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Plato (427-347 B.C.)

So far as concerns philosophy only a selected group can be explicitly mentioned. There is no point in endeavoring to force the interpretations of divergent philosophers into a vague agreement. What is important is that the scheme of interpretation here adopted can claim for each of its main positions the express authority of one, or the other, of some supreme master of thought - Plato, Aristotle, Descartes, Locke, Hume, Kant. But ultimately nothing rests on authority; the final court of appeal is intrinsic reasonableness. The safest general characterization of the European philosophical tradition is that it consists of a series of footnotes to Plato. I do not mean the systematic scheme of thought which scholars have doubtfully extracted from his writings. I allude to the wealth of general ideas scattered through them.

Alfred North Whitehead (1861-1947), from his book Process and Reality, page 39, first published in 1929.

Plato compares philosophy with preparing for death (Phaedo 67cd) and its goal with becoming like a god (Theaetetus 176b). This view of philosophy implies two doctrines central to the Platonic tradition: the immortality of the soul and the community (koionia) of the human and divine.  These ideas were not new with Plato nor did they die with him. It is the nature of the philosophical endeavor to borrow and transform the ideas of others and to pass these ideas on for others to use and adapt. Plato is arguably the single most important ancient Greek thinker, although his strength lies not merely in his innovation but also, and perhaps especially, in his critical understanding of the philosophical tradition.

John F. Finamore, Professor and Chair, Department of Classics, University of Iowa, President of the U.S. Section of the International Society of Neoplatonic Studies.

Plato (427-347 B.C.) was born in Athens to an upper class family.  On his mother's side, Plato was related to the famous 6th Century B.C. Athenian law-giver Solon, who is counted as one of the seven sages of ancient Greece.  In his youth, Plato studied under Cratylus, who had been a student of the great philosopher Heraclitus of Ephesus.  While still a young man, Plato saw the decline, military defeat and overthrow (404 B.C.) of the Athenian Democracy at the hands of Oligarchic Sparta. 

Before the Athenian defeat, Plato became a student of the philosopher Socrates in about 407 B.C.   Socrates believed that the most effective way of teaching a student to argue logically was to engage the individual in a philosophic dialogue, in which the student would attempt to argue a point.  Socrates would ask a series of seemingly innocent questions which would lead the student to a conclusion which was incompatible with his original statement.  This type of teaching is now called the "Socratic Method" and is still used by many university law schools in the United States and Europe.  Plato witnessed the death of Socrates at the hands of the newly restored Athenian democracy in 399 B.C. Shortly thereafter, fearing for his own safety, Plato temporarily left Athens and traveled in Italy, Sicily, and Egypt.  While in Italy, he learned of the teachings of Pythagoras and was probably  initiated into one of the secret Pythagorean Societies.

In 387 B. C., Plato returned to Athens and founded a school on property which had originally belonged to a man named Academos.  Thus the school came to be known as the "Academy."  This institution is often described as the first European university. It provided a comprehensive curriculum, including the four most important of the seven liberal arts, the quadrivium, i.e., geometry, arithmetic, astronomy, and music.  Aristotle was the Academy's most famous student.  The Academy of Plato became one of the longest lasting institutions of higher education in Europe, functioning for over 900 years.  It was finally closed in 529 A.D., by order of the Emperor Justinian, who claimed it was a pagan school.

The importance of mathematics to the teachings of the Academy is illustrated by the Greek inscription that was carved above the main entrance to the Academy:

Αγεωμετρητος μηδεις εισιτω

(Latin Alphabet Transliteration:  Ageômetriêtos mêdeis eisitô)

(English Translation:  No One without Knowledge of Geometry May Enter Herein)

Seizing an opportunity to combine philosophy with politics, Plato went to Sicily in 367 B.C. to tutor the new ruler of Syracuse, Dionysius the Younger, in the art of philosophical rule. The experiment failed. Plato made another trip to Syracuse in 361 B.C., but this second trip also ended in failure. The concluding years of his life were spent lecturing at the Academy and writing. Plato died in Athens at about the age of 80.

Plato is perhaps my favorite philosopher.  His dialogue, The Republic, was the first philosophical work that I ever read.  Indeed, I consider my own personal metaphysical beliefs to be nearer to those expressed by Plato and the Platonists than to any other particular belief system. I have plenty of company. If you were to ask academic philosophers, from American or European universities, to name the three greatest philosophers of all time it is probable that most would name Plato, Aristotle and Kant.

Plato was a superb writer, and his works are an integral part of the world's great literature. In fact, most scholars of the Greek language consider his dialogues to be the finest Greek prose ever written!  Throughout classical times and also during the Middle Ages in Byzantium and the Islamic world (but not in Western Europe), Plato was held in such high regard that all of his works were preserved.  He is the only classical philosopher for which this is the case.

Unfortunately, in Roman Catholic Europe the only Platonic work widely available was the cryptic dialogue Timaeus (in Latin translation).  However, due to the flight of Byzantine scholars to Italy in the 15th Century, Plato's complete works again became available to Western scholars.  The sudden availability of Plato's works and the writings of many other Greek and Roman authors, was a major factor in that great rebirth of learning in Europe which we now call the Renaissance.

