C A R L O S
C I R N E - L I M A

To Maria
And to my students

Translated by Helen Marjorie Danson Barbosa

S U M M A R Y

I. We and the Greeks
1. Heraclitus’ Garden
2. The Game of the Opposites
3. The Myth of the Cave
4. The Analysis of the World
5. The Explanation of the World

II. What is Dialectic?
1. The Logical Square
2. The Synthesis of the Opposites
3. The three Principles
4. Being, Nothing, Becoming
5. Dialectic and Antinomy

III. A System Project
1. Dialectic and Nature
2. Ethics
3. Justice and the State
4. The Meaning of History
5. The Absolute

PREFACE

I wrote Dialectic for Beginners thinking about my students. I wrote it for them, for the beginners, Incipientibus in Dialecticam, as Abaelard would say. I composed this essay for those clean-faced, shiny-eyed young people, attentive, lucid, anxious to learn, who know very well that they don’t know anything at all. That’s why they want to learn. It’s for them that I wrote this book and to them that I dedicate it. Justly, I might add. For it was with them, their questions, through discussions and debates with them that this Dialectic was born, grew and turned into reality. Not that I am self-taught, or that I slight my teachers. No, I have great esteem for those who were my professors. I owe them a lot. But it was with my students that, over the years, I learned what I give back to them, now, with this book.
A beginner is one who knows nothing, or almost nothing. A beginner is one who realizes that he doesn’t know anything. And for this reason he wants to learn, to understand the words, to understand the meaning of the sentences, to accompany the development of the argument. I wrote this book for him. I wrote it in a simple, direct style. I wrote an unpretentious Philosophy with no fussiness, no decorations, without academic rank and without aerobic demonstrations of scholarship. Most ideas exposed here are very old. There are some new things too, because everyone who earnestly studies Philosophy and enters into a struggle with the ideas, with the ideas themselves, will always discover something new. When we appropriate the richness which we inherited from tradition and try to pass it along, it gets revitalized and it grows. This work was born from the great philosophic tradition. My wish is for it to take the readers back to the great master thinkers of tradition.
By the way, you readers are Beginners-Who-Know-Nothing, right? Have you realized that while you don’t know anything and express this, you are being catapulted from the Know-Nothing to the Knowing? Because, as Socrates said, he who knows that he knows nothing is a Wiseman. This is Philosophy. Yes, and now what? Are you Beginners or Wisemen? Is this Dialectic for Beginners or Wisemen? I don’t know, discover for yourself. Look up high and observe the flight of Minerva’s Owl, don’t pay too much attention to the Thracian Slave’s laugh, discover.
Porto Alegre, May, 1996

I. WE AND THE GREEKS

1. HERACLITUS’ GARDEN

1. Initial questions
Where did we come from? Where are we going? What is the reason for the world and our life? Did the universe have a beginning? Will it have an end? Are there laws ruling the course of the universe? Are these laws for us, too? May we disobey these laws? What happens when we disobey them? Is there reward and punishment? Is there really? Or should there be? Does this happen now during this life or in some existence after death? Can we think about an eternal life, an existence after death, without contradiction? Can there be a time after all time is finished? Can there be an after after the last and final after? After all, what are we?
These are the questions which from the beginning of time, everyone who becomes an adult has asked. These are the questions which have worried all philosophers since the Pre-Socratics. Philosophy is an attempt, always frustrated and constantly taken up again, at giving a rational answer to these questions. This is what we will now develop in this essay. A final and definite answer which completely answers these questions does not exist. Even more, such a complete and finished answer is, as we will see, impossible in Philosophy. But, as many questions can be asked, many answers can and should be given.

2. Philosophy is a big puzzle
Philosophy is the science of first principles, those principles which are universally valid and which rule not only the being, but also the thinking. Today Philosophy is many times thought of as a science of ultimate rational justifications, that is, as rational foundation for all other sciences. The great theme of Philosophy is then, using a metaphor taken from Architecture, a question of the ultimate foundation. It is in this way that long ago Aristotle spoke about First Philosophy. First Philosophy deals with the first principles of the universe - the being and the thinking - principles which are the rational foundation of all the other sciences, such as Logic, Physics, Astronomy, Biology, Ethics, Politics, Esthetics etc., which earlier belonged to that great and all inclusive science that was then called Philosophy.
I don’t have anything against the conception of Philosophy as a science of ultimate foundation. It is also this. But this metaphor points to only one of the hard nuclei of that greater thing which Philosophy really is. It is as if it were pointing to a meatless, bare bone. The image of foundation is a little poor. I personally prefer another metaphor, that of a puzzle, to characterize what Philosophy is. Philosophy is, I would say, a great puzzle.
In a puzzle we must fit each piece with the neighboring pieces so that the edges of each one coincide with the edges of the neighboring pieces, making up a coherent image which appears in the end without holes or ruptures. A puzzle consists in inserting piece by piece one into each other, with perfect fitting of the edges, until all the pieces are correctly placed and the final, coherent, meaningful image becomes visible. If there are pieces left, the puzzle was not finished. If there are pieces missing, the puzzle was lacking something and the image will be incomplete. In large puzzles it is perfectly possible for us to assemble pieces of the large final image, each piece with its own figures, but without the final composition. If we continue until the end, and the puzzle is not lacking pieces, all the pieces will then fit together. There will not be any pieces missing nor any left over, and the total image will be clear and visible.
Doing Philosophy today is, in my opinion, like assembling a large puzzle. The sciences such as Physics, Chemistry, Astronomy, Biology, Archeology, History, Psychology, Sociology etc. are parts of the large puzzle that is Philosophy, the Most Universal Science. Each one of these particular sciences assembles its own part, each of them deals with some figures. None of them has to worry about or take charge of the total composition of the great mosaic, which is Philosophy, the reason, the meaning of the universe. These particular sciences do work on assembling the great puzzle, but each of them limits itself to a small part of it. To do Philosophy means to go on until the end, that is, assembling all the pieces until one can see the global image.
This is where the first difference between the puzzle and Philosophy appears. In Philosophy we don’t have all the pieces. The universe is still in the making. History is not yet finished. Many things, which we have no idea of, are still to come. The Philosopher does not have all the pieces - the future has not yet arrived - and therefore, the final mosaic will always be incomplete. Nevertheless, it is necessary to assemble the puzzle with the existing pieces, including the player himself. Each one of us who is a concrete player must jump into the ultimate mosaic of Philosophy which is the universal meaning of the universe in which we live, that is the ultimate meaning of our lives; in this way Philosophy becomes existential. But, as History and Evolution have not yet finished, the image that appears on the mosaic, although global, will always have large empty spaces. This means that, while the time of History is still passing, Philosophy as a global system of knowledge is and will always be an inconclusive project. The Great Science will never be complete and finished. Philosophy always is and will continue to be only Love of Knowledge.
No one can pretend that the particular sciences do not exist. No one should pretend, as some Philosophers today do, that Philosophy is only Philosophy of Language or Theory of Knowledge. This is also important, this is also part of Philosophy. But Philosophy is more than just a Metalanguage Theory; Philosophy is a Great Science, which contains in itself all, I repeat, a l l the particular sciences with their theories and unanswered questions. There comes a question: Is this still possible? Today, in our century, with the incredible development of the particular sciences, is it still possible to make a Great Synthesis? Of course it is necessary and it is possible. Moreover as the particular sciences developed, so did the resources available to the Philosopher trying to build the basic framework of the Great Unified Theory again. It’s a little embarrassing, but we must admit that many philosophers today have abandoned the idea of the Great Synthesis and are happy with partial subsystems; that means however, that they stopped doing real Philosophy. Happily though, as everyone can see, Physicists are still looking for the Great Synthetic Theory into which the subsystems now being worked on can be integrated. The problem is that the Great Synthesis is more than just a conciliation of the general theory of relativity with quantum mechanics. The programmatic job of Philosophy is still more ample than that of Physics at the end of the twentieth century. Biology, Psychology, Sociology, History, etc., must also enter in this synthetic theory which is Philosophy, because we want to discover which laws are valid for all things and which are valid only for some things. In the past this great task was called explicatio mundi; to do Philosophy has always been and continues to be building the explanation to the world. We will return to this word many times, because with it we can really express all that Philosophy can and should intend to be.

3. Criticism of Post-Modern Reason
After the intellectual collapse of Hegel’s system during the second half of the last century, after the political collapse of Marxism - which is a type of leftist hegelianism - in 1989, after the fall of the Berlin Wall, and soon after with the breaking up of the Soviet Union, Philosophy seems to have become a dead end street. Instead of the Great Synthesis we have only a great impasse. Reason, which was ambitious and went looking for the Great Synthesis; reason, the one reason, the unique and most universal reason is destroyed by Nietzsche’s sledge hammer. Reason, the one Reason, unique and with a capital letter, was declared dead. Reason died, the multiple small reasons live, the reasons of many different perspectives as Nietzsche said, the reasons of multiple horizons, as Heidegger wanted, the reasons of multiple language games as Wittgenstein affirmed. The one and unique Reason died, the multiple reasons with their relativisms live. This is the post-modern thesis of thought.
The positive side of this dissolution of the unity of reason, which was defined by Illuminism, is that in our century we became more modest, more understanding, more open to other cultures, more tolerant with the foreigner, more attentive to alterity. The particular, including the particular sciences, progressed immensely. Even Logic, which before was the one Logic, unique, in the singular and with a capital letter, as the Logic of Aristotle and the master thinkers of the Middle Age, has been transformed. Today we have, next to Aristotelian logic, written in small letters, many other logics. Today we speak about logics, in the plural and with small letters. What happened to Logic, also happened to Reason as a whole. Instead of Reason, today we have many reasons, in the plural and with small letters.
Post-modern reason puts one subsystem next to another, and another and still another, always one next to the other without a higher and more ample unity which encloses them; the cracks between the various subsystems remain empty. Post-modern reason denies the existence of principles or laws that are really universal, which connect the various subsystems; that is, principles that are always valid, in all spheres, in all the cracks and for everything. Furthermore, extreme Post-Modernism says that, strictly speaking, there is no universally valid proposition.
Now, whoever makes such an statement, by saying this, says just the opposite. Such an affirmation is a contradiction in itself, it causes a logical implosion. Let’s see what happens in another, simpler example. We will take the proposition that There is no true proposition. Anyone who affirms such a thing is implicitly saying There is no proposition which is true, except this one that I am now saying. Therefore the implicitly made exception denies the universality of that which was affirmed: There is no truth that a l l propositions are false, since at least this one, which is being affirmed, is being affirmed as being true. This also happens with the post-modern proposition There is no proposition which is universaly valid for all subsystems; in saying and affirming this, we are saying that at least this proposition is valid in all subsystems. The same thing happens in class when the teacher complains about the talking and little Johnny says But teacher, no one is talking. In saying this he contradicts exactly what he is saying. It is for this reason that post-modern reason is good, yes, as respect for alterity and regard for diversity, but is very bad as a substitute for universally valid reason. It cannot be universalized; if we do it, it explodes. This is why post-modern philosophy, in this sense, does not and will not ever exist. Whoever wishes to do Philosophy in the way of post-modern reason, overlapping subsystems, without ever making an encompassing theory, small as it may be, is doomed to failure by self-contradiction. My friend Habermas, forgive me, but it is impossible: it implodes. This shows that one can return to the one, unique, most universal reason. It can consist of few rules and principles; maybe it can consist of only one principle, but that such a reason exists, it exists. He who denies it, detonates and enters in self-contradiction. The explanation of the world can be maybe minimalist. But it is really possible.
The more negative side of post-modern reason is the trash that accumulates in the crevices between the various subsystems. And it is there, into these empty crevices, that we sweep the contradictions and badly solved problems. Between one subsystem and another is where the trash of reason lies. Particular theories, articulated just as subsystems, permit that between one subsystem and another the biggest absurdities sprout up and bloom. The contradictions were not resolved, they were just swept away. This is not enough. One must think about the multiplicity as well as the unity. Without unity, multiplicity enters into contradiction, as we have already seen. Multiplicity in the Unity, Unity in the Multiplicity; it is necessary to reconcile both equally legitimate and necessary poles. And it is time to rethink Parmenides as well as Heraclitus.

