Matter and Form (Ionians and Pythagoreans)

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First published 16 March 1950 CONTENTS Reprinted 1956 and 1962 First published in this style 1967 CHAPTER 1.4 1. SBN 416 44550 0 a MATTER GREEK WAYS OF THINKING (IONIANS FORM AND AND PYTHAGOREANS) First published as a University Paperback 1967 : 11. 1.2 THE PROBLEM OF MOTION (HERACLITUS, PARMENIDES AND THE PLURALISTS) SBN 416 69700 3 THE Printed in Great Britain by REACTION TOWARDS HUMANISM (THE SOPHISTS AND SOCRATES) Fletcher & Son Ltd - Norwich naeo This book is available both as a hardbound and a paperback edition. The paperback edition ts sold THE DOCTRINE OF IDEAS PLATO (II). ETHICAL AND THEOLOGICAL ANSWERS subject to the condition that it shall not, by way of VII. trade or otherwise, be lent, re-sold, hired out, or PLATO (1), TO THE ARISTOTLE (1). SOPHISTS THE consent in any form of binding or cover other than VIII. 81 101 ARISTOTELIAN 122 UNIVERSE otherwise circulated without the publishers’ prior 63 ARISTOTLE (11). HUMAN BEINGS 142 that in which it is published und without a similar SUGGESTIONS condition including this condition being imposed on the subsequent purchaser. INDEX INSTITUUT VOOR FILOSOFIE DISTRIBUTED BARNES IN AND THE NOBLE USA BY INC GuTHRIE W. K. C., Aristotle as a historian of philosophy . Some prelimin-. aries : JHS LXXVII 1957 35-41. | A propos del’ouvrage de H. Cherniss, Aristotle’s criticism of presocratic philosophy (cf. APh X 9) et de l'étude de J. B. McDiarmid, Theophrastus on the presocratic causes (cf. APh XX VI 206), mise en évidence de l'intérêt des analyses d’Aristote pour l’histoire de la pensée présocratique. | FOR FURTHER READING

MATTER FORM 28 the taste for the disinterested investigation of nature CHAPTER for its own sake reached its height. More than any other Greek did he possess the scientific temperament. Moreover the interest of the Pythagoreans in the human soul was rather religious and mystical than philosophical. We may say, however, that such II MATTER AND FORM (lonians and Pythagoreans) WE saw in the last chapter that philosophy as we shall be concerned with it has two main sides, dealexhibited by the Ionians became for ever Impossible ing on the one hand with the nature and origins of after the apparent breakdown of natural philosophy the Universe at large and on the other with human in the fifth century, and the importunate questionlife and conduct; and I warned any who might be primarily interested in ethical and political thought ings of Socrates which brought human life into the very centre of the picture. that when we go back to the beginnings of European we shall now proceed to inquire. philosophy in Greece it is speculation about the Universe that we shall encounter first. The whole period which we shall have under review is usually divided into two by the name of Socrates—with what justification we shall see as we proceed--and the characteristic mark of pre-Socratic thought is a an exclusive devotion to external nature as was How all this happened Kuropean philosophy, in the sense of an attempt to solve the problems of the Universe by reason only, as opposed to the acceptance of purely magical or theological explanations, began in the prosperous time of Socrates saw a reaction against physical commercial cities of Ionia, on the coast of Asia Minor, in the early sixth century B.c. It was, as Aristotle said, the product of an age already provided with the necessities for physical well-being consuming curiosity about the cosmos. The lifespeculation and a shifting of philosophical interest and to human affairs. Like all large generalizations, this is only approximately true. While in the Eastern The Ionian or Milesian School is represented by the part of the Greek world the Ionians were absorbed in the first attempts at a scientific explanation of the there is this much justification for calling it a school, Universe, in the West the Pythagoreans were setting Ionian city of Miletus, their lifetimes overlapped, and up the ideal of philosophy as a way of life, and the tradition at least described their relations as those philosophic brotherhood as a kind of religious order; of master and pupil. and leisure, and its motive was simple curiosity. names Of Thales, Anaximander and Anaximenes, and that all three were natives of the same prosperous the great successors of Socrates, Plato and Aristotle, while not neglecting the problems of ways. human life, were both interested also in speculation sisting through the chaos of apparent change; and about the world in which we live. For Plato indeed the human soul was at the centre; but in Aristotle they thought that they would find it by asking the 22 The object of their search may be described in two They looked for something permanent, perquestion: ‘What is the world made of?” The world