According to the Alexandrian scholar Thrasyllus (1st Century A.D.), 35 dialogues and 13 letters were genuinely written by Plato.  However, the authenticity of several of these dialogues and letters have been questioned by modern scholars.  Even so, versions of all of these documents have survived.  Thrasyllus organized the works credited to Plato into nine tetraologies (groups of four books) consisting of thirty-five dialogues, plus the thirteen Letters counted as one single work, thereby making a total of  thirty-six. 

The Tetralogies of Thrasyllus

Euthyphro  Apology  Crito  Phaedo 
Cratylus  Theaetetus  Sophist  Statesman 
Parmenides  Philebus  Symposium  Phaedrus 
1st Alcibiades  2nd Alcibiades  Hipparchus  Rival Lovers 
Theages  Charmides  Laches  Lysis 
Euthydemus  Protagoras  Gorgias  Meno 
Greater Hippias  Lesser Hippias  Io  Menexenus 
Clitophon  Republic  Timaeus  Critias 
Minos  Laws  Epinomis  Letters 


Plato and the World of Modern Physics

In my opinion, Plato's metaphysical thinking is just as relevant in the present day as it was in the world of the 4th Century B.C. The importance of Platonic thought to people living in the modern era is perhaps best described by the great quantum physicist, Werner Heisenberg (1901-1976) in his book entitled Physics and Philosophy: The Revolution in Modern Science (first published in 1958) as follows:

In the philosophy of Democritus the atoms are eternal and indestructible units of matter, they can never be transformed into each other. With regard to this question modern physics takes a definite stand against the materialism of Democritus and for Plato and the Pythagoreans. The elementary particles are certainly not eternal and indestructible units of matter, they can actually be transformed into each other. As a matter of fact, if two such particles, moving through space with a very high kinetic energy, collide, then many new elementary particles may be created from the available energy and the old particles may have disappeared in the collision. Such events have been frequently observed and offer the best proof that all particles are made of the same substance: energy. But the resemblance of the modern views to those of Plato and the Pythagoreans can be carried somewhat further. The elementary particles in Plato's Timaeus are finally not substance but mathematical forms. "All things are numbers" is a sentence attributed to Pythagoras. The only mathematical forms available at that time were such geometric forms as the regular solids or the triangles which form their surface. In modern quantum theory there can be no doubt that the elementary particles will finally also be mathematical forms but of a much more complicated nature.

The great mathematical physicist, Sir Roger Penrose of Oxford University, made the following comments during a recent interview with Science and Spirit magazine (March - April 2003 issue):

I view the mathematical world as having an existence of its own, independent of us. It is timeless. I think, to be a working mathematician, it’s difficult to hold any other view.

It’s not so much that the Platonic world has its own existence, but that the physical world accords with such precision, subtlety, and sophistication with aspects of the Platonic mathematical world. And this, of course, does go back to Plato, who was clear in distinguishing between notions of precise mathematics and the usually inexact ways in which one applies this mathematics to the physical world. It is the shadow of the pure mathematical world that you see in the physical world. This idea is central to the way we do science. Science is always exploring the way the world works in relation to certain proposed models, and these models are mathematical constructions.

The above cited observations of Heisenberg and Penrose are very profound and are still applicable to the present time.  Currently, the physics world is experiencing a new revolution, a paradigm shift of monumental proportions.  The Relativity Theory of Einstein and the Quantum Theory of Heisenberg are in the process of being transcended by a new world view - that of "M Theory."   The well known contradictions between Relativity and Quantum Mechanics are reconciled in the mathematical equations of M Theory.  Ultimate reality is explained by, mathematically described, incredibly small membranes of energy which posses the ability to vibrate in an eleven dimensional space-time universe!  Thus, our long held idea of a material universe which contains both matter and energy is false.  Matter is really only an illusion; the Cosmos consists only of energy and vibrations!  I believe that this revolutionary new weltanschauung will ultimately have a major impact on our current understanding of human and machine consciousness.


The Unwritten Doctrines of Plato

I believe that Plato's dialogues were mainly intended as popular works for educated lay people only.  His more technical and abstruse ideas were only expressed orally and only for the students at the Academy.  I offer three arguments in support of my conclusion:

1)  It is known fact that Aristotle, a pupil of Plato for almost 20 years, attributes doctrines to Plato that cannot be explicitly located in the written dialogues. Thus it is evident that Plato spoke of matters orally that he did not feature in his dialogues.

