The Greeks left the house of the myth as well as the Jews, but they left it by a different door and found themselves on a different road thereafter. In their thought the question whence the world has come was transformed into the question what the world is. To them the highest wisdom was not to hear the voice of the living God but to see the immovable essence of being.
Thales taught that the beginning of all things was water. So we are informed by Aristotle. Do these words teach a cosmogony?
Thales of Miletus is the first name we hear in the history of Greek philosophy as well as of Greek mathematics. He lived in the first half of the 6th century BC. Thus he may have been a hundred years younger than Hesiod and perhaps a contemporary of those Jewish priests who wrote the first chapter of Genesis. Very little is known about his person. I feel tempted to think of him as what the 19th century AD would have called a merchant-banker, being a citizen of one of the greatest commercial cities of his time. He would not, perhaps, be the founder of the firm but rather belong to a younger generation; thus he may have had wealth and leisure to see the world and to satiate his immense curiosity, a quality he shared with all of his nation. He was thoughtful. Once, a late anecdote tells us, when contemplating the sky he fell into a cistern, and some women laughed at the man who looked at the heavens and forgot to see what was before him. But according to another story he restored his reputation as a realist. Just as he proved to be able to predict an eclipse of the sun he even seems to have been able to predict the weather; thus by buying up all the oil mills before a season he foresaw as being a good one for the oil crop he did very good business.
The Greek noun which I have translated by “beginning” is arche. It belongs to the verb archein, which means to be the first one in every respect, whether it be as a beginner or as a ruler. It would be surprising if Thales, in using this word, did not think of a beginning in time.
In putting water at the beginning of all things, Thales does not seem to have expressed a view very different from that of the oriental myths which he no doubt knew. Apsû and Tiâmat are the water. And would Thales, who lived in Asia Minor, not have known the views of one of the greatest civilized nations of his time? He is also said to have thought that the earth as a whole was swimming on water like wood and that in earthquakes it was rocking like a ship. This seems quite a natural idea for a son of a seafaring nation, and it is not yet far away from the myth of the earth-embracing stream Okeanos.
Yet there is another nuance in his view, and probably this nuance means that the time of mythos has come to an end and the time of logos has begun. Thales calls his beginning water. This is not the name of a god and not the name of the great Divine Things like Earth, Heaven or even Sea. Water is not an individual that exists once; it exists everywhere and more recent thinkers would say that it is a universal concept, not a single thing. The mythical causality begins to be reversed: by putting water in the beginning we explain the beginning by likening it to the things of everyday life.
But then even the concept of beginning, of principle, must change its meaning. If Thales really did think that there was a time in which there was nothing but water, how can the other materials and things have originated from water? Shall we not be compelled to say that they really are water? Experience teaches us that water can be changed into ice and into steam, and that steam and ice can be changed back into water. Just for that reason we say today that ice and steam are nothing but water in a different state. And if everything has come from water, water must be what later thinkers would call the substance of the world. This is what Aristotle understood Thales to have meant. Water is then the principle of all things: all things are water. The question whence the world has come has been changed by its own logic into the question what the world is: cosmogony has been transformed into ontology.
But then the answer that all things are water or any other stuff cannot be satisfactory. If everything is water, what do we mean by “water”? How are we to distinguish that water which appears as water from the other water which appears as stones, grass and cows? Certainly we should not confound the real thing with one of its appearances. It seems that the beginning of our sentence, “all things are …” is a very profound question to which the end “… water” gives a very superficial answer. Now the water which first was seen to be the starting-point of a non-mythical analysis of the world appears on a higher level of reflection like a remnant of the mythical world-view. Perhaps we may compare this idea of water to a hook on which the fish of the question about being was caught.
Philosophies that took this question in its full seriousness have not always returned to cosmogony at all. When they did, their cosmogonies were more or less the myths of their respective ontologies; they were ways of explaining their interpretation of being in the easier language of narration. Hence from here on cosmogony cannot be separated from ontology. We shall follow the path of Greek ontology in a few rapid steps which unfortunately cannot but be somewhat superficial.
Things are perhaps water. Rather not water. But they are something. What are they? What do we mean by “being something”?
In any case they are. They exist. What is “to exist”? What is being?