MATTER AND FORM PHILOSOPHERS possible answer, It may equally be supposed that the material components of the world are in a constant flux of decay and renewal, are manifold and incomprehensible, but that the permanent and comprehensible element lies in its structure or form. If new matter as it comes along fits itself always to the same structure, it is the structure that we must try to understand. In Greece itself the champions of form against matter were Lo have their turn. At the beginning, however, the question asked was, in its simplest terms: ‘What is the world made of?’ ‘Thales of Miletus said that it was water, or moisture, an as our senses perceive it seems restless and unstable. It exhibits continual and apparently haphazard Natural growth may proceed or may be thwarted by blind external forces. In any case it is followed by decay and nothing lasts for ever. Morechange. over we observe an apparently infinite plurality of unrelated objects. that beneath Philosophy started ia the faith this apparent chaos there exists a hidden permanence and unity, discernible, if not by sense, then by the mind. This statement applies of course to all philosophy. 25 As a modern writer on philosophical method has put it: ‘There seems to be a deep-rooted tendency in the answer which might open up all sorts of interesting human mind to seek . . . something that persists through change. Consequently the desire for explanation seems to be satisfied only by the discovery that what appears to be new and different was there all the possibilities, were it not that we know scarcely anything more about his views and can only conjecture what was the train of thought which led him to his conclusion. The most obvious explanation seems to be that water exhibits itself naturally to the time. Hence the search for an underlying identity, ‘They senses, without any apparatus of scientific experiment such as was not then available, in the three forms solid, liquid and gaseous, as ice, water and steam. This is accordingly the explanation which occurs most readily to modern scholars, but it is were already philosophers, and the basic problems interesting that Aristotle has a quite different sugof philosophy change little through the ages. gestion. He, too, was guessing—whatever Thales may have written was already lost in his day—-but he was at least a Greek and nearer to Thales than ourselves. I want to suggest some reasons why he may have been right, but this is a topic to which we had better return when we have looked at the views a persistent stuff, a substance that is conserved in spite of qualitative changes and in terms of which these changes can be explained.”! That description of the philosophie mind might have been written specially for the Milesians. Central is the faith that beneath the apparent multiplicity and confusion of the universe around us there exists a fundamental simplicity and stability which reason may discover. Secondly, it seemed to the earliest speculators that this stability must be sought in the substance of which the world was made. ‘This is not the only 1 L. S. Stebbing, 4 Modern Introduction to Logic, (Methuen, And ed. 1988), p. 404. u—-aof the other two Milesians. Beyond his statement that the underlying substance of the Universe is water, we know little of Thales’s philosophical views. ‘There are one or two IGP_H

GREEK PHILOSOPHERS aphorisms, difficult to interpret without and several anecdotes. MATTER a context, AND FORM 27 water does not generate fire, but destroys it. Ilence ‘The story in Herodotus that he imagined the first state of matter to be an unhe predicted a solar eclipse, which can be dated to differentiated mass of enormous extent, in which the the year 585 n.c., may be taken to be sulliciently antagonistic elements or their properties were not bien trouvé to give us his approximate date. yet distinct, though it contained them as it were in The prediction is by no means impossible with the aid of a latent or potential form, a complete fusion. the Babylonian records of which he is said to have called it the apeiron, a word which means ‘without been a student. We know more of his younger fellowboundaries’, and in later Greek was used in two main Ile citizen Anaximander, who left writings which were senses: certainly available to Aristotle and ‘Theophrastus, infinite, and (6) without internal boundaries, i.e. in and the work of Theophrastus on the Opinions of the Natural Philosophers was the basis of the Graecoor elements, could be observed. (a) not bounded externally, ie. spatially which no distinctions of separate component parts, It is unlikely that Roman compilations which have come down to us. Anaximander had arrived at the notion of strict The thought of Anaximander was already of some spatial infinity, and although he certainly conceived subtlety. He saw this present world as a warring his matrix to be of vast and indeterminate extent, the concourse of opposite qualities, of which four were thought uppermost in his mind was probably the lack primary—hot and cold, wet and dry. The worldprocess is acyclic one. The sun’s heat dries up water, of internal distinctions, since this is the concept which water puts out fire. On a world-seale it is observable mind, that of the original condition of the opposites. in the cycle of the seasons, and though one or other of the opposites may prevail for a time, the balance as being in everlasting motion, as a result of which it is constantly being restored. Now since the essential thing about these qualities is their mutual opposiopposite qualities, or substances containing them, tion, it follows that the primary substance of the began to separate themselves out. Universe cannot be characterized by any one of them Anaximander called a seed or germ of a world, a would solve the problem that was obviously on his This primal mass was pictured by Anaximander happened, at some time in some part of it, that the Hence arose what — cannot, Anaximander