"Let no one ignorant of geometry enter"
"Tradition has it that this phrase, was engraved at the door of Plato's Academy, the school he had founded in Athens"
Who was Plato...The son of a wealthy and noble family, Plato (427-347 B.C.) was preparing for a career in politics when the trial and eventual execution of Socrates (399 B.C.) changed the course of his life. He abandoned his political career and turned to philosophy, opening a school on the outskirts of Athens dedicated to the Socratic search for wisdom. Plato's school, then known as the Academy, was the first university in western history and operated from 387 B.C. until A.D. 529, when it was closed by Justinian.
Unlike his mentor Socrates, Plato was both a writer and a teacher. His writings are in the form of dialogues, with Socrates as the principal speaker. In the Allegory of the Cave, Plato described symbolically the predicament in which mankind finds itself and proposes a way of salvation. The Allegory presents, in brief form, most of Plato's major philosophical assumptions: his belief that the world revealed by our senses is not the real world but only a poor copy of it, and that the real world can only be apprehended intellectually; his idea that knowledge cannot be transferred from teacher to student, but rather that education consists in directing student's minds toward what is real and important and allowing them to apprehend it for themselves; his faith that the universe ultimately is good; his conviction that enlightened individuals have an obligation to the rest of society, and that a good society must be one in which the truly wise (the Philosopher-King) are the rulers.
The whole Platonic teaching is based upon the concept of Absolute Goodness. Plato was vividly conscious of the immense profundity of the subject. "To discover the Creator and Father of this universe, as well as his operation, is indeed difficult; and when discovered it is impossible to reveal him." In him Truth, Justice and the Beautiful are eternally one. Hence the idea of the Good is the highest branch of study
The ancient philosopher Plato developed an idealistic concept of eros which would prove to be very influential in modern times. In general, Plato did not consider physical attraction to be a necessary part of eros. "Platonic love" in this original sense can be attained by the intellectual purification of eros from carnal into ideal form. This process is examined in Plato's dialogue the Symposium. Plato argues there that eros is initially felt for a person, but with contemplation it can become an appreciation for the beauty within that person, or even an appreciation for beauty itself in an ideal sense. As Plato expresses it, eros can help the soul to "remember" beauty in its pure form. It follows from this, for Plato, that eros can contribute to an understanding of truth.
Eros, understood in this sense, differed considerably from the common meaning of the word in the Greek language of Plato's time. It also differed from the meaning of the word in contemporary literature and poetry. For Plato, eros is neither purely human nor purely divine: it is something intermediate which he calls a daimon.
Its main characteristic is permanent aspiration and desire. Even when it seems to give, eros continues to be a "desire to possess", but nevertheless it is different from a purely sensual love in being the love that tends towards the sublime. According to Plato, the gods do not love, because they do not experience desires, inasmuch as their desires are all satisfied. They can thus only be an object, not a subject of love (Symposium 200-1). For this reason they do not have a direct relationship with man; it is only the mediation of eros that allows the connecting of a relationship (Symposium 203). Eros is thus the way that leads man to divinity, but not vice versa.
[...] Nevertheless, eros remains always, for Plato, an egocentric love: it tends toward conquering and possessing the object that represents a value for man. To love the good signifies to desire to possess it forever. Love is therefore always a desire for immortality.
Paradoxically, for Plato, the object of eros does not have to be physically beautiful. This is because the object of eros is beauty, and the greatest beauty is eternal, whereas physical beauty is in no way eternal. However, if the lover achieves possession of the beloved's inner (i.e., ideal) beauty, his need for happiness will be fulfilled, because happiness is the experience of knowing that you are participating in the ideal.
Jung's ideas on archetypes were based in part on Plato's Forms
His aim was to set forth the nature of man and the end of his being. The great questions of who, whence and whither, comprise what he endeavored to illustrate. Instead of dogmatic affirmation, the arbitrary ipse dixit of Pythagoras and his oath of secrecy, we have a friend, one like ourselves, familiarly and patiently leading us on to investigation as though we were doing it of our own accord. Arrogance and pedantic assumption were out of place in the Akademe.