It is the historic accomplishment of Parmenides from Elea to have first asked these questions clearly and abstractly. He expressed them, as usually happens, not as questions but as answers, not as doubts but as affirmations. His affirmations are so abstract that up to this day there is no agreement about their meaning. But just because their meaning remained debatable they influenced all later thought like questions. A later philosopher who wanted to assert or deny Parmenides’ position had first to restate it; he had to give his own interpretation of what being meant.
I shall not try to be wiser than ancient philosophers or modern philologists; I shall not try to explain what Parmenides meant to say. But I must quote as much of him as will be needed to understand his influence on later Greek thought:
Come now, and I will tell thee
and do thou hearken and carry my word away
the only ways of enquiry that can be thought of:
the one way, that it is and cannot not-be,
is the path of Persuasion, for it attends upon Truth;
the other, that it is-not and needs must not-be,
that I tell thee is a path altogether unthinkable.
For thou couldst not know that which is-not nor utter it;
for the same thing can be thought as can be.1
This is certainly a good and modern translation. Every translation, in a text of this degree of abstraction, is an interpretation. I prefer to express the fourth line of this text in a clumsy literal translation which tries not to make the English text more easily understood than is the Greek text. It would then read, that the first way of investigation says: “The one, that is, and that not-being is not.” It says “that is”. The “is” has no grammatical subject. Some interpreters have thought the text to be corrupt; or at least, that a particular subject should be inserted. But which subject should we insert? That something is? That an existing thing is? That nothing but existing things are? That one thing only is? That being is? I am inclined to think that the text is not corrupt, and that Parmenides would have been able to say all that if he had wanted to say it. He goes on to say: and that not-being is not. Wrong is the way that not-being is, and wrong is the way that both being and not-being are.
But then being can have no beginning.
One way only is left to be spoken of, that it is;
and on this way are full many signs that what is
is uncreated and imperishable,
for it is entire, immovable and without end.
It was not in the past, nor shall it be,
since it is now, all at once, one, continuous;
for what creation wilt thou seek for it?
how and whence did it grow?
Nor shall I allow thee to say or to think,
‘from that which is not’;
for it is not to be said or thought that it is not.
And what need would have driven it on to grow,
starting from nothing, at a later time rather than an earlier?
Thus it must either completely be or be not.
Nor will the force of true belief allow that,
beside what is, there could also arise anything from what is not;
wherefore Justice looseth not her fetters to allow it
to come into being or perish, but holdeth it fast;
and the decision on these matters rests here:
it is or it is not.
But it has surely been decided, as it must be,
to leave alone the one way as unthinkable and nameless
(for it is no true way),
and that the other is real and true.
How could what is thereafter perish?
and how could it come into being?
For if it came into being, it is not,
nor if it is going to be in the future.
So coming into being is extinguished and perishing unimaginable.2
Being thus is opposed to any temporality. According to Parmenides being “was not” and “will not be”, for this would imply change. Being is and changes not. Speaking of Thales we said that if things grew out of water they somehow still are water, so that water is the unchanging principle of being. This same thought seems here to be formulated on its adequate level of abstraction, leaving out the unphilosophical specification of being as water.
But whenever a thought is made rigid and consistent, its inherent paradoxes begin to stand out clearly. If being cannot change, change cannot be. But our world is a world of change. Is it therefore not being? What would this mean? We started asking how the world came to be. We went on asking what the world is. We then asked what being is. We found that being is unchangeable and coming to be unthinkable. Thus we found the idea of being and we lost its applicability to this world of change.
Parmenides himself, however, devoted the second half of his poem to cosmogony. The greater part of this second half is lost. But we know that he considered it not to present truth as the first half did, but doxa, i.e. opinion. Is opinion in his view false opinion? If it is, why does he propose it? If it is not, what does he mean by the distinction of opinion and truth?
Here the later philosophers take their starting point. They accept the timeless, unchanging nature of being. Then they have to explain the changing aspects of the world. They have to say either how change can be, or else in what sense the changing world we know may be not-being. They have to explain that by first saying what they understand by being. I shall describe just two different solutions of this problem: the theory of atoms of Leucippus and Democritus, and the theory of forms of Plato.
Everything that is, consists of indivisible parts, the atoms. All differences between things are differences of the shapes, positions, and motions of their atoms. All change is a change of the positions of atoms. Besides the atoms, nothing exists.