would have said, be any one fertile nucleus—for he borrowed that term from the of them, for it is most unlikely that at this early stage of thought quality and substance were differenrealm of organic nature. tiated. astronomy. Had Anaximander been asked whether, At first it must have been something like the whirling nebulas known to modern Gradually the cold and wet element when he spoke as he did of ‘the hot’ or ‘the cold’, he meant a substance or a quality, he would probcondensed into a wet mass of earth at the centre, ably not have understood the question. showed itself as a sphere of flame enclosing the If then, as Thales had supposed, all were originally water, or ‘the moist’, there could never be heat or fire, since wrapped round in cloud or mist. The hot and dry whole, which as it revolved burst apart into rings or wheels of fire around which surged the dark mist

GREEK from within the sphere. PHILOSOPHERS MATTER AND FORM 29 This is his explanation of some use of observation, supporting his notion of the sun, moon, and stars, cach of which is really a ring drying-out of the earth by the presence of fossilized of fire right round the earth, though only visible to shells in inland districts, and his argument that man us at one point where there is a hole in the encircling had evolved from a lower form of life by the observapours through which the fire streams through a puncture in a bicycle tyre. like air Under the influence of the fire at the circumference, parts of the earth were dried out and separated from the water that surrounded them. Life first arose during this process in the warm mud or slime, for the origin of life was in moisture acted upon by warmth. first animals were The therefore fishlike, and enclosed in prickly or scaly coverings. From these developed all land-animals, including man, who has evolved ultimately from a sort of fish. and rests unsupported at the centre of a spherical llere Anaximander gave, to a question which had long puzzled the Greeks, an answer which for subtlety of thought was ahead of many of his successors. What did the earth rest on? If on water, as Thales had said, then what did the water rest on, and so forth? It rests on nothing, said Anaximander, and the reason it does not fall is simply that, being at the centre of a spherical equidistant from all its universe, and hence it could have no reason for falling in one direction rather than in another. must have been a time when the young were carried about for protection by the parent, and this, he observes, is done by certain species of large fish. To assess his quality, we must not only look back on him from our own time, but see him in relation to previous and contemporary Greece. points, It is in the position of the donkey placed exactly half-way between two bundles of hay, which dies of starvation because it cannot decide which way to turn. This cosmogony of Anaximander’s, in spite of certain fantastic elements, was a remarkable achievement for the dawn of rational thought. He made His was an age when the supernatural was still taken for granted, when the forces of nature were attributed to the actions The earth in this account is cylindrical like a drum, universe. vation that, in his present state, man is helpless and dependent for a considerable time after birth. There of anthropomorphic gods, a Zeus or a Poseidon, and the origin of the Universe had hitherto been union sought in grotesque stories of heaven and earth, about a sexual conceived as vast primeval deities, and their forcing-apart by another gigantic spirit. With Anaximander human reason asserted itself and produced what, right or wrong, was for the most part an account in purely natural terms of the origin of the world and life. From Anaximenes, the remaining member of the Milesian School, we have no connected account of :osmogony, but a primary substance. new claimant for the title of This is air (Greek aer, which in ordinary speech—and there is no question at this stage of a technical scientific terminology—meant both air and mist or fog). In its natural, or what Anaximenes called its most evenly distributed state, it is the invisible atmosphere, but it is capable of being condensed into mist and water, and so, he claimed, still further into solid substances like earth

and stones. MATTER PHILOSOPHERS When it becomes still rarer, it also this one idea remmined. AND FORM 31 It was indeed a legacy from pre-rational thought, for this material conception becomes hotter and turns into fire. His chief interest seems to have lain in discovering a natural process by which it might be supposed that the changes in of the soul as air or breath is of course a primitive the primary substance take place, whereby our inaniamong savage peoples all over the world, fold world comes into being. Anaximander’s word one to which anthropologists have found parallels was certainly coupled among and it the earlier Greeks for the process which gave rise to our world had been with the idea that the world as a whole was a living ‘separating-out’, but it could fairly be said that this creature. was no more than a brilliant conjecture which could Nevertheless for these early scientists there was a not be verified in any known process of nature. For it Anaximenes substituted the observed fact of conspecial reason why it should still have seemed necessary. Besides the one question that they asked densation and rarefaction, whereby we see air reduced —What is the world made of?