4. Parmenides’ Sphere
Parmenides, one of the great thinkers of Pre-Socratic Philosophy, was in some ways, the forefather of post-modern reason. He opposed one of the two biggest subsystems to the other: the real being and the doxa, the mere appearance. Parmenides said that the real reality is only the immovable being, which is pure rest, without any movement. This immovable and immutable being is symbolized by a sphere, that is, by a geometrical figure which has no limits, where the finger runs without ever coming to a beginning or an end. And the things of this world which are in movement, which move, are born and die, well, these things, Parmenides declared, are not real reality, they are a doxa, just appearances, under which there is no real being. Appearances can fool you. On one side the subsystem of what is really real, on the other side a subsystem of appearances. But, Parmenides is not post-modern. He was more radical, he sacrificed all the appearances, the multiple things of this world in which we live, on the altar of an exasperating rationality, of a only, unique, immovable, immutable, infinite logos. That which is, Parmenides said, is. That which is not, is not. And that which is not isn’t anything, it means nothing and does nothing. The Non-Being does not exist, it cannot even be thought of.
Movement is always the passage of Being to Non-Being, or to death. Then the passage of Non-Being to Being is birth. Now, since the Non-Being does not exist, since it is nothing, there is no passage for the Non-Being. There is not, for the same reason, passage from the Non-Being to Being; from the Non-Being nothing can begin. This means that there is no death nor birth. Death and birth are illusions, they are merely appearances. Well, by logic, Non-Being is nothing. And therefore, all that the Non-Being determines is being determined as being nothing; that is, it is nothing, just illusion. Therefore, Parmenides argues, there is no movement. And if we think that something is in movement, it is just an illusion.
Zeno of Elea, a disciple of Parmenides, in order to demonstrate what he thought as the logical impossibility of movement brings the example of a race between Achilles and the tortoise and the example of the stopped arrow. Achilles races a tortoise. Since Achilles is a great hero and an excellent runner, the tortoise asks for a ten meter head start. Achilles agrees and the race begins. Notice, states Zeno, how movement is something contradictory, notice that Achilles is not going to be able to win the race. Just think. Before running the distance that separates him from the tortoise, Achilles has to run half that distance. And before running this half, he has to run half of this half. And before finishing the half of this half, he has to run half of this half. And so on. Since the quantity is infinitely dividable and there is always a new half of a half, one can conclude that Achilles will not advance one step, he will not be able to regain the advantage, and therefore he will lose the race to the tortoise. Why? Because movement, said Zeno, is contradictory, it cannot be thought of until the end without there being an unsolvable contradiction. - The same thinking is applied to the arrow shot by the archer in direction of some target. The arrow, having to pass through infinite halves of halves, remains still. Zeno thinks the stopped arrow and Achilles’s race with the tortoise demonstrates Parmenides thesis that movement is impossible and that for this reason we have to limit ourselves to the one, only, unique, infinite Being without movement which is the only being that really is. This is Parmenides sphere.
Parmenides, the great thinker of the one, only, unique and immutable being, is, despite this great mistake, the intellectual father of all real Philosophy, because he was the first who took the unity of reason and of being so seriously. Everything that exists is a part of the Whole and the One. The One and the Whole, Hen kai pan, are the beginning and the end of all true Philosophy, of the science that wants to understand all things in the frameword of the Great Synthesis. The mistake Parmenides committed, which is visible to everyone, is not taking the moment of diversity and movement equally seriously. He could not think of the Non-Being as something that in some ways is. Parmenides has the conception of the universe as the Whole and the One, but he misses the movement in which everything flows. Heraclitus is missing.

5. The garden of Heraclitus
According to Heraclitus everything flows, panta rei, everything is constantly flowing, everything is in movement. Real reality is not the immutable sphere without limits of the Eleatic, but movement which without ever stopping is always beginning again. There is no beginning and no end, in this Heraclitus agreed with Parmenides, not because there is no movement, but because everything is constantly changing. What for the Eleatic was doxa, just appearances and illusion, now is real reality itself.
Reality is not just Being, it is not, for the same reason, just Non-Being. Real reality is a tension that connects and unites Being and Non-Being. Dialectics appears here for the first time in the History of Philosophy. Being and Non-Being, thesis and antithesis, are united on a higher plane through a synthesis. Being and Non-Being, which at first seem to oppose and exclude each other, constitute in real reality a synthetic unity which is Being in Motion, Becoming. In Becoming there is an element which is Being, but there is also another element which is equally essential which is Non-Being. Being and Non-Being, well mixed, do not repel and exclude each other, but enter into an amalgam and blend together to make up a new reality.
We have there, already in Heraclitus, the fundamentals of Dialectics. In the first stage we have two opposite poles which mutually exclude themselves. Thesis and antithesis oppose each other, one excluding the other. In this first stage one pole annuls and terminates the other, they are excludent. But things don’t stop there. There is movement, there is development, there is progress. Then, in this second stage, the poles unite and come together, making up a higher step, a new unity.
The lyre, a musical instrument of the ancient Greeks, serves as an example to Heraclitus. The lyre is made up of an arch and strings. Whoever wishes to make a lyre gets a piece of appropriate wood and bends it to make an arch. But, this arch, if let loose, returns to its straight form. In order to keep the arch bent it is necessary to tie it with a string, or with several strings. The arch and the string, in this first stage, are in tension, one against the other. The arch wants to break the string, the string wants to bend the arch. This opposition, which exists at this first stage of Dialectics, if and when properly dosed, creates something completely new, something marvelous: music. The tension which exists in this first stage, the arch against the string and the string against the arch, gives in to the synthesis which is music, or yet, with a capital M, Music which is one of the nine Godesses that rule and inspire the Arts. In this first stage there is excludent opposition and conflict, in the second stage synthetizing conciliation which creates something new, something higher, more complex, more noble.
One of the most beautiful examples of Dialectics, well known in the past, but rarely mentioned today, is the fílesis, antifílesis and filia movement; that is, the dialectic movement which carries us from beginning love which proposes and asks, passing through love which, questioned, answers affirmatively, to arrive at love which, loving, knows to be loved back. This love which, being synthetic, is no longer exclusive property of one or other of the lovers, but is a unity for both. The Greeks called this filía, friendship.
Love has a beginning. Someone has to begin. The beginning is a strictly unilateral act and always risky. One doesn’t know beforehand how the other is going to react or what the other will say. This unilateral, risky act is called fílesis in Greek. Hector loves Helen. Hector loves and knows that he loves; Helen notices the invitation, but has not yet decided. The other can answer yes, but can also answer no. In the beginning this is open and contingent. If the other one, however, answers yes, then we have an antifilesis, which is also a unilateral act, but is no longer a risky act because it is no longer just a question, just an invitation, but an answer and acceptance of an invitation already made. Helen decides to accept Hector’s love and love him back. This return love is the antifilesis. Filesis and antifilesis are both unilateral acts; filesis is risky, antifilesis is not. They are both independent, complete, finished acts, one different from the other, one in relative opposition to the other; one is thesis, the other antithesis. But, when both cross each other, and on a higher plane come together in a more complex, higher, nobler, unique reality, then we have filía. In filía the two initially different, opposite poles, one which questions and the other which answers, come together to make an amalgam, something new. In filía both individual loves stop being unilateral acts and become only one act, which is bilateral, in which it is no longer important who asks and who answers, because both initial loves have lost their individual character, the I and the You, to unify into something new, the We. Hector and Helen, as they love each other, first lose themselves. The sense of existence is transfered to the other person. It is the other which fulfills the sense of life, and it is the other, the person loved, which is the center of the universe. Hector is madly in love with Helen. Hector first is lost: Whoever loves somebody is always getting lost. As Helen loves Hector back, the sense of the universe makes a complete circle and returns to Hector, who now, deeply enriched, is again full of feeling and life. This new life and new feeling of the universe are not a unilateral act just of himself, it is joint act, a bilateral act, an act in which the I is mediated through the You to make up We. It is for this reason that the love of friendship, filía, is so great and so precious. This was the reason why the Greeks and the Trojans fought for so many years. It was for this reason, only for love of friendship, that Achilles, Ulysses and Agamemnon, the peoples’ shepherds, took the Greeks with their curved ships to the unending war. It was for this reason only, that the Trojans, led by Hector, fought till death. All of this only because of one woman, Homer says in the Iliad. All of this only because of the filía, which transcends the individuals and makes up a higher and stronger synthesis. Love then becomes History. The History of the Greeks and Trojans, the Iliad and the Odyssey, the beginning of our civilization.
Thesis and antithesis are in the first stage, opposite poles which repel and exclude each other. In a second stage, both unify in a synthesis which is something higher and more noble. In this synthesis, Hegel would say much later, the initial poles are overcome and kept (Aufheben). On one hand they are overcome, because they have lost some of their characteristics. In the example of the love of friendship, the character of unilaterality and risk is surpassed and in this way disappears. But, on the other hand, the poles are kept in synthesis, because the positive nucleus already existing in them continues and is preserved. Love, when it stops being a unilateral act, becomes even more love, it becomes a higher and more noble love. Thesis, antithesis and synthesis make up that which Greek philosophers called a game of opposites. This is the beginning, the root of Dialectics.
Heraclitus, the father of Dialectics, said that we cannot step into the same river twice. The river is not the same, we are not the same. Everything is in flowing motion, it is the motion that is real reality. Reality, he teaches, is dialectically woven through a game of opposites. In the beginning all is fighting and war, because the opposites oppose and exclude each other. Pólemos patér pánton, The war is the beginning of all things. But, afterwards there is often a unifiyng synthesis that bears something else more complex, higher, more noble.
In the game of opposites there is not always a positive result. Many times what happens is only death and destruction. The opposite poles in this case act only as destructive agents. The first annuls the second, or vice versa, or both mutually annul each other. In such cases there is no synthesis, there is no Dialectic.
Is is also evident that, in order to understand the universe in his unity, we have to grasp it as a synthesis. When and why is there synthesis? That syntheses exist in the universe is quite clear. One can see it, just look at the cosmos. But the question is: Why is it that sometimes there is synthesis and sometimes not? Whoever has an answer to this has discovered the solution of the question about the harmony in the universe, about the organization of the cosmos. The main question of all Philosophy, Science of the Great Synthesis, is: Why do opposites sometimes exclude each other and sometimes unite each other?
It is between Parmenides and Heraclitus that a space has been created in which since that time we do Philosophy. Parmenides saying that Everything is the One supplies the element of universal Logos which includes everything; Heraclitus, saying that Everything flows, that all is the motion of opposite poles, supplies the element of Dialectics. Hen kay pan and Panta rei, the Whole and the One and Everything flows have since been the mottoes of any and all Philosophy. That is why in the garden which we want to represent our western Philosophy there must be a stone sphere in the center, a sphere that refers to Parmenides Oneness which is the Being. But, since Parmenides’ philosophy needs to be marked and corrected by Heraclitus, it is necessary for this sphere to be in perpetual flowing motion. Water has to spring out of the sphere like a fountain enclosing it in the flow of the water; in this way it becomes the symbol of the Great Synthesis between Rest and Motion, between Totality and Dialectic.