Never has a simpler explanation of the world been offered than this. It is not necessary to advertise it in our time, when the atom has taken over even the headlines of the newspapers. It may be more important to point out in what sense modern atomic physics does not agree with this simple picture of ancient atomism. But that is to be left to the second series of lectures. It is now my task to say more clearly what kind of a philosophy ancient atomism really was.
Leucippus, its founder, is said to have been a disciple of Parmenides. Democritus, who was the most famous disciple of Leucippus, lived to be an elder contemporary of Plato. Epicurus, the Hellenistic philosopher of wise contentment—who by one of the strange misinterpretations of which history is full has given his name to an unrestrained indulgence in sensual pleasures—carried the doctrine further, and our main literary source about it, Lucretius Carus in his poem De Rerum Natura, considers him to be its real founder.
In order to remind ourselves of the immense power of explanation of this doctrine it is sufficient to think of the transformation of water into ice or steam. This is now to be understood as changes of the order and the state of motion of the atoms. In ice the atoms have fixed places like students in their rows of seats. When the ice melts into water they begin to move past each other, but still in close contact, comparable to the students who are just leaving the lecture hall. In steam they fly freely through space just as the students will take their individual ways home alone or in little groups, the molecules. In this precise setting the explanation of the “states of aggregation” is, in fact, modern, but I think it corresponds very well to the intention of ancient atomism.
But we would not understand ancient atomism rightly if we took it to be mainly a scientific hypothesis, trying to explain observed phenomena. It is even a fact that the main development of those sciences in which antiquity excelled most, mathematics and astronomy, was closely connected with the philosophical school that was strictly opposed to the atomists, the school of Plato; I shall point to the probable reasons for this fact later. Atomism was a philosophy. It was an attempt to solve the speculative problem of being. From the point of view of modern science this may seem to be a weakness, an overloading of the boat that had to cross the ocean of experience with a ballast of metaphysical stones. I agree that its dogmatic character was a weakness. But that is the weakness of most historical philosophy. Philosophers tend to become famous not for their good questions but for their premature answers. And if I have described scientism rightly, it is a sort of unconscious philosophy itself, not less dogmatic for not being conscious of its dogmatism. In any case, quantum theory, as I hope to show in the second series of lectures, has forced back upon us physicists precisely some of those philosophical questions which the empirical atomism of the nineteenth century had thought fit to avoid.
What, then, is the solution of the Eleatic problem of being, as offered by ancient atomism?
To Parmenides being is one and unchanging; not-being is not; change is not being. The atomists start by defining more closely what they mean by being. The only existing things are the atoms. Being is one. Hence an atom is one. It has no parts. Thence it follows that it cannot be divided. While to modern thought the phrase that the atom is one would be a somewhat obscure expression of its practical indivisibility, to ancient atomism its absolute indivisibility is a natural consequence of its ontological quality of being one. You may as well argue from the unchanging nature of being. Division would be a change. Hence atoms, if they deserve the predicate of being at all, must be indivisible. The statement that atoms are indivisible is an ontological proposition.
This theory seems to offer a wonderful solution to the problem of the reality of change. Water can change, it can be transformed into ice or steam. But water does not exist in the strict sense, it is an aspect of the atoms. The atoms of water cannot change, they are truly existing. But their positions and states of motion change. Thus you can choose whether you like to call change real: it really takes place but it does not change the really existing things.
But we are allowed to doubt whether this clever trick really makes the paradox of change and being disappear. In identifying the atoms with being, the atomists have tacitly sacrificed two central ideas of the Eleatic philosophy: the uniqueness of being and the non-existence of not-being. To say “the atom is one and hence indivisible” is all right; but there are many atoms, and they are needed to explain the world. The atomists did not even consider the atoms to be equal. There are big atoms and small atoms, rough square atoms of earth, finer atoms of fire, and the very fine, round and smooth all-pervading atoms of the soul. We may avoid this objection by interpreting “being” not as a subject but as a predicate, the common predicate of all existing things, even if we have to admit that this way of expression presupposes a logic, not yet developed in Democritus’ time. But even then we do not avoid the second, or graver contradiction. Democritus says quite clearly himself that atomism has to admit the existence of non-being: to meden exists as well as to den, a pun in Greek which might be rendered in English by saying: “Nothing exists as well as ‘thing’.” He is speaking of the void.