—there seems to us to to moisture and vice versa. To illustrate the conbe another which needs answering as well, namely: nexion of rarefaction with heat and condensation if the world is at bottom, and was originally, one with cold he pointed out that if we breathe with our substance, why did it not remain so, a dead, static lips nearly closed the breath emerges cold, whereas mass of water or whatever it was? if we open our mouths to give it more room it is inotive cause which first started it changing? warmer. question occurs to us because from recent science What was the This we have inherited the notion of matter as in itself One particular tenet of Anaximeues throws light on the outlook of the whole school. He said that in something dead or inert, which needs to be called its purest and rarest form of all, the air which is the into motion by an outside force. ultimate world-substance is also the stuff of life. A tinetion between matter and force is not so obvious in small portion of this soul-stuff, which Perhaps the disproperly this century as it was in the last, nor does the natural belongs by its nature to the outermost reaches of the scientist nowadays regard it as within his province Universe beyond the adulterated atmosphere which to deal with the problem of a first cause. But philowe breathe, is imprisoned in the body of each animal sophy cannot ignore it, and we are speaking of men or human being, and forms its soul. ‘Our soul’, said to whom science and philosophy were one indivisible one of his followers, ‘is air, hotter than the air outfield of knowledge. side us, though much colder than the air at the sun.’ question of the cause of motion? This man also expressed the same thing by saying How did they deal with this As Cornford put it, ‘If we would understand the that man’s soul is ‘a small part of the god’, the god sixth-century philosophers, we must being the still minds of the atomistic conception of dead matter in thought of by these men as being alive. For all their mechanical motion and of the . . . dualism of matter astonishing freedom from theological preconceptions, and mind.’ Universe, which we thus learn is disabuse our Aristotle, who was already crilicizing

MATTER AND PHILOSOPHERS FORM 88 the lonians for (as it appeared to him) ‘lazily shelvliving body, is always a damp warmth. ing’ the question of the motive cause, remarks in one place, without comment, that none of them made nexion between heat and life, an obvious fact of experience, was insisted on by the Greeks as essential earth the primary substance. There was surely a and causative more than it is to-day.) If that was good reason for this. wanted a substance Thales’s idea, ‘They we find (‘The conit explicitly paralleled by which would explain its own movement, as in those Anaximander who accounts for the origin of life by early days it was still possible to imagine it doing. the action of heat on watery or slimy matter. One thought of the ceaseless tossing of the sea, another of the rushing of the wind, and on the threshold of rational thought the natural explanation of Seeing that these thinkers only asked their single question: ‘What is the world made of?’ it is tempting to label them materialists. their apparently self-caused movement was that they were eternally alive. Thus we find that all of them, while in other respects avoiding the language of religion and completely discarding the anthropomorphism of their time, yet applied the name God or ‘the divine’ to their primary substance. So Anaximisleading, mander called his apeiron and Anaximenes the air. and spirit had been distinguished, so that the matter which was the sole and unique fount of all existence was itself regarded as endowed with spirit or life. Thales is credited with the dictum: ‘Everything is full of gods’, which Aristotle interpreted as meaning that ‘soul is mingled in the whole’. The stuff of the since that This, however, would be term in ordinary modern speech stands for one who has made a choice between the known alternatives of matter and spirit as the ultimate causes of things, and consciously denies any originating power to the spiritual. What we must try to understand is a state of mind before matter than modern commentators are inclined to allow. As philosophy progresses, it finds it more and more difficult to maintain this two-in-one conception, and not the least interesting aspect of the development of Greek thought is that which shows matter and spirit straming increasingly at the bonds which unite His words are: ‘He got the notion probably from them. Matter has to be credited with more and more seeing that the nutriment of all things is moist, and of the attributes of spirit, including mind, until the question comes to a head and a break is inevitable. world must be the stuff of life, and that is why I think there is more to be said for Aristotle's conjectures about the reason for Thales’s choice of water that heat itself is gencrated by the moist and kept alive by it... and that the semen of all creatures For the rest of this chapter let us turn to the has a moist nature, and water is the origin of the Pythagoreans. The two main streams of tradition in carly Greek thought were spoken of in later antiquity nature of moist things.’ The lines of thought suggested by Aristotle are as the lonian and the Italian, The latter begins with those which link up water with the idea of life: the moisture which is a necessary part of food and Pythagoras, who although an Fastern Greek by semen, and the fact that vital heat, the warmth of a migrated to South Italy round about 580 u.c., where birth left his native island of Samos early in life and

