1. The Greek word kosmos (which means beautiful world-order) derives from a term that means "to weave together," to produce well-woven cloth by putting each thread in its proper place (warp and woof). The universe is a "cosmos" because, by and large, it is well-woven together; each part is where it belongs and functions as it should. This is especially true of the starry heavens, which exhibit great order and regularity, a pattern that sailing captains can rely on in order to navigate well. Astronomy closely follows mathematical symmetry and "harmony." It is no accident that Pythagoras explored the relation between mathematics, music, and astronomy. It is also no accident that Plato, himself impressed by mathematics, was profoundly influenced by the philosopher Pythagoras.

2. But if there is a place where, unlike the planets and stars, kosmos (order) has not yet overtaken chaos (disorder), it is the human city and the human soul. All of Plato's dialogues (some twenty-five or more) are, on one way or another, meditations on the problem of the life and death of Socrates. First, how could an unjust city have nurtured such an ethically committed individual as Socrates? How could he have happened, in an atmosphere that fostered personal profiteering and self-aggrandizement? Where could Socrates have learned what it means to be just? Secondly, what is the condition of the city that would put its best citizen to death, instead of rewarding him? Thirdly, what kind of a city would foster moral excellence and educate its citizens instead of corrupting or banishing or killing them? The answer to the first question was the "theory of forms," the view that a person can learn what is best -- the structure of things as they ought to be -- even though the immediate environment is far from perfect. It may be true that there is no justice in this world. It is certainly true that a just city does not put its best citizens to death. But every citizen, by using his mind, has access to justice as idea and ideal. Through hard work, rigorous dialectic, and moral training, a citizen can gradually see with his mind what he fails to see with his eyes -- a vision of things as they ought to be. The answers to the second and third questions are "suggested" in Plato's dialogues, including the Republic, in which Plato has Socrates paint the image of the perfect or just city -- a city that exists, as Socrates tells us, only in words or in the soul of the just person.

3. When a master carpenter puts together a house, he knows in advance how a house ought to be put together. He knows what materials ought to be used and how they ought to be arranged. Unlike the bystander, who thinks that a house is just so much wood or cement slapped together, the master carpenter knows the "laws" that govern a well-built house. He knows the stresses and the strains and the right proportions. How a house ought to be put together is a matter of precise interrelation of parts, of symmetry, of order. If this idea or basic blueprint is not followed, the house may not only not be a good house, it may cease to be a house at all: it may collapse. The same is true for a shipbuilder. Ships can vary in shape or size, but the structure of any ship -- if it is to float and move well -- is an idea more or less comprehended by the master shipbuilder. What makes a house work as a house and a ship function as a ship is not a matter of "opinion." Craftsmen have know-how. Beyond the specific blueprint they are working with, they have in mind a general blueprint that defines and determines the success of every finished product of a certain kind. All actual ships are imperfect; what is perfect is the idea or ideal of a perfect ship that the shipbuilder grasps however adequately or inadequately and wishes to bring into concrete existence. The intention of master craftsmen to outdo themselves -- their perfectionism -- is their presupposition that for every type of finished product, there is an idea of "the best," an ideal, a perfect model.

4. Plato's "theory of forms" can be explained in this way. Form means structure, arrangement, order -- how a thing must be put together in order to be what it is. Every concrete being, insofar as it exists, has form. Every organic being, insofar as it continues to live and function, possesses order. A squirrel exists and goes about his business because he is put together as he should be; his parts are where they belong and they work together harmoniously. The ideal form of the squirrel is the basic blueprint that all existing squirrels must replicate, however imperfectly, in order to function. The ideal form of a ship is the structure, the symmetrical arrangement, that must be imitated in order to make a ship. What makes anything good (like a good ship) or real is the degree to which it succeeds in reflecting its perfect appropriate form. A bad ship lacks form or correct arrangement. If it has no ship-form at all, it ceases to be a ship. In the specifically human or social sphere, health is the harmonious arrangement and interaction of bodily parts, individual justice is the correct arrangement and interaction of the parts of the soul, and social justice is the correct arrangement and interaction of citizens in the city. Health and justice are ideas or ideals -- forever sought by true physicians and true politicians, but never perfectly "embodied." Just as the physician ought not to believe that health is something "subjective," so the political expert must not quit the task of searching out the true meaning of justice by saying that justice is "relative," etc.

5. So Plato, a mathematician as well as a poet, saw both structure and the lack of structure in the world around him. He determined that a thing is good if it possesses appropriate order and symmetry. A good ship will sail; a bad ship will not. A good house will stand; a bad house will not. A good city will succeed and support human excellence; a bad city will fail and put good citizens to death. What makes anything good is the way it is put together, its arrangement. Good concrete arrangements imitate Forms (perfect or ideal blueprints or arrangements). These "forms" or "ideal structures" can be seen by the mind, but they cannot be seen by the eyes. They are not in the mind any more than visible objects are in the eyes. Nor can these ideas be seen easily or casually by the mind. Through the study of mathematics, the training of dialectic (both positive and negative), and the exercise of moral self-control, one can increase one's mental intuition of forms so that one can gradually see more and more clearly the peculiar structure of justice, etc. The "moral idealist" is one who sees more clearly than his fellow citizens how human lives and societies ought to be put together.

6. Though it is true to say that ideal forms or perfect blueprints are beyond space and time, as the idea of a perfect circle is not found in concrete circles, it is also true to say that words have something to do with ideas. The Greek word rendered into "form" or "idea" is eidos. Eidos means "the look" a thing has, the way a thing looks, the visible structure of a thing. For Plato, "visible" has two senses -- what can be seen by the eyes in perception (aisthesis) or what can be seen by the mind in knowledge (noesis). Saying the right words, saying the words that fit together and fit the needs of the hearer, can assist the hearer in having an "insight" or seeing some mathematical or moral structure. An insight is a mental view of how things fit together or ought to fit together. One can have an insight into a geometrical proof or into a social solution. Words, when put together well in conversation with oneself or with another, can unlock a vision of some ideal form. They need not; one person cannot make another see. He can only provide the stimulation that helps the other to see for himself. Speech together with others is the haven of insights, the means for unlocking a vision of ideal forms. Speech can do this because words are more general than objects; the dialectical arrangement and rearrangement of words mirrors the ideal arrangement of forms. If speech is true, words are put together that belong together. In a similar way, justice is the right way of putting together citizens, both in their internal attitude and in their external relation to one another. In this sense, dialogue with one's fellow citizens is an opportunity, not only to search together for some truth, but also to practice and improve interhuman relationship. Thus, conversation makes both knowledge and friendship possible. Friendship, for the Greeks, was seen as the basis of social order.

7. According to Plato, the forms are not concepts in the mind, but are existing realities apart from the mind. For this reason, truth is not seen as either mine or thine but ours, as there for all of us to behold. Forms are imperfectly reflected in human affairs and perhaps less imperfectly reflected in language, but they are not the private possession of an individual thinker. They are "out there," somewhere. This distance between the thinker and the ideas he pursues keeps him humble. What is best is the universe of ideas "beyond" the sensible world. The thinker sees what is best without owning it. One can believe in the existence of ideal standards without claiming to possess them. Belief in an absolute that one does not possess is often the best way to keep from thinking oneself absolute.