In fact, if atoms lay packed contiguously without any intervals, no motion would be possible. The space into which an atom is to move must be free for it. Atomism has always assumed the existence of empty space. Now we must not forget that the concept of absolute space as we know it from Newton is modern. Equally modern is the idea that geometry is a science whose subject matter is space. Greek geometry was about points, finite straight lines, triangles, circles, cubes, spheres and so on; it did not even have a word for space. Similarly the atomists had no word like our “space”; they spoke of to kenon, the void. But to speak of the void as existing is a paradox, if we take the Eleatic starting point of the atomists seriously. The void is empty of existing things, it is a kind of not-being. If it were being, it would have to be built from atoms itself, because we started by saying that the atoms were the only being. Thus again the rigid consequence of thought has produced a paradox. By apparently conserving the Eleatic theory of being in one point, in the atoms, this philosophy is forced to contradict the same theory of being in the other point, the void. Once it has thus incorporated the paradox in its very foundations, it can draw all its further conclusions with apparently perfect rationality. It is a pity that we do not know Democritus’ answer to this problem since all his books are lost except for a few fragments. In the popularizing poet Lucretius we cannot expect an understanding of the rigour of thought that prevailed in the great times of Greek philosophy; he says nothing about the question.
Can atomism give us a cosmogony?
Since atoms cannot change they cannot have originated. Thus cosmogony cannot mean the coming to be of atoms. They have always existed and they will exist for ever. But cosmos means order. Order can have arisen out of disorder in the world of ever-existing atoms. In this sense there is an atomistic cosmogony. In Kathleen Freeman’s book on the pre-Socratic philosophers3 it is briefly and fairly described in the following terms:
Many atoms of differing shapes separate off from the infinite mass and come together in a great empty space. Here, having collected, they form an eddy, that is, they begin to move round in a circle. As they jostle together in this revolution, like goes to like: the light atoms fly outwards, the rest stay together. Of the latter, certain hook-shaped atoms, being interlocked, form a kind of outer skin, globe-shaped, enclosing the rest; this is the sky. In the centre are the bodies borne there, and now cleaving together, except for some which fly outward and are retained by the outer skin, which keeps whatever touches it; these are the heavenly bodies. All is now revolving round the central mass, which is the material from which earth is made. The motion caused the drying up of this mass, and the squeezing out of the water, so that earth and sea were separated.
First I want to say a few words about the astronomical merits of this picture. You see that the earth is now considered to be a sphere in the centre of the world, and that the sky is another sphere, surrounding the earth. This is a great step forward compared with the earlier view which thought of the earth like a flat disk and of the sky like a hemisphere. The Greeks had recognized the spherical shape of the earth at an early time by correctly interpreting the way in which a ship disappears behind the horizon and the circular shape of the earth’s shadow at lunar eclipses. A second progress is the idea that it is not the stars which wander over the sky but that the sky as a whole is a sphere which rotates around the earth, carrying the stars with it. This view is no longer held today. But I think that just by being on a higher level of abstraction than the idea that sun and stars wander individually, it is a progress in the right direction; once the sky is understood to move as a whole in relation to the earth it will be an easier step to reverse the order of motions by saying that the sky stands still and the earth rotates. In fact, this view was held by later Greek astronomers like Aristarchus; the reason why Greek astronomy finally rejected it I shall consider in the sixth lecture.
What I have just said about the spheres of earth and heaven was common Greek knowledge at the time of the atomist philosophers. Probably their own contribution lies in the idea that this rotating heavenly sphere had originated in a huge eddy of atoms. This proved to be a very useful idea; you will see its application in modern theories like those of Descartes, of Kant and of 20th century astronomers. Nor did the atomists confine their consideration to this world, that is to this one earth on which we live with its own sky. They thought that the universe was infinite, containing an infinite number of atoms which form an infinite number of worlds which originate in the way I described and are destroyed in due course by new mixtures of the atoms. This idea, too, has been taken up by the modern theories mentioned above. Thus, in a way, scientists of our time may feel quite at home in the world of Leucippus and Democritus.
Yet there is another side of the coin. Modern science rests on a quantitative description of phenomena; it rests on the concept of mathematical laws of nature. I have not been able to find the slightest indication of this idea in Greek atomism. A critical modern scientist might find the sketch of atomistic cosmogony which I read to you very similar to some rather bad popular modern representations of the world-view of science. There is an impressive imagery of eddies, of different-shaped atoms sticking together, like going to like, light atoms moving outward, heavy ones inward without a clear concept of gravitation or of buoyancy: a story plausible to the unscientific mind, neither explaining what follows mathematically nor formulating a guarded hypothesis, but telling what might have happened as though it were plain truth; it is a tale of becoming, a myth.