2)  In his dialogue entitled the Phaedrus, Plato expresses the view that oral transmission of wisdom is superior to the use of written texts.  To make his point, Plato relates the story of the Egyptian god Theuth (Thoth) as follows:

At the Egyptian city of Naucratis, there was a famous old god, whose name was Theuth; ... his great discovery was the use of letters. Now in those days the god Thamus was the king of the whole country of Egypt; ... To him came Theuth and showed his inventions, desiring that the other Egyptians might be allowed to have the benefit of them; he enumerated them, and Thamus enquired about their several uses, and praised some of them and censured others, as he approved or disapproved of them. ... when they came to letters, This, said Theuth, will make the Egyptians wiser and give them better memories; it is a specific both for the memory and for the wit. Thamus replied: O most ingenious Theuth, the parent or inventor of an art is not always the best judge of the utility or inutility of his own inventions to the users of them. And in this instance, you who are the father of letters, from a paternal love of your own children have been led to attribute to them a quality which they cannot have; for this discovery of yours will create forgetfulness in the learners' souls, because they will not use their memories; they will trust to the external written characters and not remember of themselves. The specific which you have discovered is an aid not to memory, but to reminiscence, and you give your disciples not truth, but only the semblance of truth; they will be hearers of many things and will have learned nothing; they will appear to be omniscient and will generally know nothing; they will be tiresome company, having the show of wisdom without the reality.

3)  Also, Plato, in his famous Seventh Letter, states that he never committed to writing the most important elements of his thought.  In the letter, Plato tells us:

This much at least, I can say about all writers, past or future, who say they know the things to which I devote myself, whether by hearing the teaching of me or of others, or by their own discoveries-that according to my view it is not possible for them to have any real skill in the matter. There neither is nor ever will be a treatise of mine on the subject. For it does not admit of exposition like other branches of knowledge; but after much converse about the matter itself and a life lived together, suddenly a light, as it were, is kindled in one soul by a flame that leaps to it from another, and thereafter sustains itself. Yet this much I know-that if the things were written or put into words, it would be done best by me, and that, if they were written badly, I should be the person most pained. Again, if they had appeared to me to admit adequately of writing and exposition, what task in life could I have performed nobler than this, to write what is of great service to mankind and to bring the nature of things into the light for all to see? But I do not think it a good thing for men that there should be a disquisition, as it is called, on this topic - except for some few, who are able with a little teaching to find it out for themselves. As for the rest, it would fill some of them quite illogically with a mistaken feeling of contempt, and others with lofty and vain-glorious expectations, as though they had learnt something high and mighty. ... no man of intelligence will venture to express his philosophical views in language, especially not in language that is unchangeable, which is true of that which is set down in written characters.

In my opinion, Plato's dialogues, though well written, were chiefly meant to provide topics for further discussion and consideration by an educated readership.  Some of the ideas may have merit and others do not.  The dialogues were not final conclusions drawn by Plato, but are only a framework for further thought and debate.  Plato understood that a true philosopher is always undergoing intellectual growth and change.  As old ideas are modified or discarded, new ideas are generated.  A written document is a static object and, at best, can only describe the situation at one point in time. 

A Note Concerning the Timaeus of Plato

Most of the ideas discussed by Plato pertaining to consciousness (mind), or the soul to use his term, may be found within his two most famous dialogues -- the Republic and the Timaeus.  Probably the most difficult of Plato's dialogues to understand is the Timaeus.  This work chiefly concerns Plato's interpretation of the teachings of Pythagoras and the Pythagorean School concerning the Cosmos and the Soul.  Pythagoras, following the custom of the Egyptian Temple Schools where much of his learning had been obtained, had decreed that his teachings were to be kept strictly oral and should never be written down.  Plato, who probably was a Pythagorean initiate, disagreed with the Pythagoreans on this point.  He decided to commit to writing much of the Pythagorean philosophy in spite of this prohibition.  However, in order to protect the work from the profane and make it intelligible only to other Pythagorean initiates, he encrypted the work in such a way that someone not well versed in Pythagorean arithmetic and geometry would not be able to fully comprehend the ideas contained therein.  In my opinion, although many modern scholars have attempted to unravel the enigma of the Timaeus, no one has ever been able to fully understand it.  In modern times, probably the one person who came the closest was the renowned M.I.T. humanities professor and historian of science, Giorgio de Santillana (1902-1974).

Professor de Santillana, in his well-known book Hamlet's Mill (at pages 305 and 310-311   ) makes these comments about the importance of Plato and the Timaeus:

... if we did not have Plato’s Timaeus, it would be a hopeless task altogether to understand the reason which made it obligatory in those “archaic” times to watch the immense cosmic clock most carefully. Plato himself, to be sure, started on the way of all intellect—moving from thought to literature, from literature into philology, before flowing into nothing; but let us make it clear, this official “trend” is not going to detract us from our own unconditional respect.

This essay could spend many chapters on the Timaeus, that “topos” from which come and to which return all “rivers” of cosmological thought, and several more chapters on Phaedrus and Politikos, on the Epinomis, but we make it short. ...

... the Timaeus and, in fact, most Platonic myths, act like a floodlight that throws bright beams upon the whole of “high mythology.” Plato did not invent his myths, he used them in the right context—now and then mockingly—without divulging their precise meaning: whoever was entitled to the knowledge of the proper terminology would understand them. ...