2. THE GAME OF OPPOSITES

1. The Pre-Socratic Philosophy of Nature
The Pre-Socratic Philosophers were the first, in our culture, to sketch out a rational view of the world, saying how Nature began, how and what it is made of, and what man’s place is in it. Before these first thinkers constructed rationality, there was only Myth. Myth is the first, not yet critical form, of philosophizing, that is, of thinking about the world as one, of thinking about the universe in its totality. Myth, among the Greeks, assumes the figure of genealogy. In the beginning, in the very beginning, according to the old Greeks, there is just chaos. Chaos is the beginning of all and is, therefore, the first of the gods, father and origin of all things. From the god Chaos then appear other gods in a genealogical sequence in which one god succeeds the other as descendant, until we arrive at the present gods, the present inhabitants of Olympus, a group of gods led by Zeus.
Also in the Jewish-Christian tradition Myth takes the basic form of genealogy. In the beginning, the Jewish and Christian Bible says, there was only God. God, before creating everything, was just himself, he was alone. Then on the first day, God, the Father of everything, created light, calling the light Day and the darkness Night. On the second day, God made the firmament and separated the waters. Then there were waters below the firmament, the seas and river, and waters above the firmament, which later fell as rain. On the third day, God separated the earth and the seas, making then the land, the rich earth, the plants and the fruit-bearing trees. On the fourth day, God, the Father, created the lights in the firmament of the heavens, one greater, the sun, and one smaller, the moon, in this way dividing the day from the night. He also created the small lights in the firmament which are the stars. On the fifth day, God, the Creator, created the animals that live in the waters, the fish, as well as those that live on land, the beasts, and those that fly, the birds, each one according to its species. God then blessed them and ordered them to multiply. On the sixth day, God made man in his image and likeness, to dominate over the fish of the sea, the birds of the air, all the reptiles and over all the earth. God then looked at the things that he had created and saw that all of them were good. And on the seventh day, says the biblical myth, God rested. Starting from this beginning, all the Bible is a genealogical history, it is a history of patriarchs and their peoples, with a special emphasis on the Jewish people.
The Greek myths as well as the myths of the Jews and the Christians tell the history of the origin of the universe from its beginning until the historical sequence of the times. The past time is synthetized as one History that has a beginning and brings us to the present time, giving meaning to things and therefore to our lives. This historical summary of the past, which always contains judgments of value - the Good and the Beautiful - makes up the background in which present time is inserted. Through the insertion in this framework which links the past to the present, daily life is also penetrated by ethic and aesthetic values, allowing us to also project the future. Herodotus on one side and the Jewish-Christian Genesis on the other are a history of the first beginning of the world and of the historical sequence of the generations. Both myths have great poetic value and work as structuring archetypes of a certain vision of the world. In the Jewish-Christian myth there is a structure that contraposes, on one side, a first cause, God who creates everything and on the other side the things created, the creatures, which then enter into the scene in genealogical sequence. God, the first cause, is thought of in a genealogical way, as the Creator and Father of everything. This is why he is, in the last instance, responsible for everything and, as the saying of our ancestors goes, Deus escreve direito por linhas tortas, God writes correctly even if the lines on the paper of life are not straight. In Greek mythology there is a shift. Cause, in Greek thinking, is not thought of as an efficient cause outside of the process of the universe, but as an internal cause, an internal principle of self-determination which molds the universe from the inside out. The first god is chaos. The god Chaos, as the name suggests, is totally undetermined; in him there are no things or beings with limits and outlines. But it is from this chaos, from inside this God Chaos, that a well-ordered universe appears. The chaos organizes itself, molds itself, and from itself creates its determinations. Chaos, upon determining itself gives itself shape and form. From this the other gods appear and, after them, men as well.
The Pre-Socratic Philosophers know the Myth and appreciate its savage beauty and pedagogical relevance. But we must think and argue rationally. This is Philosophy, and this is why there are philosophers. This means that the process of Genesis of the universe should be analyzed and described with the exactness and cold objectivity that characterize science. It is in geometry that the first thinkers got inspiration for their spirit of scientific objectivity. The Philosophy of Nature should be as exact, as objective, and as convincing as Geometry. The Pre-Socratics tried hard, but they didn’t get there.
Thales of Miletus thought that the origin and the beginning - the arkhé - of everything is water. The things are made up and differ one from one another by the level of humidity. The god Ocean is therefore the Father of all things. Anaximander also from Miletus, probably a disciple of Thales, said that the first principle is a being totally undetermined, with no limits or determinations, the ápeiron, which is then totally characterized by determinations which limit it more and more, until it forms the determined things which we see in the sensitive world. This initial indeterminate being, the áperion, embraces and circumscribes everything, rules and governs all. Anaximenes of Miletus, disciple of Anaximander, accepted the doctrine of his master about the infinite being, which makes up the beginning of all things, but thought it did not have such an abstract form and defined it as air. The air, according to him, is the beginning of all things. Here we observe, in the Philosophy of Nature of the Ionic philosophers, a first and primitive form of the game of opposites. The first principle is opposed to the differentiated things that originate from it and which are explained through it. Philosophy here is just an explicatio mundi, an explanation of the world. The world is known as a process which originates starting from one unique principle and which develops according to determined rules. It is not yet a modern Physics doctrine about the Big Bang, but it is the first beginning.
Pythagoras and the Pythagoreans took one step forward and discovered the number as the beginning of all things. The mathematization of the world started there to end nevermore. The relations which the numbers establish between themselves make up the rules which determine the process of the explanation of the world. The universe is derived from a first principle according to numeric rules and proportions, which determine the whole process and give form to things. Each number therefore has its own meaning and gives things a determinate form. The number ten is considered a perfect number and is visualized as an equilateral triangle in which each side is made up from four numbers; in the center of the of the triangle there is only one point, the central point, totaling the number ten. The so-called numbers mystic of the Pythagoreans, which will later influence Plato and all the neoplatonic school, is the cradle from which the modern Physics equations are born.
Parallel to the doctrine of the numbers the Pythagorean ultimately developed the game of opposites. Numbers already have a relationship of opposition among themselves. The number One opposes the Other which is then called Two. From this first opposition come the numbers 1 and 2. But there must be synthesis, it is necessary to think not only of the 1 and 2, but also of a new conjunction, and from that comes 3. Thesis is 1, antithesis is 2, and the synthesis is 3. That’s why, according to the Pythagorean, the odd numbers are more perfect: in them we perceive, beyond the opposition of two contrary poles, a synthesis. The triangle formed of ten points, or 10 in the form of a triangle is perfection itself. After we reach 10, everything else is just a repetition. That is how the decimal system of counting and calculating appeared in our civilization to never again leave it.
This mysticism of the numbers then adds up to a list of ten pairs of opposites - the elementary substances - which, according to combinations among themselves give form to all things:
1. Limited....................................Unlimited
2. Odd.........................................Even
3. One.........................................Multiple
4. Right.......................................Wrong
5. Male........................................Female
6. Motionless..............................Motion
7. Straight...................................Curved
8. Light........................................Dark
9. Good.......................................Evil
10. Square..................................Rectangular
The game of opposites is presented here as a basic table of opposites. According to the Pythagorean, whoever learned to play with these ten pairs of opposites, which are the constitutive elements of existing beings, is able to make up the internal constitution of each thing. This is the first form, still very coarse and primitive, of what we call today the Table of Elements in Chemistry. The atoms of present chemistry are thought of according to the atomic model of Niels and Rutherford. One electron turns around an atomic nucleus, the positive and negative electricity get into balance and then we have a stable molecule, we have hydrogen. If instead of one electron there were two turning in orbit, then we would have the second element of the Table of Elements, and so on and so forth until we arrive at element 107 which can only be made in a laboratory. The Chemists of today don’t usually realize it, but they are direct descendants of the Pythagoreans.
Along the same line as his predecessors, always making the game of the opposites, Empedocles is the first who expressly tries to solve the problem exposed by Parmenides and Zeno of Elea. He realizes that the Non-Being does not exist and can not even be properly thought of. He accepts the initial premise of the Eleatics’ argument, but does not accept the conclusion. One cannot conclude, he affirms, that movement be unthinkable, be contradictory, and for that reason be impossible, and therefore non-existent. On the contrary, movement exists, only it is not the passage from Being to Non-Being or vice versa, but mixtures and dissolution of the four fundamental substances which are eternal and indestructible: water, earth, air and fire. The basic elements are not ten, but two pairs of opposites. The determinations of things vary according to the composition of these four elements in them. The dose of liquid and solid, of fire and of air, the proportion in which these elements mix with each other is what gives shape and form to the things. Anaxagoras of Clazomenae also accepted the premise that the Non-Being could not exist and continue thinking the world as a process of composition and dissolution of basic elements. Contrary to Empedocles, Anaxagoras judged that it was not possible to construct the real diversity of things from just the four elements. He assumes for this the existence of spermata, of sperms. The word itself, which in Greek means the male spermatozoid, shows the biological tendency of this Philosophy. The sperms would be numerically infinite, of infinite variety, each one divisible within itself without losing its germinating and determining power. This initial mass of sperm is the raw material of the world. The determinations of the things are then produced by an Intelligent Orderer, the nous, which mixes the sperm in an ordered way. The figure of God the creator appears here, not as an external cause, but as an internal cause which, starting from within the chaos, gets it to organize itself. After the sperm of Anaxagoras, we then have the atoms of Leucippus and Democritus, the first atomists. According to them, who also accepted the principle that the Non-Being could not exist, these first principles of all things, all of which are qualitatively equal, they are a-toms, that is, they are indivisible. Tomein means cut, atom is what is no longer cuttable, which cannot be cut because it is a primary element. The atoms, indiscernible one from the other, initially make up a shapeless mass. These uncountable atoms are first encountered in free fall. Chance - here again is the god Chaos - allows for small detours to one side and the other on these vertical free fall lines. These small detours make the concentration of atoms more or less dense. These variations of density make up the nucleus of the explanation of the world. Each thing is what it is due to a change in the atom concentration. The atoms and Chance make up the two elements which explain the nature of things. The atoms will be met again in modern Physics. Only they are not in free fall, but moving in circles. The electrons turn in orbit around a nucleus. By increasing the number of electrons in orbit, the specific weight of the elements gradually changes from hydrogen, element number 1, to the element number 107. Chance we will meet again in Heisenberg’s relation of uncertainty, in Physics, and especially as the chance mutation in modern Biology.

2. The Sophists
Sophist is a term which initially meant the wise, sofia means wisdom; therefore Philosophy etymologically means love of wisdom. The term Sophist as well as the word Sophism only later, after Aristotle’s debate with Plato, acquires the pejorative meaning. It is Sophists who first transplant the game of opposites of Heraclitus from the plane of Philosophy of Nature to the plane of social relations. The Sophists are occupied not so much with nature as with the lives of the people of the cities; they are interested in the demos, the people, and in the pólis. This is the time when, in Greece, the old aristocracy goes into a slow but inexorable decadence and when the power of the people becomes stronger and stronger. It is the people who do business, who go from one city to another, who break from the narrow limits of the old world and through trips and travelers open new horizons and inaugurate new values and virtues. The polis is no longer an isolated city with its own constitution and traditional virtues, it discovers itself as a city among many others. Then something new appears, the intellectual and political necessity of discussing and redefining what is virtue, what is Good, what is Evil. It is no longer clear and certain that a determined way of acting is virtuous just because tradition says so. The inertial force which tradition has no longer serves as the only legitimating source of virtues. As new horizons appear, new questions appear about what Good is and what Evil is. Virtue has to be newly discussed and redefined. After all, what is virtue? What is right? What is morally wrong? These are the questions that the new times put before us, these are the questions that imposed themselves. The first answers were given by the Sophists. The Sophists were, in their time, extremely important thinkers. Portagoras, Gorgias and Prodicus were men of their time who tried to think critically about the problems of their time.
The greatest positive characteristic of the Sophists was the ulterior elaboration of the game of opposites as a methodical way to think and act; Dialectic appears there more and more clearly. The game of opposites, transported to the scheme of social relations, means that each man is just a pole of an opposition. In order to understand a pole, to know what a pole in reality is and what it means, it is necessary to think of this first pole in relation to its opposite pole. Each man, in his social relationships, is just one pole, a part. To understand this first man it is necessary to see him in his relationship of opposition with the other man which is his opposite. Fílesis is only well understood if we think of it in relation to the antifílesis; and still more, both contrary poles can only be correctly and completely understood when we put them together in a greater and higher unit, in filía, in which both are superseded and maintained. This is the reason why human relations should be analyzed in the light of the game of opposites.
This is especially valid in two fields of human relations, in Law and Politics. In law the game of opposites appears as one of the oldest and more important rules of any and all justice: May the other side also be heard, Audiatur et altera pars. The man that looks for justice in a court is always one part. He is just one part of the greater whole. For justice to be done, it is always necessary to hear the other side. This other side, the other pole in the game of opposites, does not always need to be right. It is possible that only the first part is right, or that only the other part is right, it can be that both parts are right, that both parts are partiality right and partially wrong. In any case, always, if there is to be justice, it is necessary to also hear the other part. The first part, the first pole of opposition, is always only part in the literal sense, a piece of a greater whole. Justice requires that the reason of each part be measured and evaluated in the larger context of the synthetic position, that is, that greater and more noble whole, in which each part is just a piece, a constitutive element of a greater unit. Justice is exactly this and only this. Justice, therefore, what we call Law, is a constant and systematic form of the game of opposites. Penal Law is also such but in this case one of the parts is always the people. To this day, the penal processes in the countries of Anglo-Saxon tradition have titles like The People versus A. Smith. For this reason until now jurists of the latin languages speak of the necessity of the contradictorium. The term contradictorium means here the dialectic context which comes to us from the ancient times, the principle of hearing the other side, because justice is always the formation of a synthesis, never thesis or antithesis alone, one without the other. The part in the system of Laws is always only a part, a piece which needs its other part, its opposite, in order to establish justice. Even today. The jurists today do not always realize this: they are dialectical, we are all dialectical.
The function of the game of opposites in Politics is as important as in Law, especially in the assemblies of citizens which exist in democracy. Before decisions are made by political consensus, there are discussions and debates. During these there is usually a polarization, at times a rupture. The opinion and desire of one group of citizens diverge from the opinion and will of the other group of citizens. Then two groups with different opinions and wills are formed. The unity is broken in two parts and the political parties appear. The political party can only be understood and justified when compared with it’s opposite party. Both groups need to debate and converse, because the identity of each one is determined by the identity of the other. That’s how Politics is done. It can be that one group is one hundred percent right and can convince the other group of this; it can also be that each group is only partially right, and making concessions little by little make up the general will. The general will is, then, that higher and more noble unit, the synthetic position in which and only in which the parties, which are just parts, acquire sense and justification. On the other hand we can immediately see that Politics only exists when there are two parties. In Politics, a single party is a monster, not only in the despotic regimes of the ancient Greeks, but also in the twentieth century totalitarianisms. Here again we find the old game of opposites. For sure, the Sophists were not the inventors of Law and Politics, but they were the first philosophers in our culture who theoretically thought of the game of opposites as a constitutive and essential element of social relations. This honor must be given to them. In this they were right.
Aside from this, they made some grave mistakes and committed some stupidities for which History does not forgive them to this day. To this day the Sophists are infamous and the word sophism has a highly negative connotation. This is because they committed a great theoretical error which today we can argue precisely. Instead of saying that the thesis as well as the antithesis are false, and that the synthesis and only the synthesis is the complete truth, the Sophists inverted the signs and said that the thesis as well as the antithesis were equally true.
Let us schematisize. True and correct dialectic affirms that each part is only part, or that thesis as well as antithesis are false because they are partial. Sophists say: Thesis as well as antithesis are equally true. The consequences of this logical error are incredible and extremely heavy in Politics. If thesis as well as antithesis are true, one can defend one as well as the other. The Sophists, now in the derogatory sense of the word, began to defend one side as well as the other, as if both sides were equally right. Justice then does not exist. The sense of right and correctness flies away and the sophist mentality that any position is good as long as one has the verbal skill to debate installs itself. The Sophists, in the bad sense of the word, defend anyone, any part, any party, as if it were, itself, the total truth. And still worse, the Sophists do so because that is what they are paid for, because they request and receive payment. The payment in money, requested and accepted so that one part be represented as if it were the whole, such is the great mistake and the great guilt of the Sophists. Socrates, Plato, Aristotle, no one ever forgave them. With reason. After recovering and reinventing dialectics, they went away from it. They forgot that a part is always and only part; a part which only with its corresponding counterpart forms a greater whole. The game of opposites, when perverted and inverted turns from best to worst.