I should like to call the atomistic cosmogony a myth of science. The god in whom these myth-tellers believe is the blind necessity of atomic collisions. This anti-religious element of atomism was consistent. If there are man-shaped gods at all they cannot be anything but bodies formed from atoms since atoms are the only existing things; thus before there might have been a god who planned a creation there must have been a blind agglomeration of atoms out of which the god originated by pure chance. This is, of course, only a late consequence of a view which denies the gods of the myth from the outset. Whenever I dare to say precisely what is the nature of every existing thing the god who is greater than all my thoughts has disappeared; this complete objectivation of the world is identical with a negation of the numinous. And this is what atomism intends. Epicurus is courteous enough to admit the existence of gods who live a life of inactive bliss in the intermundia, the empty spaces between the “worlds”; they do not concern themselves with human life. Lucretius writes his poem for a friend in order to free him from the fear of gods and of punishments in another world, those inventions of priests longing for power. After having described how Iphigenia was sacrificed to priestly prejudice he writes the famous line: Tantum religio potuit suadere malorum, so powerful was religion to mislead mankind towards evil. When in the later centuries of antiquity even the intellectuals longed for a revival of religion, this anti-religious tendency proved fateful for the atomistic school of philosophy. It had to wait for the 17th century to be resumed.
Let us now come to the other solution of the Eleatic problem: Plato’s philosophy. I read to you a part of Plato’s cosmogonical dialogue, the Timaeus, in Cornford’s translation.
We must then, in my judgment, first make this distinction: What is that which is always real and has no becoming and what is that which is always becoming and never real? That which is apprehensible by thought with a rational account is the thing that is always unchangeably real; whereas that which is the object of belief together with unreasoning sensation is the thing that becomes and passes away, but never has real being. Again, all that becomes must needs become by the agency of some cause; for without a cause nothing can come to be. Now whenever the maker of anything looks to that which is always unchanging and uses a model of that description in fashioning the form and quality of his work, all that he thus accomplishes must be good. If he looks to something that has come to be and uses a generated model, it will not be good.
So concerning the whole Heaven or World—let us call it by whatsoever name may be most acceptable to it—we must ask the question which, it is agreed, must be asked at the outset of inquiry concerning anything: Has it always been, without any source of becoming; or has it come to be, starting from some beginning? It has come to be; for it can be seen and touched and it has body, and all such things are sensible; and, as we saw, sensible things, that are to be apprehended by belief together with sensation, are things that become and can be generated. But again, that which becomes, we say, must necessarily become by the agency of some cause. The maker and father of this universe it is a hard task to find, and having found him it would be impossible to declare him to all mankind. Be that as it may, we must go back to this question about the world: After which of the two models did its builder frame it—after that which is always in the same unchanging state, or after that which has come to be? Now if this world is good and its maker is good, clearly he looked to the eternal; on the contrary supposition (which cannot be spoken without blasphemy), to that which has come to be. Everyone, then, must see, that he looked to the eternal; for the world is the best of things that have become, and he is the best of causes. Having come to be, then, in this way, the world has been fashioned on the model of that which is comprehensible by rational discourse and understanding and is always in the same state.4
This is the beginning of a long description of the creation of the world, and it is a very condensed summary of Plato’s philosophy. Three elements are to be distinguished in it: First the world that somehow has come to be. Secondly he who made it, whom Plato at times calls the God, at times the craftsman (demiourgos), and in a few poetic parts the father of the universe. Thirdly that invariable being that served as a model according to which the world was made.
Here again we have the changing things which are not strictly being and the being that changes not. But their relationship is again a different one: the immovable being is the archetype, the changing things are its copies. What did Plato mean by archetype and copies?
Since it is science we want to understand, let me use a scientific example. Take a pencil and a sheet of paper and draw a circle. Please do it yourself; it is an experience not to be replaced by just thinking of it. You will not produce a good circle. A second or third one may be better but not satisfactory. With a compass you will do better. But look at it with a magnifying glass or even use a microscope. You will see hills of graphite, roughly round like the mountain-ranges on the moon. Finally you will have learnt your lesson: we are unable to produce a perfect material circle. There is no real circle in this world.