... Creating the language of the philosophy of the future, Plato still spoke the ancient tongue, representing, as it were, a living “Rosetta stone.” And accordingly—strange as it may sound to the specialists on Classical Antiquity—long experience has demonstrated this methodological rule of thumb: every scheme which occurs in myths from Iceland via China to pre-Columbian America, to which we have Platonic allusions, is “tottering with age,” and can be accepted for genuine currency. It comes from that “Proto-Pythagorean” mint somewhere in the Fertile Crescent that, once, coined the technical language and delivered it to the Pythagoreans (among many other customers, as goes without saying). Strange, admittedly, but it works. It has worked before the time when we decided to choose Plato as Supreme Judge of Appeals in doubtful cases of comparative mythology ...

Plato knew ... that the language of myth is, in principle, as ruthlessly generalizing as up-to-date “tech talk.” The manner in which Plato uses it, the phenomena which he prefers to express in the mythical idiom, reveal his thorough understanding. There is no other technique, apparently, than myth, which succeeds in telling structure ... The “trick” is:  you begin by describing the reverse of what is known as reality, claiming that “once upon a time” things were thus and so, and worked out in a very strange manner, but then it happened that... What counts is nothing but the outcome, the result of the happenings told.  Generally it is overlooked that this manner of styling is a technical device only, and the mythographers of old are accused of having "believed" that in former times everything stood on its head ...


Plato's Ideas on the Nature of the Human Soul and the Mind (Ontology)

This section identifies some of the more important ontological ideas that Plato discussed in his dialogues, particularly regarding the structure and nature of the human soul and/or mind.  Where possible, I will provide direct quotations from his extant works to support the ideas discussed.

Structure and Location of the Human Soul (Mind)

Plato seems to have believed in a tri-partite soul or mind.  This soul was one part immortal and two parts mortal.  He suggested that the immortal, intellectual part of the soul (logistikon) was contained in the head, the mortal emotional part (thumos) in the region of the heart and the mortal physical part (epithumêtikon), containing basic drives and appetites, in the belly. The brain was thought to be the organ which provided the interface between the physical body and the immortal part of the soul.  Pertinent extracts from the Timaeus are as follows:

The creator ... constructed the universe, which was a single animal comprehending in itself all other animals, mortal and immortal.  Now of the divine, he himself was the creator, but the creation of the mortal he committed to his offspring. ... They, imitating him, received from him the immortal principle of the soul; and around this they proceeded to fashion a mortal body, and made it to be the vehicle of the soul, and constructed within the body a soul of another nature which was mortal ... and so framed man.  Wherefore, fearing to pollute the divine any more than was absolutely unavoidable, they gave to the mortal nature a separate habitation in another part of the body, placing the neck between them to be the isthmus and boundary, which they constructed between the head and breast, to keep them apart. 

And in the breast, and in what is termed the thorax, they encased the mortal soul; and as the one part of this was superior and the other inferior they divided the cavity of the thorax into two parts ... and placed the midriff to be a wall of partition between them.  That part of the inferior soul which is endowed with courage and passion and loves contention they settled nearer the head, midway between the midriff and the neck, in order that it might be under the rule of reason and might join with it in controlling and restraining the desires when they are no longer willing of their own accord to obey the word of command issuing from the citadel.

The heart, the knot of the veins and the fountain of the blood which races through all the limbs, was set in the place of guard, that when the might of passion was roused by reason making proclamation of any wrong assailing them from without or being perpetrated by the desires within, quickly the whole power of feeling in the body, perceiving these commands and threats, might obey and follow through every turn and alley, and thus allow the principle of the best to have the command in all of them. ...

The part of the soul which desires meats and drinks and the other things of which it has need by reason of the bodily nature, they placed between the midriff and the boundary of the navel, contriving in all this region a sort of manger for the food of the body; and there they bound it down like a wild animal which was chained up with man, and must be nourished if man was to exist. 

The first principle of all of them was the generation of the marrow.  For the bonds of life which unite the soul with the body are made fast there, and they are the root and foundation of the human race. ... God ... made the marrow ... to be a universal seed of the whole race of mankind; and in this seed he then planted and enclosed the souls, and in the original distribution gave to the marrow as many and various forms as the different kinds of souls were hereafter to receive.  That which, like a field, was to receive the divine seed, he made round every way, and called that portion of the marrow, brain, intending that, when an animal was perfected, the vessel containing this substance should be the head; but that which was intended to contain the remaining and mortal part of the soul he distributed into figures at once round and elongated ...