PHILOSOPHERS he settled and founded his brotherhood in the town of Croton. For political reasons they were persceuted and dispersed, and by the fifth century scattered Pythagorean communities were to be found in various parts of Greece. ‘To say nothing about the Pythagorean tradition would be to give a very onesided view of Greck philosophy and to omit something that was a potent influence on the mind of Plato. Yet it would perhaps defeat our present purpose to devote much space to them here, owing to the obscurity which envelops much of their doctrine and their history. For this obscurity there are good reasons, Among the Pythagorcans, the motive for plulosophy was not what it had been for the lonians, simple scientific curiosity. They were a religious brotherhood, and this had certain consequences. Some at least of their doctrines were held to be secret, and not to be divulged to the profane. The founder himself was canonized, or regarded as semi-divine. ‘This meant in the first place that a haze of miraculous legend gathered about him, from which it is difficult to disentangle the life and teaching of the historical Pythagoras. In the second place it was considered a pious duty to ascribe any new doctrine to the founder himself, and considering that the school had a long history, including a particularly flourishing revival among the Romans in the time of Cicero, it is obviously difficult to find out just what were Pythagoras’s own beliefs or those of the school in its MATTER AND FORM 35 only as man but also in the bodies of other creatures, With this is connected the most important of Pythagorean taboos, their abstention from animal tlesh, For the beast or bird which you eat may haply be inhabited by the soul of your grandmother. If that is so, if the transmigration of souls is possible and usual, then all life is akin, and the kinship of nature is another Pythagorean tenet. It went further than we might think, for the animate world extended further for them than it does for us. They believed indeed that the Universe as a whole was a living creature. In this they agreed with the lonians, but they saw implications in it which were foreign to Anaximander or Anaximenes and came rather from mystical religious than from rational sources. ‘Ihe cosmos, they held, is surrounded with a boundless quantity of air or breath, which permeates and gives life to the whole. It is the same thing which gives life to individual living creatures. From this relic of popular belief, rationalized as we saw by Anaximenes, a religious lesson was now drawn, The breath or life of man and the breath or life of the intinite and divine Universe were essentially the same. The Universe was one, eternal and divine. Men mortal. But the essential part of man, his soul, were many and divided, and were was not mortal, and owed its immortality to this fact, that if was a fragment or spark of the divine soul, cut off and imprisoned in a mortal body. Man had thus an aim in life, to shake off the taint early days. of the body and, becoming pure spirit, rejoin the Ou its religious side, the core of Pythagoreanism was a belief in the immortality of the human soul, universal spirit to which he essentially belonged. and its progress through a series of incarnations not continue Until the soul could purify itself completely, it must undergo a series of transmigrations,

MATTER AND PHILOSOPHERS FORM 87 This meant the The religion of Pythagoras embodied, as we have retention of individuality so long as the allotted cycle of births was incomplete, but there can be little doubt that the ultimate aim was the annihilation of self in reunion with the divine. These beliefs the Pythagoreans shared with other seen, a kind of pantheism. The world is divine, tt is therefore good, and is a single whole. If it is good, mystical sects, notably with those who taught in the exchanging one body tor another. alive and a whole, that is because, said Pythagoras, it is limited, and displays an order in the relations of its various parts. Full and efficient life depends on But the originality organization. We see this in individual living creatures, which we call organisms to indicate that of Pythagoras is seen when we ask what are the means they have all their parts arranged and subordinated whereby the aim of purification and union with the divine may be attained. Hitherto purity had been sought by ritual, and the observance of mechanical to the end of keeping the whole alive (Greek organon taboos such as the avoidance of corpses. Pythagoras well as good and living, is that it has fixed limits and name of the mythieal Orpheus. = tool or instrument). So with the world. The only sense in which it can be called a single whole, as retained much of this, but added a way of his own, is therefore capable of organization. the way of the philosopher. of world-phenomena was thought to support this. The doctrine of the kinship of nature, which may The regularity Days succeed nights and seasons seasons in due and be said to be the first principle of Pythagoreanism, invariable