But we have wonderful mathematical propositions about circles, e.g. that the circle of all closed figures of equal circumference is that which has the largest area. These propositions are true, they can be proved. But what are they about if there are no circles in the world? Material so-called circles just look like true circles. Mathematical propositions are about what sense-objects look like. The way a thing looks would in Greek be called its eidos or its idea. Mathematical propositions are about the eidos, the idea, they are about the archetype of which sense-objects are unsatisfactory copies. They are not about this or that thing we may call a circle, they are about the circle itself. You can also say: physical circles are supposed to be shaped according to the mathematical circle. Mathematical propositions are not about material things but about shapes. The material thing “is” not a shape, it “has” or “takes on” a shape. It thus has or takes its part (it participates, metechei in Plato’s Greek) in those structural qualities which strictly speaking only belong to the shape in its rigorous mathematical sense. Shape is called morphe in Greek, forma in Latin. Mathematical propositions are about forms. Form is the word by which many modern English texts translate Plato’s idea now, in order to avoid confusion with the completely different meaning of the English word idea. English idea means something in the mind, something merely subjective; Plato’s idea means the highest degree of objectivity. For the idea is the only thing about which there is strict science. How this change of meaning has come about I shall explain in the next lecture.
But are forms real? Mathematics is a science about things thought of. To the modern mind this implies that it is not about real things, since we are accustomed to call sense-objects real. If you want to understand Plato you will have to eradicate this view from your minds. You will be permitted to re-introduce it in following the further course of history. But now follow this argument: Mathematical propositions are precise and their truth does not depend on time. Statements about sense-objects are ever unprecise, and what was true yesterday may be false today. Yesterday my car’s wheel was something like a circle; this morning I had an accident and now the wheel is egg-shaped. But, as Parmenides said, being is without change, and truth is about being; about changing things there is but changing opinion. Hence mathematics, just because it relies on thought and not on sense-perception, is about existing things, while physics is about their unreliable copies in the world of the senses.
This, I think, explains why mathematics flourished in the Platonic school but not in the school of the atomists. Both schools agree that true understanding is possible only about real being. Now, if atoms are the only real being, how can statements about such imaginary things as mathematical spheres, triangles and so on be true knowledge? Precisely if the atomists took their philosophy in a strict sense they could not develop strict mathematics; then there cannot be a science about “the circle” but only about circular arrangements of atoms. Thus, I think, atomism lacked the most important ingredient of the idea of mathematical laws of nature: the belief in the relevance of mathematics. Platonism, on the other hand, lacked the less important part: the belief that mathematics can be strictly applied to nature. Thus atomism produced no mathematical physics at all, while Plato in his Timaeus says that one cannot give a strict science of nature but that we must here be satisfied by “telling a likely story”. The Greeks are the only nation which came close to a mathematical theory of nature before modern times; they even gave some beautiful examples of such a theory, e.g. in astronomy. Still they did not achieve it in its full breadth. One of the hindrances may well have been that their philosophical theories did not lead them to consider a full mathematical description of nature as possible. If this were true, just the rigour of their philosophical thought in their most productive period may have proved detrimental to their natural science, while it so intensely promoted the development of their equally rigorous mathematics.
Now, speaking of mathematics, I did not choose Plato’s own starting-point. His first concern was not about geometry but about man. Following Socrates he did not ask about the circle itself, but about bravery itself, about beauty itself, about virtue itself, of which the single instances of bravery, of beauty, of virtue are nothing but incomplete examples or copies. Love, Eros, kindled by the sight of a beautiful body reminds the soul of beauty itself. The myth of reincarnation tells us that the soul has seen beauty itself in an earlier, now forgotten life. He who remains longing for the beloved beautiful body will not understand his own love better than the mathematician, if he confounds the circle on paper with the true circle, has understood his mathematics. Both content themselves with a mocking reflection of the true light. He who understands the truth of his own love will love the soul of the beloved one. For the soul is the place in which the truth appears, and true love is only possible to souls who find each other in the love of truth. The same structure prevails in the political field. The true order of the state can only be found if we follow the example of original truth. Political passion which understands itself rightly is the longing for the realization of the unchanging order of truth in the changing medium of human life. Therefore the true statesman must be a philosopher.