Need for Harmony Between the Three Parts of the Soul (Mind)

In my opinion, the most important and profound idea expressed by Plato in all of his dialogues concerns the need of all humans to integrate and harmonize the three parts of their individual souls.  This idea is perhaps best expressed in Book 4 of the Republic as follows:

But in reality justice was such as we were describing, being concerned however, not with the outward man, but with the inward, which is the true self and concernment of man: for the just man does not permit the several elements within him to interfere with one another, or any of them to do the work of others, --he sets in order his own inner life, and is his own master and his own law, and at peace with himself; and when he has bound together the three principles within him, which may be compared to the higher, lower, and middle notes of the scale, and the intermediate intervals --when he has bound all these together, and is no longer many, but has become one entirely temperate and perfectly adjusted nature, then he proceeds to act, if he has to act, whether in a matter of property, or in the treatment of the body, or in some affair of politics or private business; always thinking and calling that which preserves and co-operates with this harmonious condition, just and good action, and the knowledge which presides over it, wisdom, and that which at any time impairs this condition, he will call unjust action, and the opinion which presides over it ignorance.

In other words, humans are considered to be tripartite beings.  The tribulations and sufferings in human life occur because these internal or inward three parts of a man are fragmented and are not in the proper relationship to each other.  The main purpose of human life on Earth is twofold: 1) internally integrate each of these three aspects of the self to eliminate their internal fragmentation and 2) harmonize these three aspects, not only with each other but also with the external natural world. Only when these conditions have been achieved can a man truly be called just.

Plato's Allegory of the Chariot

Plato's metaphor comparing the human soul to a Chariot is a famous philosophical device. Plato created this allegory to provide a more lucid explanation of his ideas concerning the nature and dynamics of the human tripartite soul. This allegory is a very significant component of Plato's philosophy, but the complete narrative is quite lengthy. However, I strongly recommend that the entire text be studied. The complete Chariot Allegory is set forth in Parts 2 and 3 of Plato's dialogue called the Phaedrus. A translation by Benjamin Jowett is freely available on the Internet. A brief excerpt is as follows:

Of the nature of the soul, though her true form be ever a theme of large and more than mortal discourse, let me speak briefly, and in a figure. And let the figure be composite -- a pair of winged horses and a charioteer. Now the winged horses and the charioteers of the gods are all of them noble and of noble descent, but those of other races are mixed; the human charioteer drives his in a pair; and one of them is noble and of noble breed, and the other is ignoble and of ignoble breed; and the driving of them of necessity gives a great deal of trouble to him. I will endeavor to explain to you in what way the mortal differs from the immortal creature. The soul in her totality has the care of inanimate being everywhere, and traverses the whole heaven in divers forms appearing; -- when perfect and fully winged she soars upward, and orders the whole world; whereas the imperfect soul, losing her wings and drooping in her flight at last settles on the solid ground -- there, finding a home, she receives an earthly frame which appears to be self-moved, but is really moved by her power; and this composition of soul and body is called a living and mortal creature. ...

... As I said at the beginning of this tale, I divided each soul into three -- two horses and a charioteer;  and one of the horses was good and the other bad: the division may remain, but I have not yet explained in what the goodness or badness of either consists, and to that I will proceed. The right-hand horse is upright and cleanly made; he has a lofty neck and an aquiline nose; his color is white, and his eyes dark; he is a lover of honor and modesty and temperance, and the follower of true glory; he needs no touch of the whip, but is guided by word and admonition only. The other is a crooked lumbering animal, put together anyhow; he has a short thick neck; he is flat-faced and of a dark color, with grey eyes and blood-red complexion; the mate of insolence and pride, shag-eared and deaf, hardly yielding to whip and spur.

Tarot of Jean Noblet, VII The Chariot, JC Flornoy restoration

The Chariot tarot card appears to have been based upon the Chariot Allegory of Plato.  This example is from the tarot deck designed by Jean Noblet; it was created  in Paris in about the year 1650.  The original deck is preserved in the French National Library.


Plato's Ideas on Human Knowledge (Epistemology)

In Plato's opinion, true knowledge primarily relies on the reasoning part of the tripartite soul (logistikon).  This part of the soul makes use of intuition and places little emphasis on the information provided by our five senses. The human senses are physical entities, and therefore provide data which are corruptible, subject to error, and changeable. To Plato, the reasoning part of the soul operates by a process of remembering what it knows about the World of the Forms; all true learning is only recollection.  Data which is not about the Forms is derived from the World of Appearances. This information comes from the senses and is not entirely real, permanent or universal. This kind of information is not real knowledge; it is opinion. Differences between the "World of Appearances" and the "World of the Forms" may be summarized as follows:


World of Appearances World of the Forms
l.   Is not about the Forms. l.  Is about the Forms.
2.  Is obtained through our senses. 2. Can be obtained only through reason and not through the senses.
3.  Is never absolutely true. 3. Is always certain and true.
4.  Changeable with respect to time and place, and from one person to another. 4. Is unchangeable everywhere and forever, and for everyone.
5.  May give contradictory answers to the same question, e.g., candy is bad -- candy is good. 5. Has only one answer for any one question; contradictory answers are impossible.


Plato's Divided Line Analogy

Perhaps the best-known geometrical analogy in Western philosophy is Plato's Divided Line.  In Book 7 of his dialogue entitled The Republic, Plato describes his 4-level hierarchical theory of human knowledge using the device of a harmonically proportioned line (see below).