order. is a relic of ancient belief, having much in common thought) eternal and perfectly circular motion. The wheeling stars exhibit (as was with the notion of magical symputhy. Its second short the world may be called a kosmos, an unprinciple is something rational and typically Greek. translatable word which combined the notions of That is, the emphasis laid by Pythagoras on form or order, fitness, and beauty. Pythagoras is said to have structure as the proper object of study, together with been the first to call it by this name. In If, as a classical Pythagoras, being by nature a philosopher, argued professor recently stated in his inaugural lecture, a that if we want to identify ourselves with the living characteristic mark of the Greeks is their preference cosmos, to which we believe ourselves to be essenfor ‘the as tially akin, then while not neglecting the old religious opposed to the fantastic, vague and shapeless’, then rules, we must first and foremost study its ways and Pythagoras was the foremost apostle of the Hellenic find out what it is like. spirit. moral closer to it, as well as enabling us to conduct our dualists, drew up two columns under the headings lives in closer conformity to the principles which it of good things and bad things. In the good column, reveals. Just as the Universe is a kosmos, or ordered along with light, unity and the male, came limit; in whole, so Pythagoras believed that each one of us is a kosmos in miniature. We are organisms which an exaltation of the idea of limit. intelligible, The determinate, Pythagoreans, as mensurable, convinced the bad column, with darkness, plurality and the female, is placed the unlimited. This in itself will bring us reproduce the structural principles of the macrocosm.

by MATTER AND FORM PHILOSOPHERS studying these structural principles, we develop and encourage the elements of form and order in ourselves. The philosopher who studies the Kosmos becomes kosmios-—orderly—in his own soul. Pythayoras’s own interests were first and foremost mathematical. It may be taken as established that this does not mean simply a superstitious playing with numbers, but that he made real and considerable advances in mathematics. The discoveries which he made were totally and astonishingly new. by the figure called the tetraktys, i.e. 4. 59 The octave is produced by the ratio2:1, the fifth 8 : 2, and the fourth 4:3. Now if one aid not know this, it is not the sort of thing that would occur to one while playing the lyre, and perhaps picking out the notes with a certain amount of trial and error. The discovery lay in the existence of an inherent order, a numerical organization within the nature of sound itself, and it appeared as a kind of revelation concerning the nature of the Universe. irrefutable The general principle which it was taken to illustrate was that of the imposition of limit (peras) on the unlimited (apeiron) to make the limited (peperasmenon). This was the general Pythagorean formula for the making of the world and all that it contains, and it was coupled with the moral and aesthetic corollary that limit was good and the unlimited evil, so that the imposition of limit and the formation of a kosmos, which they claimed to see in the world as a whole, was evidence of the goodness and beauty of confirmation, on purely rational grounds, to these the world and an example to be followed by men. earlier ways of thought, Owing to Pythagoras’s discovery, music provided for his followers the best instance of this principle at work. Its suitability was enhanced by the beauty of music, to which Pythagoras like most Greeks was sensitive, for the word kosmos carried to a Greek the suggestion of beauty as well as order. It was thus further evidence for the equation of limit with goodness that its imposition on the field of sound brought beauty out of disharmony. The whole field of sound, then, ranging indefinitely in opposite directions—high and low—is an instance of the unlimited. Limit is represented by the numerical system of ratios between concordant notes which If we do not realize how exciting and fresh they must have seemed, we shall not be in a state of mind to sympathize with the extraordinarily wide application which it seemed right to him to give them. We must allow for a remnant of primitive thinking too: we remember what has becn said about the savage’s irrational confusion objects numbered. coveries must between numbers But his own have seemed to and the remarkable disgive His most striking discovery, and the one which is said to have exercised the widest influence over his thought and to have been the foundation of his mathematical philosophy, was in the ficld of music. He found out that those intervals of the musical scale which are still (I believe) called the perfect consonances can be april arithmetically as ratios between the numbers 1, 2, 8 and 4. These are the numbers which, added together, make 10, and the number 10, in the curious Pythagorean combination of mathematics and mysticism, was called the perfect number. It was illustrated graphically