3. Socrates, the last of the Sophists
Socrates is many times called the last of the Sophists. This is correct if we understand the term Sophist in its positive connotation. Socrates was the great Dialectic thinker, the great defender of moral and political subjects, of the game of opposites which complete and unite themselves to make up a greater whole. Socrates is the great voice which rose in Athens to criticize the perversion the Sophists caused to Dialectics. It is not possible to defend the thesis as well as the antithesis as if both were equally true. It is not correct, it is exactly the opposite. Both positions are false. Truth is just the synthesis from which both is created. Virtue, therefore, does not consist of defending a thesis - or antithesis -, as if this were a total and complete truth, and yes, on the contrary, in uncovering thesis as well as antithesis as being wrong, that is - which is the same-, as being only partial elements in a greater whole. Only the greater whole, only the synthesis is what is true. The Sophists argued at times in favor of the thesis; at times in favor of the antithesis. In many concrete cases in political life, the same sophist, paid by one group, argued first in favor of the truth of the thesis and then, paid by another group, in favor of the truth of the antithesis. Then, right away, with the money in his pocket, he left the citizens behind perplexed with the contradiction.
This is what Socrates raised his voice against. The game of opposites has to be done correctly. A part is just a part, it is not the whole. Or, it is first necessary to argue showing the falseness, that is, the partiality of the thesis, then showing the falseness of the antithesis, which is also partial, in order to then suggest the conciliation of the two, the greater, more noble truth.
Socrates is a thinker of Morality and Politics. Like the Sophists, he applies the game of opposites to social relations, but contrary to the Sophists, he reestablishes the correct form and structure of the game of opposites. It is not true that thesis as well as antithesis are equally true, the correct thing is that usually both are partial and therefore false. That is why one must always listen to the other side as well. Only in this way can we discover and create the truth. To know how to listen to the other part means, in practical life, to establish a dialogue, to converse with each other. This, Socrates said, is doing Politics in a city of free and rational citizens. Better still, it is only in this way that one acquires true knowledge and discovers which of the ancient virtues is not just foolish tradition but a morally correct attitude, a moral virtue. For Socrates to philosophize is knowing how to engage in conversation.
For Socrates, virtue, always the fruit of the game between thesis and antithesis, is found only through real dialogue done on street corners and in public squares. Socrates listens, Socrates asks, Socrates answers. Socrates probes the inner voice of the conscience which he, personifying it, calls daimon, the good demon, the good spirit. Socrates does not write. We have nothing of his written down. Why write if the important thing is to converse concretely, person to person? When Plato, Socrates’ disciple and follower, teaches and writes in the Academy, the rule continues to be valid that the literary form of treating philosophic subjects, even if written, is always the dialogue. From this come Plato’s Dialogues.
Socrates, the man of ethical and political dialogue, was, as we know, condemned to death by his fellow citizens. With his dialogues he has committed a great crime against the gods of the city of Athens and attempted against the good customs, perverting the youth. The great thinker of I know that I don’t know anything, the great master of dialogue in Ethics and Politics, died conversing. The dialogue Apology of Socrates in which Plato relates the happenings and ideas that surrounded the condemnation and death of Socrates is one of the great master-works of our civilization.

3. THE MYTH OF THE CAVE

1. Plato and the game of opposites
In the game of opposites, even when the logic plan is transposed to the level of social relationships, three things can happen. First, it can be that the first pole is true; then the second pole is false and has to be abandoned. Second, it can be that the second pole is the true one and then the first must be abandoned. But third, it can also be that both poles are false and the partial truths held in the opposite poles must be discovered piece by piece, uniting them, conciliating them, in order to create a real unity of a higher synthesis. - This never happens, because it is logically impossible for both poles, thesis and antithesis, to be true. This is the logic mistake in which the Sophists incurred, this is the logical-systematic fundament of the moral and political errors they committed.
The game of opposites in Plato is taken to perfection. Perfect is that which is done till the end, that which becomes complete and finished, in which nothing is missing and nothing is left over. Perfection is that which Plato points us to when he does Philosophy. Never before him, never after did man point so high up. How can that be? Isn’t it exactly the opposite? Everyone knows that Plato is a philosopher of aporias, that is, of dead end streets. Plato, in his dialogues, gives a rough draft of thesis, outlines the antithesis, but a good synthesis he almost never elaborates. How can Plato then be called a synthetic thinker who takes the game of opposites to perfection if he never, or almost never, points to synthesis? Without synthesis Dialectics dearticulates itself; thesis and antithesis remain, one against the other, both negative and aware of their falsity, without ever arriving at a conclusion. This we aready know and we have seen through the error commited by the Sophists. And is it not true that Plato’s dialogues are almost always aporetic, with no final synthesis? It is absolutely true.
There are two doctrines in Plato which complement and complete each other, the exoteric doctrine and the esoteric doctrine. The exoteric doctrine - the prefix ex indicates this - is destined for the use of people outside, it is done and explained for the beginners and those from outside without the necessary prerequisites, not yet in condittion to understand the hard nucleus of the doctrine. The exoteric doctrine is easier, it is more didactic, more introductory. In it the game of opposites really stays almost always open, with no final synthesis. Plato brings up a thesis; he discusses, debates, examines it from all angles and then finally refutes it. The thesis is always demonstrated as false. Then the antithesis is raised and is also examined and debated, being in the end invariably refuted. We have then a false thesis and an equally false antithesis, both useless, in our hands. This is aporia, this is the dead end.
Plato’s dialogues, almost all of them - except for a few from his old age - are aporetic, that is, they come out at a dead end. Dialectics, the game of opposites, is not taken to the end. Synthesis is always missing, as it is among the contemporaries of the School of Frankfurt. There dialectics is a negative dialectics, a dialectics without synthesis. But this, we shall see, is not good dialectics. Right. And Plato, discipule of the Heraclitean philosopher Cratylus as well as of Socrates, knew this very well. He also knew that Dialectics is not done by magic in one instant, with the blink of an eye, but in a long, serious, difficult, many times painful process of overcoming existent contradictions between thesis and antithesis. Dialectics is education and as such, is done in a slow learning and maturing process. A child does not become a man in one day, a tree does not grow in one week, Dialectics as well needs time and hard work. The opposites have to be worked upon seriously; if they are not, the synthesis will be hollow and empty. That is why for the beginners and those outside Dialectics is not immediately exposed and explained completely, it appears under the shape of an exoteric doctrine. In an exoteric doctrine contraries are raised in all their seriousness, one refuting its opposite, but in the end Plato leaves his listeners and readers in suspense. Really there is no expressly formulated, spoken or written synthesis. It is necessary for the reader himself, alone, to try to fit the pieces in the puzzle. It is necessary for him to try and experiment gathering pieces taking the intellectual risk of the task. It is necessary that this somewhat shapeless mass of contrary opositions without synthesis, of opposites without conciliation, spends some time simmering so that great synthetic ideas can emerge. These great syntheses, when they sprout and emerge, make up the estoeric doctrine, the doctrine which the initiated argue among themselves, the doctrine which the beginners can not even begin to understand. Because the final syntheses are so simple and so bright that those who seek them directly without running the long course of maturing the opposite poles become blinded and cannot see anything correctly. It is the same as looking directly at the sun. The beginner, if he looks directly at the great syntheses of esoteric doctrine, becomes so blinded that he thinks he is seeing absolutely nothing. That is why the hard work of playing with the opposites must be done previously.
That is why Plato’s doctrine for beginners seems to be a dualistic system of Philosophy, a game of opposites in which the opposites never come together. He who only hears and only studies the exoteric doctrine, without ever arriving at the final synthesis of the esoteric doctrine, thinks that Plato considers the world of ideas and the world of things as two spheres of being existing side by side, one outside of the other, one in opposition to the other. The world of things and the world of ideas are then two opposite poles, one against the other, without there being - apparently - a real conciliation between them. There is perfect conciliation in Plato, but this will just appear clearly and completely in the esoteric doctrine, in the so called Unwritten Doctrine. The exoteric doctrine is a strictly dualistic Philosophy in which the opposite poles never completely conciliate. Material world on one side and spiritual world of ideas on the other oppose each other like excluding poles. Material and spiritual poles then never unify in due harmony. The spiritual opposes the material, the ideas oppose the things. The hard dualism, the opposites without synthetic conciliation, the Dialectics without synthesis, this is the intellectual axis of the exoteric doctrine.
Unfortunately many authors, when they speak of Plato, only study and mention this exoteric doctrine. This is just a first approximation on the climb that takes one to the philosophic doctrine which is frequently mistaken as Plato’s Philosophy. Plato is so violently disparaged. Instead of being understood as the thinker of the Great Synthesis, he is thought of as a new sophist who grabs the two opposite poles without unifying or concilating them, leaving them as two opposite, conflicting, irreductible principles. This has been called working by dichotomies since the ancient times. Cut in two, construct the opposite poles, incite one against the other, let one destroy the other, or better, let both the poles turn around each other like two warriors in mortal combat, this is Dialectics without synthesis. The true Plato is a thinker of the Great Synthesis, of Dialectics in it’s full sense of unification and conciliation of opposites, but the Plato that is studied in most of our books - and this is very serious - the Plato of a large part of academic tradition is just the Plato of the exoteric doctrine, the Plato of opposites without synthesis, the dualistic Plato. And this then is an intellectual disaster because it will generate dichotomies in which the opposite poles will nevermore be reunited. Opposite poles in a full Dialectics and taken to it’s appropriate synthesis are excellent, they are movements that point and conduct us further on. In a negative Dialectics with no synthesis, the dicotomic poles become unsolvable problems.
Unfortunately in our philosophic tradition this happens a lot. The world of things and the world of ideas, materiality and spirituality, the great opposition of two poles that should be unified and conciliated is transformed into an unsolvable dichotomous problem which passes to the later philosophers and enters our culture and our education, leaving a trail of theoretical errors and serious ethical deformations. Let us think about the wrong idea - imputed to Plato -, which entered in our Christian tradition, that the spirit is good, the body, however, and especially sex is a moral evil. The Agostinian doctrine which is assimilated by the overwhelming majority of the Christian thinkers and that comes until our century says that concuspiscence, or sexual desire, which we now call hots, is evil in itself, is the original sin itself. And being a sin it is always something morally negative, something that is a guilt, something we must be embarrassed about. This here is a good concrete example of how an apparently small misunderstanding in the beginning brings about a serious mistake in the end. When the Exoteric Doctrine is taken as if it were the Esoteric Doctrine, when the negative dialectics is taken as the legitimate Dialectics, the Dialectics of Great Synthesis, then disasters of great intellectual and cultural dimensions occur. Sexual desire then becomes a sin, the body is debased, man loses the synthetic unity which is body and soul and becomes a completely ridiculous entity. Man in this dialectics without synthesis turns into a caricature, he turns into an angel riding a pig. This is what happens when one does not make the necessary synthesis.
This is why we must study this first binomial of Platonic philosophy, the world of ideas and the world of things, with attention, examining it carefully on both sides. First as two opposite poles which apparently exclude each other, then as two elements which unify, come together and then become one more noble, higher unit. We men are not angels mounted on pigs, nor centaurians, but men, a synthetic unit in which the originally opposing poles, body and soul, disappear while they are opposites and become a new perfect and finished reality.