1. Intelligible World of Unchangeable Being 2. Sensory World of Change and Opinion
Knowing the Higher Forms (Nous) Reason (Dianoia) Belief (Pistis) Illusion  (Eikasia)
____________________________________________________ ________________________________ _________________________________ _______________
A B C D                            E

Plato postulates two epistemological worlds: 1) the intelligible world of Being and 2) the world of the five senses, as existing on a line (see above) that is divided into two harmonically proportioned (1.618:1, the Golden Mean) line segments. The upper (leftmost) line segment (AC above) represents the intelligible world of unchangeable forms; the lower (rightmost) line segment (CE above) represents the changeable visible world of the senses.

Each of these two line segments may again be divided so that the four resulting line segments are proportional to each other as follows:  AE/AC = AC/CE = AC/AB = AB/BC = CE/CD = CD/DE = 1.6180339887 ... .  The ratio 1.618 ...  is well known to most artists and mathematicians; it is called the "Golden Mean" or Golden Section" and is an algebraically irrational number that cannot be expressed exactly. Its mathematical symbol is the Greek letter phi or "φ".  The precise reason why Plato chose to use the phi ratio in this line segment analogy is beyond the scope of this introductory webpage.

The changeable, sensory world (line segment CE) is now divided into a lower segment (DE), "illusion," which represent such things as shadows, reflections, subjective paintings, poetry, etc., and an upper segment called "belief," which includes knowledge of ordinary visible objects that are subject to change over time, such as horses, dogs, houses, etc.

The intelligible world line segment (AC) is also divided.  The lower segment (BC) "reason" includes things such as theorems and laws of mathematics and physics which require that some aspects be accepted without further proof. The upper line segment (AB), "true knowing," includes knowledge of the higher forms such as intellectual beauty, justice, the idea of "The Good," and of "The One," etc.

There is a descending hierarchy of reliability between the world of segment AB (most reliable) down through line segment DE (least reliable). Segments AB and BC refer to the World of Unchangeable Being; Segments CD and DE belong to the World of Change or Becoming, i.e., the sensory world, which for Plato is not the real world!

You cannot possess true knowledge about anything in the World of Change, you can only have an opinion based on imperfect sensory knowledge. Conversely, the World of Being provides intelligible knowledge, the knowledge of the Forms, which constitute the unchangeable reality or, as the philosopher Immanuel Kant (1724-1804) would say, the Noumenal World!


Plato's Cave Allegory

This engraving of Plato's Cave Allegory was created by the Dutch artist, Jan Saenredam, in 1604.  In the cave, light is provided by a fire contained in a bucket suspended from the ceiling.  The fire light casts shadows of the "carriers" on the wall. The man shown speaking with the deluded people facing the wall seem to be trying to tell them of their plight.  The three figures shown just outside the entrance to the cave are in the sunlight outside and have thus gained access to the real world of the "forms."


Perhaps the most famous allegory in all of Western literature is Plato's Allegory of the Cave.  In Book 7 of his dialogue entitled The Republic, Plato provides his view of the plight of most of humanity on Earth. They are imprisoned in the World of Appearances, which is likened to being in a cave in the depths of the Earth, where the inhabitants are not aware of their very limited and false perspective. Occasionally, an individual escapes the limitations of that cave and, through a long and difficult intellectual journey, finally discovers the higher realm of true reality - the World of the Forms.  Such a person has achieved knowledge of ultimate reality and not just a superficial knowledge of the world derived from sensory perception. Unfortunately, such enlightened individuals will usually be misunderstood by the deluded people back in the cave who haven't shared in the intellectual insight.  The prisoners in the cave do not see reality, but only a shadowy representation of it. Plato's believed that there are many marvelous truths lying under the apparent surface of things, but only those who have achieved enlightenment can grasp them. The prisoners in the cave are accustomed to the world of sensory illusion and most of them stubbornly resist enlightenment, just as students resist education. However, those gifted few, who are able to achieve enlightenment, should become the leaders and rulers of all the rest. Plato believed that education is not a process of putting knowledge into empty minds, but of making people realize that true knowledge is already within them if they but know how to access this knowledge. To Plato, the way to access this knowledge was through introspection and meditation.

The following is a condensed quotation from Book 7 of The Republic (Benjamin Jowett translation) describing the cave:

Imagine people living in a underground cave that has a distant entrance open to the outside . . . they've been here since childhood, their necks and legs chained so that they can only see in front of them . . . above and behind them a fire is burning, and between them and the fire is a low wall like a screen over which puppeteers display their puppets . . . and imagine people behind the wall carrying artifacts, figures of people, animals, and so on.  Some of these people are talking, others are not . . . the prisoners see only the shadows of artifacts cast on the cave wall by the fire . . . there are echoes so that when the carriers speak the sound seems to come from the shadows on the wall . . . there is a steep and difficult ascent to the outside world where the sun, moon, and stars are clearly visible . . .