Even from the point of view of clear understanding, mathematics does not deserve the highest rank in Plato’s thought. The mathematician, it is true, draws strict conclusions from given premises, but the premises themselves he just assumes without being able to prove them. I shall remind you of this deep insight into the nature of mathematics when, in the second series of lectures, I shall speak about mathematics from a modern point of view. In the view of Plato, true cognition ought to give an account even of the presuppositions of mathematics. This account is one of the tasks of his theory of forms. What do we mean by saying that only the “circle itself” has true being, while “circles” of the sensual world, coming-to-be and passing away, have their imperfect being only by their “participation” in the being of the “circle itself”? The simple sentence “this pencil-drawn curve has the shape of a circle” contains the whole problem. What do we mean by “it has a shape” (“partakes in it” as Plato says)? What “is” a shape? Plato uses the terms archetype and image. Yet evidently this is itself a simile. If true cognition refers to the form only, then the participation of changing things in the form can essentially be expressed only by the same imprecise imagery by which we must be satisfied in speaking of the world of change itself.
What, then, is a form? This very question is the question about the highest element of Plato’s thought, the idea tou agathou, the Form of the Good. The good of which he speaks here is not primarily the morally good; on the contrary, Plato’s ethics can only be understood by an interpretation of what he means by the good. Schematically we may describe the Form of the Good as the Form of Forms, the Essence of Essence. If you draw a circle well, it is a “good circle”. Yet it will not be really good; the only really good circle is the true circle, the circle itself, the form of the circle. The good circle is that in which all the different empirical circles participate as far as they are (relatively) good. In philosophy we are interested in different forms, you can say in different goods: that of the circle, of bravery, of beauty and so on. They have something in common: they are all forms, they are all good. What is the form in which they thereby participate? It must be called the form of forms, the Form of the Good. In the Simile of the Cave the changing things are likened to shadows. He who leaves the cave sees the things themselves—that is the forms—in the light of the sun. The sun in whose light they are seen is the idea tou agathou.
In investigations like this the very meaning of all the available words is in question at every step. Hence Plato must make use of similes on every level. Thus we ought not to consider the relationship of the form of the good to the realm of forms to be a schematic repetition of the relationship of the single forms to the world of the senses. And we can be assured that Plato did not ascribe to his forms a thing like existence, some hypostasized “being in itself” in a “heaven of ideas”. Plato was most certainly not what modern logicians call a Platonist. If he defines the form as that which is, then only the form of the forms, the idea tou agathou itself represents what we would schematically call the quality of being, and he explicitly says that it is not existent in the sense in which the other forms exist; it is “beyond existence”. Hence it would be contrary to his explicitly stated view to explain the being of forms by comparing it to the existence of sensual things. We cannot here follow these central problems of Plato’s philosophy, but we ought to see how they are mirrored in the Timaeus.
Besides the changing copies and the unchanging archetype our text from Timaeus contained a third element, the god who has formed this world as a copy of the archetype. This is not one of the known gods of Greek religion. It seems that no Greek thinker or poet before Plato had ever uttered the idea of a creator of the world. No wonder that the Christians of later times understood Plato to be the pagan sage who came closest to the revealed truth. On the other hand interpreters who have tried to understand Plato strictly in philosophical terms, from the ancient Academy to the modern philologists, have commonly thought of this divine craftsman as a mythical circumscription of an abstract thought. As far as Plato’s conscious intention goes I am inclined to share this second view. It is well known how often Plato resorts to a mythos, a tale, where he does not consider an abstract exposition possible or understandable to the reader. Plato’s myths are never naive; they are works of art which admit of strict interpretation. I think the only strict interpretation possible for the demiourgos is that he is such a work of art pointing to something else. This need not inhibit Christians, however, from thinking that something more than his conscious philosophical intention may have guided Plato’s artistic inspiration when he wrote the Timaeus.
The interpretation which I follow here thinks that Plato chose the myth of creation in order to describe as a sequence in time what he really considered to be the timeless structure of the world. This is similar to the way in which a complicated geometrical structure is explained by drawing it on paper step by step before the eyes of the pupil. Similarly a fictitious process of foundation serves Plato in his Republic to analyse the structure of a model community. In this sense I should like to call the Timaeus a scientific myth, a story told by a scientific mind and somehow in terms of science. What Plato certainly meant was that the world was “always becoming”, which seems to indicate that everything in the world has a beginning and an end. But it does not follow that the world itself had a beginning; and Plato explicitly denies that it will have an end. Aristotle who never resorted to myths certainly held the world to be without a beginning and an end, thus transferring an aspect of Parmenidean being to the world as a whole just as the Atomists had transferred it to the atoms. I see no necessity to assume Plato to have held a corresponding view but it seems more plausible to me than the contrary. In any case Plato does not treat the demiourgos as a god to be religiously revered and he never speaks of him in any work besides the Timaeus.