2. The world of ideas and the world of things
The Sophists argued in favor of the two poles, indistinctively defending one or the other equally, many times arguing in favor of both: argumentari in utramque partem. Socrates, the last of the Sophists, teaches us that this is not possible: Two contrary poles cannot be true simultaneously. Socrates teaches us to ask and to find the answers, to discover the synthesis between thesis and antithesis. This synthesis is not made up of the strength of the stronger, as the Sophist Gorgias would say, but of the virtue. What is virtue? Socrates said that he did not know and told us to converse.
This is still the main theme and Plato’s big problem. After all, what is virtue? If it is not the brutal force of the stronger pole that decides everything, then what does virtue consist of? The answer to this question is the beginning of all Plato’s philosophy: Virtue is that which should be. The world that does in fact exist, as it is in front of our eyes, does not always coincide with that which should be. The Should-Be is an ideal to be reached, the Should-Be is the Idea. In that way the Platonic idea is born. The condemnation - unjust - of Socrates showed Plato clearly that the World-Which-Really-Is does not always coincide with the Ideal-World-Which-Should-Be.
The Sophists thought that virtue, the Should-Be, was something floating, something relative, something that varied from situation to situation and which did not have principles valid for all cases. Plato does not accept this relativity. There are ethical principles which always have the same value for everyone, and these principles are universally valid, even before being adopted by political communities; they are general principles of the order of the world. Plato elaborates a practical philosophy, Ethics and Politics, based on the principles which man must adopt because they are principles of order of all the cosmic universe. Plato’s Ethics is based on an Ontology, a doctrine about Being in general, a doctrine about the order of the universe.
How can we know that a determined rule is not just an invention of some tyrannical governing power or, not that bad, a mere convention constructed by mankind. Conventions, even when good and useful, are contingent; that is, they can be such but they can equally be different. How shall we know that a determined rule or principle is, more than a mere convention, an unquestionable rule, a rule that cannot be denied, that cannot be changed or transformed, that it is like that and must be like that, now and forever, all over the world.
Is it possible to find and bring such fundamental principles about the order of the Universe to light? Plato smiles and shows us that it is. In the Menon Dialogue an illiterate slave is brought to the presence of Socrates who was debating with friends about the existence or non-existence of general principles of the being of the Universe and all knowledge. Some doubted that it was possible to discover and elaborate such principles. After all, where were such principles written? Where, in what book, in what monument would they be written? Socrates, always the central figure for Plato, answers: The first principles are written on the pith of the being and therefore on the pith of our soul. Do you want to see? This slave never studied anything, he does not know how to read or write, and he never studied Geometry. If he never studied Geometry, he does not know the Pitagoras theorem. Well, I am going to talk to him, I am going to ask him questions - just questions -, and let him answer. And Socrates then began to gently ask, drawing lines in the sand on the ground and making the figures. And if I draw this line here, what happens? And what if I add this one? And in that way, step by step, Socrates always just asking, the slave was advancing, discovering the links and being able to formulate the great theorem of Geometry. How is it that the slave was able to do this? How did he know? Plato answers: He already knew, he had always known, he only needed to remember what he already knew and had just forgotten. This knowledge was inborn, it was in the slave’s soul. And it was there because it is a principle that is in each being, each thing, because it is a principle of the order of the Universe itself. These principles of the order of the Universe, inborn in each thing, are universally valid and always present. They organize the Universe from inside out, they are what makes the things of the world be not an unordered mass and chaos of events, but a well-ordered cosmic Universe.
The Idea, says Plato, for whom ontology of participation exists in the core of each thing, is the principle of order that determines and commands its development. In a duck’s egg it is this principle of order which makes that egg develop into ducklings. From a hen’s egg, chicks are always born. And that’s the way with all things. This founding principle of all things, Plato calls form. Form determines what the thing is and how it is going to develop.
All the ducks that exist have, all of them, the same form of the being duck. The many chicks have the same chick-like form. Only one form, only one basic design is made in various individuals. The Form is like that of a drawing made by the designer; one thing is the project of the motor, the basic design, another thing is the thousands of individual motors that are made according to the project. We then have on one side the plurality of individuals that exist in the world of things, and on the other side the unity of Form.

3. The Myth of the Star
The Forms have always existed, they are the ruling forces which determine the order of the cosmos. Before the cosmos existed, however, they already existed and had value. It is also because of this that they have universal validity. The ordered things of the cosmic universe came after. First, before the things existed, before the things of our world had started to exist, the Forms already existed. Is our cosmos not ruled and determined by them? Then, they aready existed before. They make up a whole world that consists only of forms. This world Plato calls the World of Ideas and he locates it on a ficticious star. In this World of Ideas, which has always existed on the star, separated from the World of Things, there are also the individual souls of each man who will be born. The souls see the Ideas face to face and therefore know the specific determinations of each thing; they know everything of everything. When here on the World of Things a man is born, his soul, which has always existed on the star in the World of Ideas, is thrown into the prison of the body. This violent dislocation makes the soul forget everything, or almost everything that it had seen on the Star. But, when man develops and grows up, upon meeting with the things of the world, on stumbling upon them, he remembers the Idea that he saw on the Star during the preexistence of his soul and, remembering, he knows. Knowledge is always a memory, an anámnesis, knowledge consists in remembering the Universal Idea of one thing, and then, facing that individual thing, in saying: Ah-ha, this is a man, this is made in the form of a man; that is a duck, in that the form of a duck is being made real. This explains why the ideas are always universal, even though the things are always individual. Ideas are from another world. And our language - strangest thing - says the individual things always in a universal manner. Because the names, in language, represent forms and the forms are always universal. Even though we are living in this world of individual things, our language, the logos, has the character of a universal idea.
We, therefore, have a wonderful explanation of the world. The things of the world are what they are, they are determined that way and not any other way, because they participate in the original Form that exists on the Star, in the World of Ideas. This is the Ontology of Participation. Like an individual motor participates in the designed project of an ideal motor, in the same way things participate in a determined idea and that is why they are like they are. On this Ontology, that is on this Doctrine of the Being, Plato based his Theory of Knowledge. Knowledge is the act by which the soul now remembers that which it had seen before, during the preexistence on the Star, in the World of Ideas. Knowledge is correct and science is universally valid, says Plato, because it is based on Ideas which are the Forms of the Universe.
But, how do I know, when I stumble upon something, that I am really remembering its Form? Are there no mistakes? Illusions? Of course they exist. That is why the philosopher must converse, argue, question, and examine each question, in order to be sure that what he found is exactly the Idea of the thing. No more and no less. Plato then, always in the Myth for Beginners, in his Exoteric Doctrine, asks: Is there an Idea for a thing? We know there is an Idea for Man, he says in the Dialogue The Sophist, and also the Idea of Good, of Justice. But, is it necessary to have an Idea of Mud? Does mud, such a simple and low thing, need to have an idea of its own? Plato leaves the question in the air. After all, such questions cannot be answered in the scope of the Myth of the Star, such questions can only be satisfactorily worked on in the Esoteric Doctrine with those who aready know more than just the first principles.

4. The Myth of the Cave
We find in the sixth Book of the Republic the more important and more well-known Myth of Plato, the Myth of the Cave. In no other image is Plato’s Doctrine so well represented.
We imagine men who live in a cave. Since their birth they are prisoners in there, chained by the feet and by the neck, in such a way that their eyes are always looking to the back of the cave. They can only see this wall in the back. Behind the prisoners, at their back in the entrance to the cave, there is a wall approximately the height of a man. Behind this wall walk men, this way and that, carrying on their shoulders figures which they raise over the wall. Farther back, right at the entrance to the cave, there is a bonfire. The bonfire gives light, the light illuminates the scene and projects the shadow of the figures over the wall to the back of the cave. The prisoners only see the shadow projected by the figures. They also hear the echos of voices - the men who are carrying the figures behind the wall - and think that this echo is the voice of the figures themselves. What the prisoners sense is just this game of shadows and echos. They have been chained there since birth and think that the world is this and only this. The world is this, they say, just this.
Imagine now that one of the prisoners manages to free himself from his chains. Going to the entrance he immediately sees the wall and realizes that the shadows projected on the back of the cave are just this, shadows. He also realizes that the figures are just figures. He jumps over the wall and goes out; then he sees the men carrying the figures, hears the voices, sees the bonfire, the entrance to the cave and outside the light. When he leaves the cave and tries to look at the sun, he is blinded. He lowers his eyes, lowers his head and puts himself together again. When this man now returns to the cave, to free his companions, he k n o w s. He knows that the shadows are just a sham. The real reality is the reality of the light and the sun, the reality of things themselves in the sunlight. All the rest are shadows, illusions. Man, when freed from the chains that hold him prisoner, discovers himself free and clear, he sees then the reality that is really real, he sees the lightened reality of the Ideas. He will never again confuse reality with the shadow of the sham of reality. He who has seen the light knows.
There we have all Plato. We have all of an Ontology of Participation, a theory of Knowledge, and Ethics, Pedagogy, Politics. But then we mostly have, always again, the Myth that puts the two opposite poles in their counterposition, one strongly against the other, without taking us to a truely synthetic position. After all, where is the unifying conciliation between the World of Ideas and the World of Things? Between universal Form and individual Thing? Between necessary Form and contingent Thing? Plato, in the Myths of the Exoteric Doctrine, does not give us an answer. The synthesis is always missing. This will only be presented and discussed when the beginners are no longer beginners and become initiated. For the initiated, for these, yes, there is an answer. Plato thought that this doctrine, since it was so important and so difficult, could not be written. That is why there is the dialogue - never written by Plato himself, but the existence of which is very well documented - About the good, in which the Esoteric Doctrine is exposed.
Before turning to Plato’s Unwritten Doctrine, however, we must see, in order to contrast them well, Aristotle’s conception of the world. Aristotle was Plato’s disciple for many years, but no one criticised him so much, no one elaborated a philosophic project so different, no one is so less platonic than he. After looking at Aristotle’s Philosophy we will then return to Plato’s Esoteric Doctrine, the doctrine for the initiated.

4. The Analysis of the World

1. The Passage from Dialectics to Analytics
Until Aristotle all Philosophy worked with the game of opposites. The various pairs of opposites were the elements from which things were constructed. Plato, in the dialogue The Sophist, says that Dialectics is the Philosophic method itself. Whoever learns Dialectics and knows how to play the game of opposites, Plato thinks, knows how to compose the great mosaic of the meaning of life, knows how to make the explanation of the world, and has the Great Synthesis. Aristotle, on outlining a panoramic synopsis of the History of Philosophy from the Pre-Socratic philosophers up to his time for his students and readers, always mentioned the game of opposites as a methodical nucleus around which various opinions were structured. He, himself though abandoned the game of opposites and went to a totally different path: Analytics. Analytics, discovered and widely elaborated by Aristotle, will constitute a method and a vision of the world which will influence our western thinking in a decisive way.
All that we think and are in the western world comes from two sources, Dialectics and Analytics. From Heraclitus and Plato we have the Dialectics branch. From Parmenides and Aristotle we have the Analytic branch. Both lines of thinking run through all History of Philosophy and our culture and accompanies us until today. The platonic project goes from one hand to another through Plotinus, Proclus, and in part, Saint Augustine in the classic times; through Johannes Scotus Eriugena, through the Chartres School and many other neoplatonic thinkers of the Middle Ages; through Nicolaus Cusanus, Ficino, Giordano Bruno during the Renascence; through Spinoza, Schelling, Hegel and Karl Marx in Modern times.
Lamarck, Charles Darwin and almost all the great contemporaneous biologists, like Richard Dawkins and Stephen Jay Gould; the physicists of today with their theory of the Big Bang, with black holes like Stephen Hawking, all of them are neoplatonic thinkers. They generally do not realize this, they don’t know it but they are clearly platonic thinkers. The project that they raise and upon which they develop their theories is the platonic project of the Great Synthesis through Dialectics. The aristotelian project of Analytics in the Middle Ages passes through Albertus Magnus, Thomas Aquinas, Dun Scotus and William of Occam; in the Modern Times it passes through Descartes, Leibnitz, Kant, Frege, Wittgenstein and through the Analytic Philosophy of our times. In the continuation and later elaboration of the Aristotelian project, under the guidance of the analytic method, Logics, Mathematics and Physics prospered. In this analytic tradition of Aristotle there are all the logicians and a large part of the physicists of today. Galilei, Copernicus, Newton and Einstein are thinkers of the analytic tradition. But, after all, what does Analytics have that is so powerful and interesting that it produces so much fruit for such a long time? What is Analytics?
All Analytics is based on two things, both discovered and elaborated by Aristotle: The analysis of proposition and the syllogistic system of arguing. A large part of our culture and our technology is based on this. On his foundation of analytic logic Aristotle developed, as we will later see, an Ontology, an Ethics and a Politics, a complete philosophic conception of the world that is characterized by his extremely static character. He is much closer to Parmenides than to Heraclitus.

2. Logic and Language
2.1. The analysis of the proposition
Man speaks in sentences that, in our languages, are always composed of a subject and predicate. Socrates is fair is just such a sentence. This is a complete and well-formed proposition; it is not a question, nor an imperative or an invitation, but a statement. It says that something is this and not that. Socrates is the logical subject of this proposition, the predicate is is fair.
Socrates runs is also a well-formed proposition; there we clearly and distinctly have the subject and the predicate. All men are mortal and Some Brazilians are gauchos are also well-formed propositions; these last two present the Aristotelian quantifiers All and Some. Propositions when well-formed always have a subject and a predicate; in Logics and today’s Mathematics we speak about argument and function. When this proposition is not complete, when it is not well-formed, we can not understand it; we do not know what the speaker wants to say, it is not possible to say if the proposition is true or false. A fragmented, incomplete, badly formed proposition has only a subject, no predicate: Socrates. Socrates what? Say more! Say the rest! Without a predicate this proposition is not well-formed and makes no sense. The same with the verb that is the predicate. If one says only is fair, this makes no sense and soon one asks: Who are you talking about? Who is it that is fair? What is the subject of the proposition? This is the basic structure as it is analyzed by Aristotle. It is clear that there are vocatives like Hi, Socrates, as well as propositions in which the logical subject is not expressed but understood. This we call the implied subject.