Plato's Ideas on the Nature and Structure of the Universe (Cosmology)

Plato has provided one of the first descriptions, in all of Classical literature, of the basic structure of the Cosmos.  This account is contained in the Myth of Er, a story which is found at the end of the 10th Book of the Republic.  The Cosmos is depicted as being a series of eight concentric spheres with the Earth at the center, then seven spheres each associated with one of the seven planets, the last or eighth sphere being the realm of the fixed stars. Plato says:

... they came to a place where they could see from above a line of light, straight as a column, extending right through the whole heaven and through the earth, in color resembling the rainbow, only brighter and purer; another day's journey brought them to the place, and there, in the midst of the light, they saw the ends of the chains of heaven let down from above: for this light is the belt of heaven, and holds together the circle of the universe, like the under-girders of a trireme. From these ends is extended the spindle of Necessity, on which all the revolutions turn. The shaft and hook of this spindle are made of steel, and the whorl is made partly of steel and also partly of other materials. Now the whorl is in form like the whorl used on earth; and the description of it implied that there is one large hollow whorl which is quite scooped out, and into this is fitted another lesser one, and another, and another, and four others, making eight in all, like vessels which fit into one another; the whorls show their edges on the upper side, and on their lower side all together form one continuous whorl. This is pierced by the spindle, which is driven home through the centre of the eighth. The first and outermost whorl has the rim broadest, and the seven inner whorls are narrower, in the following proportions --the sixth is next to the first in size, the fourth next to the sixth; then comes the eighth; the seventh is fifth, the fifth is sixth, the third is seventh, last and eighth comes the second. The largest (of fixed stars) is spangled, and the seventh (or sun) is brightest; the eighth (or moon) colored by the reflected light of the seventh; the second and fifth (Saturn and Mercury) are in color like one another, and yellower than the preceding; the third (Venus) has the whitest light; the fourth (Mars) is reddish; the sixth (Jupiter) is in whiteness second. Now the whole spindle has the same motion; but, as the whole revolves in one direction, the seven inner circles move slowly in the other, and of these the swiftest is the eighth; next in swiftness are the seventh, sixth, and fifth, which move together; third in swiftness appeared to move according to the law of this reversed motion the fourth; the third appeared fourth and the second fifth. The spindle turns on the knees of Necessity; and on the upper surface of each circle is a siren, who goes round with them, hymning a single tone or note. The eight together form one harmony; and round about, at equal intervals, there is another band, three in number, each sitting upon her throne: these are the Fates, daughters of Necessity, who are clothed in white robes and have chaplets upon their heads, Lachesis and Clotho and Atropos, who accompany with their voices the harmony of the sirens --Lachesis singing of the past, Clotho of the present, Atropos of the future; Clotho from time to time assisting with a touch of her right hand the revolution of the outer circle of the whorl or spindle, and Atropos with her left hand touching and guiding the inner ones, and Lachesis laying hold of either in turn, first with one hand and then with the other.

Plato's basic concept of an Earth-centered universe of eight spheres, all operating in a kind of musical harmony one with another, became the standard model of the universe.  This Earth-centered model was used by Europe and the Near East down to the 17th Century A.D., at which time a sun-centered universe became the standard model. Plato's ordering of the spheres, from the outermost shell downward, was: Fixed Stars, Saturn, Venus, Mars, Mercury, Jupiter, Sun, and Moon.  By Hellenistic times (ca. 300 B.C.) and thereafter, the ordering of the spheres become arranged by the apparent speed at which each planet moved around the Earth.  Thus the ordering became: Fixed Stars, Saturn, Jupiter, Mars, Sun, Venus, Mercury and Moon.


Platonic Numbers and the Octave as Described in the Timaeus

It is important to understand that the Pythagoreans, the Platonists and the Neo-Platonists, derived the natural numbers from ratios. Set theory, developed in the 19th century, is used by modern mathematicians to derive the natural numbers; however, this method was a totally alien way of thinking to the ancient Greeks.

According to the Timaeus of Plato, the World Soul was created from the application of certain special ratios, the components of which we call the “Platonic Numbers.”

The following is the pertinent passage from the Timaeus where the action of the Creator is described:

Now God did not make the soul after the body, although we are speaking of them in this order; for having brought them together he would never have allowed that the elder should be ruled by the younger; but this is a random manner of speaking which we have, because somehow we ourselves too are very much under the dominion of chance. Whereas he made the soul in origin and excellence prior to and older than the body, to be the ruler and mistress, of whom the body was to be the subject. And he made her out of the following elements and on this wise: Out of the indivisible and unchangeable, and also out of that which is divisible and has to do with material bodies, he compounded a third and intermediate kind of essence, partaking of the nature of the same and of the other, and this compound he placed accordingly in a mean between the indivisible, and the divisible and material. He took the three elements of the same, the other, and the essence, and mingled them into one form, compressing by force the reluctant and unsociable nature of the other into the same. When he had mingled them with the essence and out of three made one, he again divided this whole into as many portions as was fitting, each portion being a compound of the same, the other, and the essence. And he proceeded to divide after this manner:--First of all, he took away one part of the whole (1), and then he separated a second part which was double the first (2), and then he took away a third part which was half as much again as the second and three times as much as the first (3), and then he took a fourth part which was twice as much as the second (4), and a fifth part which was three times the third (9), and a sixth part which was eight times the first (8), and a seventh part which was twenty-seven times the first (27). After this he filled up the double intervals (i.e. between 1, 2, 4, 8) and the triple (i.e. between 1, 3, 9, 27) cutting off yet other portions from the mixture and placing them in the intervals, so that in each interval there were two kinds of means, the one exceeding and exceeded by equal parts of its extremes (as for example 1, 4/3, 2, in which the mean 4/3 is one-third of 1 more than 1, and one-third of 2 less than 2), the other being that kind of mean which exceeds and is exceeded by an equal number (e.g. - over 1, 4/3, 3/2, - over 2, 8/3, 3, - over 4, 16/3, 6, - over 8: and - over 1, 3/2, 2, - over 3, 9/2, 6, - over 9, 27/2, 18, - over 27.). Where there were intervals of 3/2 and of 4/3 and of 9/8, made by the connecting terms in the former intervals, he filled up all the intervals of 4/3 with the interval of 9/8, leaving a fraction over; and the interval which this fraction expressed was in the ratio of 256 to 243. And thus the whole mixture out of which he cut these portions was all exhausted by him.

This entire compound he divided lengthways into two parts, which he joined to one another at the centre like the letter X, and bent them into a circular form, connecting them with themselves and each other at the point opposite to their original meeting-point; and, comprehending them in a uniform revolution upon the same axis, he made the one the outer and the other the inner circle. Now the motion of the outer circle he called the motion of the same, and the motion of the inner circle the motion of the other or diverse. The motion of the same he carried round by the side (i.e. of the rectangular figure supposed to be inscribed in the circle of the Same) to the right, and the motion of the diverse diagonally (i.e. across the rectangular figure from corner to corner) to the left. And he gave dominion to the motion of the same and like, for that he left single and undivided; but the inner motion he divided in six places and made seven unequal circles having their intervals in ratios of two and three, three of each, and bade the orbits proceed in a direction opposite to one another; and three (Sun, Mercury, Venus) he made to move with equal swiftness, and the remaining four (Moon, Saturn, Mars, Jupiter) to move with unequal swiftness to the three and to one another, but in due proportion.

Plato, in the above quotation, tells us that the Creator God constructed the World Soul through the use of certain special numbers. Today, we call them Platonic numbers. This is the reason that such numbers were considered very important to Platonists and Neoplatonists down through the centuries, including the European alchemists who lived during the Renaissance. The Platonic even numbers were calculated based upon doubling these numbers starting with unity or the number 1. The Platonic odd numbers were calculated based upon tripling each number starting with unity or the number 1.


Platonic Numbers and Platonic Table:

The first seven levels of the Platonic numbers (including the number 1) may be arranged in a table as follows:


Even Numbers Doubled

Odd Numbers Tripled


1 X 2 = 2

1 X 3 = 3

2 X 2 = 4

3 X 3 = 9

4 X 2 = 8

9 X 3 = 27

8 X 2 = 16

27 X 3 = 81

16 X 2 = 32

81 X 3 = 243

32 X 2 = 64

243 X 3 = 729

54 X 2 = 128

729 X 3 = 2187


Lambda Pattern of Nicomachus - 28 Numbers at the Seventh Level:

The Platonic Table was reformatted by Nicomachus of Gerasa (60-120 A.D.) as a more convenient arrangement for writing. The following table is in the form of an upper triangular portion of a rectangle. The table is developed as far as nine columns of numbers, but may be indefinitely extended in continued geometric progressions. The first seven levels are highlighted in red. One should note that, at this seventh level, there are a total of 1+2+3+4+5+6+7 = 28 platonic numbers in all. Nicomachus regarded the number 28, together with 6, 496 and 8128, to be the first four of the so-called Perfect Numbers.  The number 28 has been long regarded as being of significant esoteric importance, but as to the exact nature of this importance I cannot say!
















































Pythagorean or Platonic Octave:

Platonic numbers were also important to music. As the following table indicates, the ratios used on a stringed musical instrument to produce the various notes or frequencies of the musical octave were all platonic numbers.


Musical Notes Expressed in Semi-Tones for an Ascending Octave


Musical Notes per the Pythagorean Scale, also known as the Ionian or Major Scale


Ratios Expressed in Platonic Numbers as Defined in the Timeaus


Ratios Expressed in Modern Decimal Numbers











































Per the above development, please note the critical points between Me and Fa and between Ti and Do. They are critical in that there is only a half-interval or one semitone between them. All other intervals in the Pythagorean Scale have a full tone or two semi-tones between them. From the viewpoint of Platonic metaphysics, this relationship was believed to be of great esoteric significance.  Two 20th century mystical philosophers, P. D. Ouspensky and G. I. Gurdjieff, have made these critical points the focus of their metaphysical and cosmological belief systems.