"Out of Plato" says Ralph Waldo Emerson "come all things that are still written and debated among men of thought." All else seems ephemeral, perishing with the day. The science and mechanic arts of the present time, which are prosecuted with so much assiduity, are superficial and short-lived. When Doctor James Simpson succeeded his distinguished uncle at the University of Edinburgh, he directed the librarian to remove the text-books which were more than ten years old, as obsolete. The skilled inventions and processes in mechanism have hardly a longer duration. Those which were exhibited at the first World's Fair in 1851 are now generally gone out of use, and those displayed at the Centennial Exhibition at Philadelphia in 1876 are fast giving place to newer ones that serve the purposes better. All the science which is comprised within the purview of the senses, is in like manner, unstable and subject to transmutation. What appears today to be fundamental fact is very certain to be found, tomorrow, to be dependent upon something beyond. It is like the rustic's hypothesis that the earth stands upon a rock, and that upon another rock, and so on; there being rocks all the way down. But Philosophy, penetrating to the profounder truth and including the Over-Knowledge in its field, never grows old, never becomes out of date, but abides through the ages in perennial freshness
Allegory of the Cave. Left (From top to bottom): Sun; Natural things; Shadows of natural things; Fire; Artificial objects; Shadows of artificial objects; Allegory level.
Right (From top to bottom): "Good" idea, Ideas, Mathematical objects, Light, Creatures and Objects, Image, Analogy of the Sun, and the Analogy of the Divided Line
Plato then supposes that one prisoner is freed. This prisoner would look around and see the fire. The light would hurt his eyes and make it difficult for him to see the objects casting the shadows. If he were told that what he is seeing is real instead of the other version of reality he sees on the wall, he would not believe it. In his pain, Plato continues, the freed prisoner would turn away and run back to what he is accustomed to (that is, the shadows of the carried objects). He writes "... it would hurt his eyes, and he would escape by turning away to the things which he was able to look at, and these he would believe to be clearer than what was being shown to him."
Plato continues: "Suppose... that someone should drag him... by force, up the rough ascent, the steep way up, and never stop until he could drag him out into the light of the sun." The prisoner would be angry and in pain, and this would only worsen when the radiant light of the sun overwhelms his eyes and blinds him.
"Slowly, his eyes adjust to the light of the sun. First he can only see shadows. Gradually he can see the reflections of people and things in water and then later see the people and things themselves. Eventually, he is able to look at the stars and moon at night until finally he can look upon the sun itself (516a)." Only after he can look straight at the sun "is he able to reason about it" and what it is (516b). (See also Plato's Analogy of the Sun, which occurs near the end of The Republic, Book VI.)[4
Return to the cave
Plato continues, saying that the freed prisoner would think that the world outside the cave was superior to the world he experienced in the cave; "he would bless himself for the change, and pity [the other prisoners]" and would want to bring his fellow cave dwellers out of the cave and into the sunlight (516c).
The returning prisoner, whose eyes have become accustomed to the sunlight, would be blind when he re-enters the cave, just as he was when he was first exposed to the sun (516e). The prisoners, according to Plato, would infer from the returning man's blindness that the journey out of the cave had harmed him and that they should not undertake a similar journey. Socrates concludes that the prisoners, if they were able, would therefore reach out and kill anyone who attempted to drag them out of the cave (51
His leading discourses, those which are most certainly genuine, are characterized by the inductive method. He displays a multitude of particulars for the purpose of inferring a general truth. He does not endeavor so much to implant his own conviction as to enable the hearer and reader to attain one intelligently, for themselves. He is in quest of principles, and leading the argument to that goal. Some of the Dialogues are described as after the manner of the Bacchic dithyrambic, spoken or chanted at the Theatre; others are transcripts of Philosophic conversations. Plato was not so much teaching as showing others how to learn.
A TheosophistThus you see there are what Plato, in order to save words, very briefly calls two 'souls' — one the author of good, and one the author of evil; i.e., one the source of law and beauty and harmony, and the other the great material aspect of life, which, because it is material is imperfectly evolved, and therefore can abstractly be called the 'author of evil.'
But now, mark you, any such Hierarchy is but one of countless multitudes of other similar Hierarchies alike unto it, scattered through the infinite fields of Boundless Being; so that, therefore, 'World-Souls' are literally infinite in number. I point this fact out with some particularity so that my answer will not seem to contain the 'Supreme Personal God' idea.
This, therefore, is the real meaning of Plato in the passage which you quote, and which Christians find it extremely difficult to understand, because of their education and mental bias along Christian lines. Plato of course was a Polytheist, or a believer in a Universe filled full with divinities and beings less than divinity, forming a Cosmic Family, just as we Theosophists teach. In fact, Plato was a Theosophist.