2.2.The affirmative proposition
Propositions can be either affirmative or negative. In the affirmative proposition we take a determined subject, be it individual (Socrates), particular (Some Brazilians) or universal (All Brazilians), and put it into a bigger whole that is the predicate. Let us look at the graphics drawn in the way of Euler, the mathematician:

Socrates is fair

The logical individual subject, Socrates, here in the example, is put into a bigger whole that is the predicate is fair. The smaller set, which represents the logical subject is contained within a larger set which is the predicate.

All Brazilians are mortal

The logical subject All Brazilians is a smaller set that is contained in the larger set which represents all that is mortal. All Brazilians are mortal, but not all mortals are Brazilian. There are people of other nationalities, as well as plants and animals that are also in this set of mortal things. That is why the logical subject All Brazilians is completely within the larger set of those that are mortals. - In the proposition Some Brazilians are gauchos things get a little more complicated: Not all Brazilians are gauchos, and not all gauchos are Brazilian, there are also Uruguayan and Argentinean gauchos. Therefore the drawing is a little different:

Some Brazilians are gauchos

This is not the same as before, in which one set is completely contained within another larger set. Here, the set expressed by some Brazilians is partially contained by the set are gauchos, but at the same time it is not completely in it. This is easy to see in the diagram. The two sets enter into a partial overlapping.

2.3. The negative proposition
In the negative proposition the predicate does not have its own subject, but opposes it. The subject is not within the predicate, the predicate is not in the subject. One is outside the other.

Men are NOT gods

The set of the subject is on one side, the set of the predicate is on the other, like in the game of opposites of the Dialectic. But here, in Analytic Logic, one does not look for synthesis; here there is no conciliation, here there is no movement. One pole excludes the other. That’s it. The only ulterior differentiation that Aristotle does in his Analysis is, as we see in the Logical Square, the distinction between opposites that are contrary and opposites that are contradictory. This very important distinction is going to be the battlefield on which analytic and dialectic philosophers are going to fight for more than two thousand three hundred years.

2.4. The Logical Square
Medieval thinkers illustrated Aristotle laws of inference with the geometrical figure of the square. The Logical Square was drawn later, but the basic ideas and the laws that rule it were all - almost all - discovered by Aristotle. Laws of inference are the logical rules that permit the logical transit from one point to another in the Logical Square. Does one set include the other? Or does it exclude it? Or is it neutral and then can include it or not? Does the truth of a proposition given imply the falseness of what opposes it? And what does the falseness imply?

A E

I O

There are various types of opposition. The opposition between A and O and between E and I is called the opposition between contradictories. The opposition between contradictories crosses through the middle of the logical square. The opposition between A and E is called opposition between contraries; both are universal propositions. One is positive and the other is negative. The subcontrary opposition is what is between I and O, between two particular propositions, one affirmative and the other negative. The opposition between A and I, on the left side of the Logical Square, and between E and O, on the right side, is called subaltern.
For each type of opposition there are different rules of inference. Aristotle discovered and described all of them. From the truth of proposition A can we conclude the falseness of proposition O that is its contradictory opposite? Yes, always, answers Aristotle, the truth of A logically follows the falseness of O. And the passage of A to E? And A to I? For each type of opposition there are specific rules. Aristotle elaborated the rules of the Logical Square by consequently applying the same method that he used to analyze the internal structure of the proposition, that is, asking if a proposition included or excluded the other. For any example we can make the for propositions of the Logical Square and draw Euler’s corresponding diagrams. The passage of A to I is easy. If it is true that All men are mortal, then it is also true that Some men are mortal. The larger set obviously includes the smaller set. The truth of A always implies the truth of I. The passage of E to O is equally obvious. The whole always contains its parts. The truth of E always implies the truth of O. The reverse is not viable, because the truth of proposition I or O does not say anything about the falseness of the corresponding A and E propositions. It is true that Some men are bad, but this does not mean that All men are bad. This also as well as other logical paths that follow the other sides of the Logical Square or cross through it, we shall see later in more detail when we return to discussing what Dialectics is, since it is right here that Analytics and Dialectics clash.
The difference between the opposition of contraries and the opposition of contradictories is simple enough to understand, but, as easy as it may be, it is here that everyone stumbles. We stumble and fall, as we know. Thales of Miletus was looking at the stars and distracted by fell into a hole. And the Thracian slave laughed at him. The Thracian slave continues laughing at the Analytics and Dialectics who in the twentieth century continue stumbling and falling. The Thracian laughs because they do not understand each other. Because they still do not know the difference between contraries and contradictories. Because they do not know how to put together the game of opposites.

2.5 Syllogism
Syllogism, the second great discovery made by Aristotle, consists of the logical connection of two propositions which, articulated between them, make a third proposition result from it. If the two initial propositions, the premises, are true, then the proposition resulting from them, the conclusion, will always and necessarily be also true. An example.

Premise no. 1 All men are mortal.
Premise no. 2 All Brazilians are men.
Conclusion Then, all Brazilians are mortal.

There is a connection between the first and the second proposition in this logical construction. The subject of the first premise is the predicate of the second premise: Men. This logical set, that is in both premises and serves the first as a subject and the second as the predicate, does not appear again in the proposition which is the conclusion. It is something intermediary, a kind of common denominator which connects the subject of the second premise with the predicate of the first and therefore serves as a mediator so that the proposition which will be the conclusion can appear. This is called Middle Term. The traditional diagram illustrates well what we mean. M is the middle term:

M - P
S - M
_____
S - P

In the first premise, the Middle Term is the subject of the proposition; in the second it is the predicate. In the conclusion, that which was the subject of the second premise appears as the subject of the predication, and as the predicate of the predication is what was the predicate of the first proposition. Euler’s diagram intuitively shows this logical link of inclusion better than words. One can see there that syllogism is just an ulterior elaboration of the inclusion/exclusion method that we have already seen in the structure of the proposition.

mortals

men

Brazilians

We can clearly see what the Middle Term is and how it works. Between the subject and the predicate of the conclusion a mediation is made so that the larger set includes a smaller set, which in turn includes an even smaller set.
It is on this basic model that Aristotle develops his doctrine about syllogism and calculates exactly which syllogistic forms are logically valid and which are not. This syllogistic system was so well constructed by Aristotle that this first elaboration became the final one. The Aristotelian doctrine about syllogism continues valid of course, and even today makes up the backbone of all Logic. Only with Frege is Logic going to have a new impulse, a new fundamentation and an expansion.
According to the Middle Term position, there are four basic forms of syllogism:

1 2 3 4

M - P P - M P - M M - S

S - M M - S S - M M - P
______ ______ ______ ______
S - P S - P S - P S - P

The syllogisms in the ancient times and in the Middle Ages, received names; it is clear that the names meant something important. The first syllogism of the first figure is called Barbara. The three A’s of this name - Barbara has the letter A repeated three times - indicates that both the premises and also the conclusion are A propositions in the Logical Square, that is universal affirmative propositions. The second syllogism is called Darii. The first premise then is A, a universal affirmative proposition; the second premise and the conclusion are I, particular affirmative propositions. The third syllogism is Ferio. The larger premise then is an E proposition, universally negative; a smaller proposition is I, a particular affirmative proposition, and the conclusion is O, a particular negative proposition. The names of the syllogisms are the following. First Figure: Barbara, Darii, Ferio. Second Figure: Cesare, Camestres, Festino, Baroco. Third Figure: Derapti, Felapton, Disamis, Datisi, Bocardo, Ferison. Fourth Figure: Bamalip, Calemes, Dimatis, Fesapo, Fresison.
For the mere combination of letters there would be a much larger number of syllogisms. But only the above mentioned syllogisms are logically valid, that is, only these always work so that from the truth of the premises comes the truth of the conclusion. All the other combinations are invalid. Por example, a syllogism with the A - I - A sequence in the first figure is invalid. The Barbara syllogism, A - A - A, and the Darii, A - I - I are valid; an A - I - A syllogism is not valid. Why not? How does one know? When one tries to make Euler’s diagram of an invalid syllogism, the diagram does not work. It is impossible to draw such a diagram, since the sequence of continent and content becomes subverted. The diagram simply does not form. Or better, upon forming, one sees right away that it does not work. We will take as an example an A - I - A syllogism that in the first figure is not valid:

All Brazilians speak Portuguese
Some Gauchos are Brazilian
Therefore, all Gauchos speak Portuguese

The larger premise is true, the smaller one is also. But the conclusion is false, because some Gauchos, the Uruguayan and Argentinean Gauchos, do not speak Portuguese. Where is the mistake? In the incorrect logic Form, as we see in the corresponding Euler diagram:

speak Portuguese

all Brazilians

all Gauchos

The set of all Gauchos is only partially inside the set of all Brazilians. The correct conclusion would be an I proposition (Some Gauchos speak Portuguese) and not a universal proposition A (All the Gauchos speak Portuguese). Classic thinkers for this reason created various rules for construction of syllogisms. The most important of them says: the conclusion always follows the worst part. That is, if there is a negative or particular proposition in the premises, the conclusion should also be negative or particular. In the above example, the second premise is particular and for this reason the conclusion should also be particular. To make a universal conclusion then, having a particular premise, is incorrect. That is why the conclusion does not conclude anything and is wrong: There are Gauchos who do not speak Portuguese.

2.6 The Non-Contradiction Principle
Aristotle’s central ideas, which are the doctrine about predication and the system of syllogisms, take us to a position radically contrary to the Dialectic of Plato and the game of opposites of the Pre-Socratic Philosophers. According to him, the game of thesis, antithesis and synthesis simply does not work. For Aristotle, to affirm the truth of the thesis and at the same time the truth of the synthesis is pure foolishness. Everyone who affirms one thing, and at the same time and under the same aspect affirms the contrary, is saying foolishness. Dialectic in Aristotle changes its meaning; it is no longer a correct and very important procedure, like in Plato, but that foolishness which the Sophists did. This is the highly pejorative sense of the word Sophist. Because everyone who says something and at the same time says the opposite is not saying anything, he is being foolish.
And then what happens to the old master Plato and his Dialectics? If Dialectics is foolishness, is Plato just a fool? Aristotle does not say this, Aristotle changes the subject. It is obvious that he does not frontally attack his old and respected master, Plato. But a meditated reading of the book Gamma of Metaphysics shows us how Aristotle gets more and more distant from Plato and the game of opposites. Nothing of playing around with thesis and antithesis. Nothing comes from this. Nothing rational results from this. If one of them is true, the other simply is false, or vice versa. To try and follow the thesis and antithesis at the same time is pure foolishness. This is Aristotle’s main and toughest objection to Plato, this is the Analytic Philosophers’ objection to the Dialectic Philosophers. It was like that in the classic times and continues like that today. This is the main theme of this book. Is Dialectic a foolish thing?
Against Plato and against Dialects Aristotle raises and formulates the Principle of Non-Contradiction. The Principle says the following: It is impossible to predicate and not predicate the same predicate of the same subject under the same aspect at the same time. One who states and at the same time and with the same aspect unstates what he said, is not saying anything. He is talking foolishness. The rose cannot be at the same time and under the same aspect red as well as green, that is, not red. It can happen that the rose is green and then becomes red, this can be, because it is happens at different times. It can also be that the rose is red and green at the same time. But then there are different aspects. The rose petals are red and the stem is green. They are two different aspects. But they cannot exist under the same aspect, that is impossible. We have here, again, old Parmenides’ main thesis: The Being is, the Non-Being is not. Aristotle deals with this subject in a more subtle way through the introduction of the aspects of being. But once again, the rule is valid: That what is cannot under the same aspect not be. And that is why one cannot, under the same aspect, affirm and negate a predicate of the same subject. Parmenides’ main idea, farther differentiated in Aristotle, dominates the philosophic thinking again, excluding Heraclitus’s All Flows. The static character of Aristotle’s Philosophy begins to appear. Parmenides’s sphere shines again.
Aristotle and, even more clearly, the Aristotelian philosophers of the Middle Ages, added to the Principle of Non-Contradiction a practical rule of the art of thinking and debating correctly. The Principle of Non-Contradiction is always valid. Right. But if, in practice, we have two propositions with the same subject but opposite predicates, and both appear right, what do we do? In these cases there is a rule of procedure: Make the necessary distinctions. Let Socrates is less than 1.50 meters tall be one proposition, and Socrates is more than 1.50 meters tall the other. Here we have two propositions with the same subject, Socrates, whose predicates say opposite and excluding things. But we have good reasons for defending either one or the other. What do we do? Should we here defend the Dialectics? No way. In such cases Analytics tells us to make the necessary distinctions in the logical subject of the predicate.

Logical main subject Socrates
Aspects added to the main
subject 1. insofar as he is sitting, is less than 1.50
meters tall
2. insofar as he is standing, is more than 1.5 meters
tall

The opposite predicates, after making the necessary distinctions, are attributed to the same subject, Socrates, but under different aspects (while sitting, while standing). Even though the person, Socrates, is the same, Socrates while he is standing has an attribute that Socrates sitting cannot have. This is perfectly acceptable. Then we create a double subject. The first, Socrates, is the logical initial subject. With the introduction of ulterior logical aspects (while sitting and while standing) one creates an enlargement and reduplication of the subject. The logical subject, which was one and simple, because of the reduplication becomes a double subject which then allows us to conciliate the initially excluding predicates. From this comes a practical rule of procedure: When there are predications with two opposite predicates and the same subject, and if it is true that one does not exclude the other, then we must carefully verify until we can find two logical aspects in this single subject that allow us to predicate opposites without offending the Principle of Non-Contradiction. In practice, however, if there are two opposite predicates either one eliminates the other or it must be a logical subject that contains two different aspects. Nothing of Dialectics, nothing of the game of opposites. Either one opposite eliminates the other, or there is one subject with two different aspects. This is Aristotle, this is Analytics.