If I were speaking of Plato’s cosmogony on its own merits I now ought to devote a further lecture to the details of the Timaeus, for instance his elaborate mathematical models of what in his view correspond to the atoms. In our actual context, however, I shall only mention one further point: the origin of that which is not good.
It is as natural to Plato as to the Bible to see God as the source of the existence of all that is good. When the Biblical report of the creation was interpreted as representing a creation out of nothing, the insoluble theological problem of the origin of evil was born. Plato does not yet see a problem here.
The maker of the universe is good. To imagine his work to be other than as good as possible is a supposition “which cannot be spoken without blasphemy”. Still the world is not perfect; it is only as perfect as possible. For the demiourgos is not almighty, and he has not created the world out of nothing—two views which Plato probably never considered even as possibilities. Speaking in speculative strictness the very sense of the concept “good” implies that there is something that is not good; hence interpreting being itself by the form of the good means to admit the presence of something opposed to the good. But what do we now mean by “presence” and “something”? The answer to these questions is given in mythical language in the Timaeus.
The god took over all that is visible—not at rest, but in inconstant and unordered motion—and brought it from disorder into order, since he judged that order was in every way the better.5
For the generation of this universe was a mixed result of the combination of Necessity and Reason. Reason overruled Necessity by persuading her to guide the greatest part of the things that become towards what is best; in that way and on that principle this universe was fashioned in the beginning by the victory of reasonable persuasion over Necessity.6
Thus there are two principles acting in the world: the order of divine reason and the chance of blind necessity. To a modern ear it may sound strange to find necessity identified with chance. Here we must remember the atomists. Plato accepts their interpretation of necessity. Necessity is the inevitable effect of the collision of the spatial elements, the atoms; and those collisions are not guided by any law that would be understandable to reason, they happen blindly. Modern times, giving the concept of necessity a new, precise, sense by means of the concept of mathematical laws of nature, thus interpret necessity itself, quite differently from Plato, by means of that order which Plato calls the form. Here we see why Bentley, still using Plato’s concept of blind necessity, was inconsistent after the invention of the concept of all-pervading mathematical laws of nature. To Plato necessity is what we cannot foretell while all that we can foresee is a planned work of reason. Thus to him the perfection of the world is caused by its participation in the divine forms, its imperfection by the action of necessity.
This Platonic description of the universe is the starting point of two later views on the origin of evil that were often used in combination: One of them considered evil to be non-being, the other one derived evil from matter as opposed to the spirit.
The view that evil is non-being can be justified in Platonic terms. A thing is good as far as it participates in its form. Since the form alone has true existence, that in the sensible things which is not good appears as a lack of existence. But can this doctrine be reconciled with the Biblical understanding of Good and Evil? Perhaps it offers a very profound interpretation of the Biblical thought that good means life, evil means death; only that which is good has true existence, that is true life. Yet in the Bible, which does not use philosophical abstractions, evil appears as a reality in face of which a decision is needed. Plato’s writings abound in exhortations that we must make the decision for the good; and yet we seem to feel that evil in the Biblical sense is still different from Plato’s kakon, the absence of the good. And the interpretation of evil as non-being does not remove the paradox of creatio ex nihilo; why should God, if he is all-bountiful, have made creatures that are so horribly lacking in being?
If we derive evil from matter, and if we mean by matter what the demiourgos “took over”, then this is the same doctrine as before. There is no knowledge of formless matter, precisely because it lacks what alone can be known, namely form; it cannot even be said what formless matter is. In the same sense Aristotle calls prote hyle, matter apart from all form, unknowable. Yet later dualistic systems considered matter to be a positive power which was opposed to light, to reason, to God. It would be worth while to contemplate these systems in their sombre grandeur. Here this would lead us too far. In any case they are neither Biblical—for the Bible does not originally know the concept of Matter—nor are they Platonic—for the Greeks of classical times did not know the Biblical understanding of evil.