PHILOSOPHERS MATTER AND FORM 41 reduces the whole to order. It is marked out accord: they expressed their new-found conviction by saying ing to an intelligible plan. This plan is not imposed that ‘things were numbers”? on it by man, but has been there all the time awaiting his discovery. In Cornford’s words: ‘The infinit e variety of quality in sound is reduced to order by the exact and simple law of ratio in quantity. The system so defined still contains the unlimited element in the blank intervals between the notes; but the unlimited is no longer an orderless continuum: it is confined within an order, a kosmos, by the imposition of limit or measure.’ | This process, grasped here in a single striking instance, the Pythagoreans supposed to be the ruling principle at work in the Universe as a whole . It is here that their cosmology differs essentially from the lonian type, giving one the right to call it a philosophy of form and theirs a philosophy of matter. They spoke of a mixture of opposites and left it at That gives their general line of thought, and we cannot here go into its many individual applications. One, however, may be mentioned as an illustration, and for the powerful influence which it exercised over a very important branch of Greek science, a branch of science in which Greek, and hence ultimately Pythagorean, ideas were still regarded as canonical throughout the Middle Ages and beyond, in the Mosler East as well as in the Christian West. That is, the study of medicine. Limit and order are good, and the well-being of the world and of every creature in it depends on a right mingling (krasis) of the elements of which it is composed. It is then in a state of harmonia, the word which (in Greek as in English) primarily applied to music being extended to cover the whole field of nature. "Fo the that. The Pythagoreans added the notions of order, microcosm this doctrine was applied in the theory proportion, and measure, i.e. they laid the stress on quantitative differences. Each separate thing was that bodily health was dependent on the rightly proportioned mixture of the physical opposites: hot and cold, wet and dry. If they are in a state of harmonia in the body, then, as the doctor in Plato’s what it was not because of its material elements (which were common to all), but becau se of the proportion in which those elements were mixed : and since it is in this element of proportion that one class of things differs from another, so they argue d that this, the law of its structure, was the essential thing to discover if one wanted to understand it. The emphasis is shifted from the matter to the form. Structure is the essential thing, and this structure could be expressed numerically, in terms of quantity. Is it now surprising, considering the inchoate state of philosophy at the time, and the absen ce of any systematic study of logic or even of grammar, that Symposium puts it, the most mutually hostile elements in it are reconciled and taught to live in amity: ‘and by the most hostile 1 mean the most sharply opposed, as hot to cold, bitter to sweet, dry to wet’, This dogma of the importance of maintaining—or restoring in the case of sickness—the right quantitative relationships between opposite qualities became the corner-stone of Greek medicine, which started in a Pythagorean atmosphere with the work of Alcmaeon of Croton. Pythagorean notions have had such a long history

THE GREEK PHILOSOPHERS in philosophy and literature that other illustrations will easily suggest themselves. I cannot for example go into the doctrine of the harmony of the spheres, against whose appealing but fragile beauty the prosaic mind of Aristotle directed some of its heaviest logical batteries. But at least we have seen something of the field of thought in which such a strange idea was born, and have a glimpse of the world which lay behind the words of Lorenzo to Jessica as they rested on the moonlit bank outside the house of Portia: Sit, Jessica. Look how the floor of heaven Is thick inlaid with patines of bright gold. There's not the smallest orb which thou behold'st But in his motion like an angel sings, Still quiring to the young-eyed cherubins. Such harmony is in immortal souls; But whilst this muddy vesture of decay Doth grossly close it in, we cannot hear it. CHAPTER III THE PROBLEM OF MOTION . (Heraclitus, Parmenides and the pluralists) THE next philosopher in the succession is the enigmatie Heraclitus, who earned even in antiquity the nicknames of ‘The dark one’ and ‘The Riddler’. Although the exact dates of his life are unknown, his position in the history of philosophy is fixed well enough by the fact that he criticized Pythagoras by name and is himself fairly obviously alluded to by Parmenides. He must have been at work just about the turn of the sixth and fifth centuries B.c. If we find him difficult to understand, this is not only because we possess no more than a few fragments of what he actually wrote. He had clearly a haughty and contemptuous mind, and delighted in throwing out isolated oracular sayings rather than developing a patient and continuous line of argument. His method of communication is like that of the Delphic oracle, which, he says, ‘neither utters nor hides its meaning, but shows it by a sign’. Nevertheless it is worth trying to get at some of the ideas underlying his disjointed pronouncements. They reveal an interesting stage in the history of thought. ‘ The target of his criticism in Pythagoras and others was their investigation into external nature, their search for facts. ‘Polymathy—the learning of many things—does not teach understanding,’ he wrote. ‘Otherwise it would have taught Hesiod and Pythagoras, Xenophanes and Hecataeus.’ Such learning