3. Metaphysics
3.1 Substance - essence and accident
Metaphysics was the name given by Andronicus of Rhodes, who organized Aristotle’s works, to the Books that come after Physics. From the etymology, then, there is nothing spectacular nor profound in this word. The word meta ta physica, which meant nothing important, took the meaning of the nucleus of a whole philosophic vision of the universe. It is in these books, that come after Physics, that Aristotle sketches the rough draft of his explanation of the world. In the same way that language obeys the laws of grammar, which is Logic, the cosmic universe, the world of things, does the same, also obeying a grammar, and that is why it is perfectly ordered. On one hand we have language with its clear and exact laws - see the rules about the proposition and system of syllogisms -, on the other hand we have the cosmos also ordered by laws. Aristotle’s great thesis is that the same grammar that is the grammar of language is also the grammar of the world. The same laws that rule the articulation of logical speech also rule the course and relationship of things. The great laws of Logic are also the great laws of Ontology. The things have the same structure that a well formed proposition has, says Aristotle. In the proposition we have the subject and the predicate. The logical subject, sub-jectum, hypokeimenon, that which is subjacent to the predicated proposition, is indispensable to the proposition; without it one does not know what one is talking about. In the same way there must be a hard subjacent nucleus in the things. The logical subject of language, support of the predicative articulation, corresponds to the substance, that which is under the things themselves, supporting them, the sub-stance. The logical substract, the sub-jectum, corresponds to the sub-stance. Things, in their fundament, in their hard core, are first of all substances, ousia in Greek. On top of this hard nucleus, which is the subjacent substance, there can be other determinations. These are called accidents. They happen to things, or better, sometimes they happen, sometimes they don’t. These ulterior determinations are non-necessary determinations, that is why they are called accidental, which exist over the substract of the substance which supports it from underneath. What is substance? What is accidental?
In the logical structure there are certain predicates that are necessarily required by the subject, there are others that are allowed. In this way, the logical subject triangle always requires the predicate has three sides and three angles. The link between this subject and this predicate is necessary. It is not possible to think or speak triangle without the characteristics of having three sides and three angles. These necessary predicates correspond to the essence of things. The logical structure corresponds to the ontological structure. According to Aristotle, essence is the substance determined by its necessary characteristics. The allowed predicates, the non-necessary predicates of things correspond to the accidents. Accidental is a characteristic that a substance can equally have or not have. A triangle can be blue or red. The color is accidental. It is a logical predicate and an ontological characteristic which is not necessary.
The mutations which occur in nature at times affect the substance itself. The living thing is born and then dies. Birth and death are transformations that affect the substance itself of the thing. Aristotle, with his own terminology, speaks of generation and corruption. There are many other mutations that are merely accidental. The animal that is now awake is also the same that later is sleeping. Be-Awake and Be-Sleeping designate accidents, that is non-substantial relationships. The color of the geometric figures is always something accidental.

3.2 Substance - form and matter
The essence of things is different from the accidents. The essence is necessary for the thing to be what it is, accidents are not necessary. Okay up to here. But, does that mean that substance and essence are the same thing? Is substance, which is under the accidents and gives them support, the same as the necessary essence for the Being-this-way of the thing? Aristotle says no. Substance contains within itself two constitutive elements; one of them is the essence that works as form, the other is the matter. There is here, in the heart of Aristotle’s Ontology, a conceptual articulation that sends us back to Plato’s Theory of Forms. Aristotle, Plato’s disciple, completely abandoned the dialectic method of his teacher, but he did not abandon the Theory of Forms. Here it is, back again.
Substance is made up of form and matter. Form is the determining factor that gives outline and determination; matter is that in which form is realized. Aristotle, in this context, explains the four causes. Each thing always has four causes. The efficient cause and the final cause are the external parts of each thing, the formal cause and the material cause are the internal parts. Let’s take a statue made in honor of Apollo. The sculptor is the efficient cause; the honoring of Apollo, the reason for which the statue was made, is the final cause. Both are outside the statue itself. The marble is the material cause, the form of Apollo is the formal cause of the statue. Form and matter are elements that enter into the composition of the statue of Apollo, they are within it. The statue is the form while realized in matter. Without form, the matter is something undetermined; the unshaped marble is not yet the statue of Apollo. The pure form, without matter is just an idea in the head of the sculptor and of mankind. An idea? Exactly, now we are back to the Theory of Ideas, Plato’s Theory of Forms. The idea of Apollo is the formal cause, the ideal form, that upon being sculptured in marble will acquires materiality and becomes a statue of Apollo. Form and matter together, the form of Apollo plus the marble, as a whole, make up the substance. Almost all substance is made up of form and matter. And what about the accidents? Accidental in the statue is the fact that it is marble, of being this or that color; remember that the Greeks used to paint the statues which we today admire in the museums only with the natural color of marble.
Let us review. The being, or as you may, the concrete thing to which we point is something made up of substance and accident. Accident is that which is not necessary, it is that which just happens. Substance is the being subjacent to what happens. Water, which at times is liquid, at times evaporates and becomes gas, at times becomes solid as ice, the water is a substance. The liquid, solid and gaseous states are accidents of the water. Substance, on the other hand, is made up of essence and material. Essence is the formal reason that determines that the Water-Being as water. Matter is that matter from which and within which form becomes a concrete determination. But, what is matter after all? Matter is the undetermined, the emptiness, Aristotle is going to say. Matter itself and from itself has no determination, it is shapeless, inert, it is the mere passive possibility that something can be done on it and from it. Matter is something unsayable. All comes to it from form which is the principle that molds it, determines it and gives it shape and outline. Within substance the essence is the formal cause; the matter, the pure potentiality, is the material cause. It is there in this hard nucleus of his Metaphysics that Aristotle continues being a neoplatonic philosopher. It is also there that the Aristotelian theory about the genesis and the structure of knowledge, the Metaphysics of Knowledge, takes root.

3.3 Metaphysics of knowledge
The things in this concrete world in which we live act upon our senses and, starting from the sensations that we perceive, elaborate a sensitive image that within us shows us how something is. This sensitive image however is something mixed with the body, it is something corporeal, something determined by space and time, something susceptible to production and corruption. The image given by the senses changes as the things present themselves or do not present themselves. The image elaborated by the imagination, an internal sense, is something more independent, something more interior. The image of the imagination, a more elaborate product of the knowledge process, represents the things even when they are absent, therefore, when they are not anymore acting upon the external senses. The imagination is a powerful internal sense. Everything passes through it. But it is only sensitive, it is not an intellection. The imagination represents things, re-presents them, makes them present again even when they are absent, like a signal that, being a signal, remits to a real thing that is not itself. The image produced and elaborated by the external and internal senses is always just a sensitive signal. But how do we arrive at the intellection, the concept? If the sensitivity is still corporeal, contaminated by space and time, how do we pass from it to a universal concept out of space and time?
Things are individual, they are extense, spacial and temporal. Concept is universal, unextense, out of time and space. How can individual, extense, space-temporal contingent things that act on our senses produce universal, unextense, concepts necessary in their nexuses. How does one pass from the world of things to the world of ideas?
Things cannot, on their own, make this change, teaches Aristotle. He who produces the concepts is the intellect itself while actively function, while active intelect. There is in man, in all men, a powerful active intellect. This nous bows itself to the image produced by the external and internal senses and brightens it with its light. Under the light of the active intellect, Aristotle says, then the Form that was within the sensitive image and of course also within the thing itself shines. This is again Plato’s Theory of Ideas now in the hard nucleus of Aristotle’s Metaphysics of Knowledge. In his heart, Aristotle is still Plato’s disciple. The conceptual nucleus of the Myth of the Cavern appears again here more soberly, more prosaically, with less images. Here is the Platonic idea again. The Form that gives shape and outline to something - as a vital principle within each thing - is the same Form that is implicit in the sensitive image reproduced by the senses. Only under the light of the active intellect does this Form acquire visibility and become transparent to itself again. Form is extense, space-temporal and contingent in the thing; this is its material way of existence. Under the light of the active intellect Form stands out from the matter which individualizes and holds it and returns to being pure Form, Form without matter, necessary, unextense, out of space and time form, intelligible form. The triangles, which exist in the material world of things are contingent, they are space-temporal, they have various sizes, they are colorful. But the concept of a triangle is necessary in its nexusses, it is unextense and abstract; it is no longer space-time related, allowing us to think about it in different sizes. Form, pulsing in the heart of things, when it penetrates our senses under the light of the active intellect, transforms itself and acquires its real characteristics. Forms are ideas, they are necessary, unextense, out of time and space. The triangle, the Form of the triangle, is eternal and forever valid, throughout time and everywhere. It is this eternal Form that comes from the light when our active intellect acts. Then we see the universal and eternal forms of the individual and contingent things.
Form, when it was in matter, was just a potentiality. It could be thought of, it could be transparent to itself. It could be, but it really was not. This Could-Be, Aristotle called potentiality. Form, in the individual things that exist in our sublunar world, are infected with materiality. That is why they are not transparent to themselves. A table does not know that it is a table, a cat does not have the concept of a cat. But, when it is thought of by man through the light of the active intellect, the Form frees itself from the matter and returns to itself; it becomes transparent, intelligible, and one knows how it really is, as a universal with its necessary nexusses, out of space and time. In the inanimate things and the animals of our sublunar world the Form exists only in its potentiality, it is just sleeping. Through the light of the active intellect the Form is actualized; it goes back to be in act again, it goes back to being the actuality of itself, it becomes transparent and aware of itself. Act and Potentiality, the Being and the Can-Be are here interwoven. The active intellect is the Act that actualizes the Form that was sleeping in its potentiality within the thing itself and within the image produced by the senses.
Aristotle developed more technical concepts, but we note that he continued thinking and defending Plato’s Theory of Forms. But, Aristotle said that the Forms are inside the things, Plato had said that the Forms exist in the Stars, in a separate world. This would be the great difference between Aristotle and Plato. Foolish thing. Who does not yet realize that the Star is just a mythological form used by Plato to say the same thing? Aristotle and Plato had various differences between them. But not here.

4. Ethics and Politics
The descriptive propositions say just how things really are. This table has a broken leg is a descriptive proposition. But the table should not be like that, the leg should not be broken. This Should-Be, in the case of the table with the broken leg, is something merely functional. For this table to work well as a table it is necessary that it be firmly set, which means that the leg can not be broken. In the world of useful things the Should -Be is determined by functionality.
In the relationships of people with other people, what is the criteria of Should-Be? What s h o u l d my relationship b e with other men? There, says Aristotle, we enter into a completely new territory. Until now we were moving around the land of the theoretical reason, workimg with the propositions that are either necessary or contingent, which say what necessarily is or what in fact is like this and not like that. Now we enter a new territory, the territory of Ethics, that is, the Should-Be.
Things have nexuses that are substantial and necessary. They have others nexuses that are merely accidents, that can happen or not happen. This is the extent of contingency: one thing can be like that, but it can also be different. It is within this range of contingency, full of alternatives, that Aristotle places Ethics, the empire of the Should-Be. There are situations in which a man, face to face with another man, can act one way or another. Sometimes there are dozens of ways to act. Well, this is the rein of the Should-Be. Man, upon interacting freely with other people, has various alternatives to choose from, and s h o u l d choose of his own free will that alternative which is Ethical.
What is Ethics? What act is ethical? That act - Aristotle teaches us - which is done according to virtue. But what is virtue? Plato has already discussed this to extent. Virtue is a habit, virtue comes from far, virtue comes from local tradition. To be virtuous is to obey the rules of the land where we are. - Is virtue then, pure conservatism? Tradition is most important, according to Aristotle, but is not the deciding factor. The deciding factor of ethics, the last criteria, is straight reason, straight logos, orthos logos. A straight line, in geometry, is the shortest way between two points. In architecture it is the lineament that one draws and gets by stretching a rope. Following the line, in construction, we get the architectural lines of floors, walls and ceilings. Orthos is the logos, straight is the reason that obeys the grammar of the practical logos. Here Aristotle introduces the idea of practical reason as something different from and opposed to theoretical reason. Practical reason, Ethics and Politics, do not obey the same rules as theoretical reason. The rules of practical reason are more flexible, they are less exact. They are a different kind of logos.
How then, when in doubt, does one find the straight reason? A good practical criterium, Aristotle says, is to stay in the middle. The golden rule, as it will be called in tradition, says that we should not opt for extremes, which are ethically wrong, but we should stay in the middle. Cowardliness and recklessness are extreme poles which are both ethically wrong. Virtue is in the middle. Virtue is in the courage that is in the middle between cowardliness and recklessness. If there is a fight, one should leave, not so slowly as to look audacious, nor so quickly as to look cowardly. Those who live by practicing middle of the road actions will be happy. Happiness, eudaimonia, is the crowning of a virtuous life. Aristotle knows very well that the rule of the middle road, of mesotes, is just an auxiliary rule. The philosophic criteria if the Should-Be consists in the straight reason.
Anticipated here in Aristotle’s Ethics, is the dichotomy between theoretical reason and practical reason which we will find again in the medieval classics, in Kant and almost all the other contemporary Ethics. The rein of theoretical reason does not coincide with the rein of practical reason. The principles of the first do not coincide with the principles of the second. The grammar of theoretical reason is not the same as the grammar of practical reason. This mistake - I consider this to be a great mistake -, that is found neither in Plato nor in the neoplatonic philosophers, caused and will continue to cause big problems. To separate two opposite poles without making the slightest attempt at conciliating them at a higher level is something typical of Analytics. In these situations Dialectics, the game of opposites, orders us to continue the search for a synthesis, a conciliation between theoretical reason and practical reason. Both reasons overlap, therefore there must be some principles common to both. But Aristotle does not look for this, this in Analytics by the inertia of reasoning is neglected. For Dialectics the great question continues to be, even after Aristotle and Kant: How do these reasons overlap? What principles are common to both?
Men live with each other, men need each other. Only the beasts do not need anyone and live alone. That is why men organize themselves in States. The man who lives within the structure of a State is a citizen. The main virtue of a citizen is justice. Justice is the straight reason that says how the many men, equal among themselves as citizens of the same State, should treat each other. Equal to equal. That is why a fair law is that which is the same for all. If it is not the same for all it is not a law, but a privilege (privi-legio, private law), they said in the Middle Ages. - That Aristotle, in this context, has forgotten that the slaves, which existed in his time, could not be slaves, shows us how even the greatest among the great thinkers could have periods of blindness. There are various forms of governing the State, but all of them should strive for the common good, the well-being of all citizens. Even when there is only one head of government - Monarchy -, he governs in the name of common good and for the common good of all citizens. This is why a king, even being an individual, must speak in the plural. When he speaks, all the citizens are speaking, when he decides, all are deciding. The same happens when a few govern - Aristocracy -, or when the public assemblies govern - Polity -. When the governing power loses the view of common good and governs for the good of some, contrary to the good of others, then the government degenerates. When the government of one degenerates, despotism comes into being. When the government of a few degenerates, there is an oligarchy. When the government of many meeting in assembly degenerates, there is democracy. In Aristotle democracy, as we can see, has a strong pejorative meaning. What we call democracy today - the only ethical way to govern and be governed - Aristotle called Polity. But Aristotle did not realize that this was the only ethical way to structure the State. We only discovered this in Modern Times.

