parallelogram_ again can be explained to a Greekless person, but it will be far better understood by one who sees in it the two words pa?a?????? {parallelos} and ??a? {gramme} and realizes that it is a short way of expressing that the figure in question is contained by parallel lines; and we shall best understand the word _parallel_ itself if we see in it the statement of the fact that the two straight lines so described go _alongside one another_, pa?' a????a? {par' allelas}, all the way. Similarly a mathematician should know that a _rhombus_ is so called from its resemblance to a form of spinning-top (???? {rhombos} from ?e?

{rhembo}, to spin) and that, just as a parallelogram is a figure formed by two pairs of parallel straight lines, so a _parallelepiped_ is a solid figure bounded by three pairs of parallel planes (pa?a??????

{parallelos}, parallel, and ep?ped?? {epipedos}, plane); incidentally, in the latter case, he will be saved from writing 'parallel_o_piped', a monstrosity which has disfigured not a few textbooks of geometry.

Another good example is the word _hypotenuse_; it comes from the verb ?p?te??e?? {hypoteinein} (c. ?p? {hypo} and acc. or simple acc.), to _stretch under_, or, in its Latin form, to _subtend_, which term is used quite generally for 'to be opposite to'; in our phraseology the word _hypotenuse_ is restricted to that side of a right-angled triangle which is opposite to the right angle, being short for the expression used in Eucl. i. 47, ? t?? ????? ????a? ?p?te????sa p?e??a {he ten orthen gonian hypoteinousa pleura}, 'the side subtending the right angle', which accounts for the feminine participial form ?p?te????sa {hypoteinousa}, _hypotenuse_. If mathematicians had had more Greek, perhaps the misspelt form 'hypot_h_enuse' would not have survived so long.

To take an example outside the Elements, how can a mathematician properly understand the term _latus r.e.c.t.u.m_ used in conic sections unless he has seen it in Apollonius as the _erect side_ (????a p?e??a {orthia pleura}) of a certain rectangle in the case of each of the three conics?[3] The word _ordinate_ can hardly convey anything to one who does not know that it is what Apollonius describes as 'the straight line drawn down (from a point on the curve) in the _prescribed_ or _ordained_ manner (teta?e??? ?at??e?? {tetagmenos kategmene})'. _Asymptote_ again comes from as?pt?t?? {asymptotos}, _non-meeting_, _non-secant_, and had with the Greeks a more general signification as well as the narrower one which it has for us: it was sometimes used of parallel lines, which also 'do not meet'.