5. The analytical conception of the world
Aristotle, an excellent observer of things, already knew that the planet on which we live is round. In the treaty On the Heavens, he wrote that the eclipses of the moon are caused by the position of the earth. Earth in its movement puts itself between the sun and the moon, causing in this way the eclipse. Since the shadow which the sun projects on the moon is always round, we must conclude that the earth is round. If the earth were flat, like the majority of the thinkers of that time imagined, the shadow of the earth projected on the moon could not be round.
But Aristotle, following the opinion of his time, thought that the earth was fixed, that the earth was an immovable point in the center of the universe. The sun, moon, planets and stars turn in circles around one central point that is the earth. This idea is later elaborated by Ptolomy who in the 2nd century described the universe by perfecting the Aristotelian cosmological model. The fixed sun, moon, planets and stars turn in eight orbits around the earth. The fixed stars are the highest and last sphere. Next come the orbits of, in order, Saturn, Jupiter, Mars, Sun, Venus, Mercury and the Moon. The moon makes up the first sphere, the lowest one, that is nearest the Earth. From the moon down we have the sublunar world, that is the world in which we live. In the world above the lunar orbit there is no individual movement, the only movement is the turning of the spheres themselves. That is why the stars are fixed. The stars, the planets, the sun and the moon make up a world that moves itself, yes, in its eternal and immutable orbit, but there is neither generation nor corruption in it, there are no transformations nor accidental movements. There is no chance nor contingency in it. In the world of the stars everything happens in absolutely regular cycles, day, night, lunar month, seasons of the year. This immutable world in which the only sound is the music of the celestial spheres is almost as static as Parmenides’ sphere.
In the sublunar world however, the Forms are mixed with matter. In this concrete world of ours the Forms, upon entering into substantial composition with matter, become extense, space-temporal, they are delivered to the process of generation and corruption. Plants, animals, and men are born, live and perish. This space of movement, full of chances and contingencies - space in which the freedom of choice of man is permitted -, is not a complete chaos because it is ordered by the Forms. The Forms, principles of order and determination, are eternal. Man is man because he has the Form of the Man-Being. A dog is a dog because it has the Dog-form, and so on with cats, fish, plants and everything else. In our sublunar world all that stays, all that remains, all that is stable is like that because the eternal Forms give them stability. Everything else is accidental, it appears and disappears, comes and then goes. In this mesh of accidental events the individual man, as well as the men united in Polis, many times has more than one alternative way to act. It is there, in this space opened by contingency, that the free choice, the freewill is processed. If man chooses the correct alternative, his act is ethically good. If not, it is bad. But even in this sublunar world of ours there are necessary nexuses, and that is why it is possible to have a science that knows these necessary nexuses. Not only the necessary nexuses existing inside the things, but also the theoretical science about these necessary nexuses are based on the Theory of Forms and are explained from there. Until Copernicus, in the XVI century, Aristotle’s geocentric model was accepted and used by all as the explanation of the cosmic universe. In 1514 Copernicus proposed a more complex but much more exact model: The sun is the center of the system, around which the planets, including Earth, turn. Copernicus’ model explained something which the geocentric theory could not explain, the reason why at times the planets turn in the opposite direction. The geocentric theory, defended for so many centuries, then entered into a collapse and was abandoned because it could not explain a phenomenon observed by all those who studied the starry sky. Copernicus’ heliocentric model, later elaborated on by Kepler and Galilei, is a theory that explains well all that happens, including apparently strange movements of some planets, and which permits exact predictions. Only much later, in 1687, is Newton going to explain through some very simple principles how this whole universe functions: through the Law of Gravity. With Newton the analytic thinking begun by Aristotle and the Greek geometrists, passing through Copernicus, Kepler, and Galilei conducts us to Modern Times, to the Physics and Cosmology of today, to Hubble and Einstein.
Aristotle’s conception of world is also the conception of the world of the great Medieval thinkers. Except that these, following the biblical tradition of Christianity, do not consider the universe as something eternal, like Aristotle, but as a creation made by God. In the beginning there is God, the All Powerful, that is the beginning and end of everything. God created the beings. The beings created are God’s creatures. The whole universe, Earth, sun, moon and stars are creatures of God. God created the stars - and here the Aristotelian model is incorporated - as something fixed, as something that moves in perfectly regular orbits. Guaranteeing the place of God the Creator, the Aristotelian thinkers of the Christian Middle Ages defended almost everything of the Aristotelian model. When Copernicus and Galilei brought up the heliocentric model, the catholic thinkers were strongly against it. Galilee was condemned by the Catholic Church for subverting the celestial order. But almost no one realizes that both models deep down have the same Aristotelian structure, the static conception of Aristotle’s world and of the Analytic Method. Even Newton and Einstein himself are still Aristotelian thinkers and use the analytic method, without realizing that there is another important and rich model that has an enormous explanatory strength, the platonic model of the Explanation of the World. Until now a large number of philosophers and physicists still think of the universe as a great clock in the Aristotelian and Analytic way. Those who believe in God say that there was, in the very beginning, the Great Architect or the Great Watchmaker who planned and executed everything down to the smallest details. The others, with no God, those called Atheists, say that there is no need for any architect, that everything is the work of some great laws - still not totally discovered - that determine everything, that rule everything, that explain everything, down to the last iota. Einstein, we know, searched tirelessly until his death for what he called the formula of the world. A simple formula, like that of energy, in which and by which everything, all the universe, could be explained.
Contemporary physicists, especially from Heisenberg on, took chance and contingency more seriously. Einstein on this point kept the old way of thinking; he thought that there was no chance in Nature. There is no chance at all in the processes of nature, he thought. What there is, is that many times we still do not know the laws that rule certain events. Then we speak of chance. We should not speak of chance; there is in reality no chance but just a deficit of knowledge. When we research more, we discover laws that rule the apparently casual event and what seemed to be chance disappears and is shown as a process ruled by totally determined laws. This, in the existing discussion, was transposed into a religious image. It was asked if God threw dice, if God used chance as an instrument of his creating act. The question here is not religious, one does not want to know if God exists or not, but if chance exists or not in nature. Einstein thought that there was no chance in nature. Einstein thought that God did not throw dice. I think that Einstein was wrong, and Heisenberg was right. God throws dice. In the discussion of the XX century, we do not ask any more if a God the Creator threw dice or not, but if there is contingency or chance in Nature. Does Nature throw dice? Einstein and many others say no, Heisenberg and many others say yes. I think that yes, there is contingency and chance in the course of things. I think that if there were not this contingency, there would not be space for free decisions, for free will, for moral responsibility, for justice, for political democracy, for historicity. I think that these things are interwoven. He who does not accept chance and contingency there in the core of Logic and Ontology, cannot, later speak of liberty, free will, democracy and true historicity.
This, in my opinion, is one of the neuralgical points of Philosophy in the last one hundred and fifty years. After the collapse of Spinoza’s system and of the German Idealism, after the collapse of Hegel’s theoretical system and Karl Marx and Lenin’s practical-political system, what was there to do? What was wrong? Nietzsche, Heidegger, the second Wittgenstein, Popper are going to tell us: Historicity, contingency, chance were missing. The Philosophy System had to admit that within the things and relationships between things there is contingency and chance. That is why so much emphasis was given to the concrete existence of the individual (Kierkegaard, Sartre), the horizons of time (Heidegger, Gadamer), the multiple games of language (Wittgenstein, Analytic Philosophy). This emphasis is right. God, that is, Nature does throw dice. This, by the way, Plato already knew. This is the central point of Plato’s Unwritten Doctrine. This is the important element of that which is called the Explanation of the World in our tradition.

5. The Explanation of the World

1. To explain is to unfold
Plica in Latin means fold. Ex-plicare means unfold, or open the folds. Explanation, that is to explain something, means to reproduce thoughtfully in the mind or in a speech the unfolding of a determined thing. The thing itself comes to be through an unfolding procedure. The great leafy tree is born from a small seed. Many animals are born from an egg. There, inside the egg, is everything; all that will result is preprogrammed there in its basic design. It is from inside the egg that everything will develop and un-fold. Like a Japanese origami, those folding and unfolding toys, everything is folded up inside, inside that initial egg. It is only then, upon opening, that the folds, folds, and more folds appear until the real figure is formed. That is the way, exactly in that way, that the neoplatonic philosophers think the universe. It is all inside the initial egg of the universe. Everything is inside. From there everything will unfold. Fold by fold, plica by plica. To give an explanation of things means to mentally reconstruct this process of unfolding. A great, complete explanation requires us to have do the unfolding process from the first beginning, from the initial egg. This is an explicatio ab ovo, an explanation from the initial egg. This is Philosophy.
There are things in the universe that have this structure, this no one doubts anymore today. Greek biology already knew the phenomenon of development from an egg, present day Biology only amplified and deepened this knowledge. Present day Biologists think of the world of living things as a great evolution process in which everything develops from a first extremely simple structured living being. In the beginning there is something like an egg, a first live cell. This cell has a center, a nucleus. This nucleus, which is alone in the beginning, unfolds into two in the evolution process. Then the same cell has two nuclei. Then comes the dividing wall, the initial cell unfolds into two, each nucleus staying in its own cell. From the original cell two cells then developed. Now we no longer have one, but two cells. These two cells also later develop through bipolar duplication of their nuclei and turn into four. And so on and so on, making the cellular tissue. Present day biologists have no doubt about this process of development starting from the first living being.
Rediscovered and reformulated in modern times by Lamarck and Darwin, the Theory of Evolution, now accepted and defended by all, is scientifically proven. It is just that the Biologists do not realize that this is all Neoplatonic Philosophy. The Neoplatonics said exactly this; except that they did not speak only of the evolution of living beings, they spoke of all the universe. The Neoplatonic Philosophers taught that everything began in an initial egg and that from there, by unfolding, everything originated. In the beginning there is a first being that is the One that is everything that exists. In the beginning the One is the Whole. Then comes the bipolar opposition: From within the One that is the Whole in the very beginning two poles appear, one opposing the other. Then, if one pole does not annul the other and if the poles do not mutually destroy each other, we have a new ontological structure: A Being, that is the One and the Whole, from which then come two opposing poles. From within the One comes the multiple, that is, two poles in opposition to each other. These poles acquire their own being, that comes from a dividing wall between them, then we have two beings, each of them is a One. Both together form the new Whole. If each enters again into the process of unfolding, we will then have four beings, and so on. The ontological process of unfolding thought of by the Neoplatonics is a paradigm from which the Biologists developed their theories. It is just that the Biologists normally do not know this, they do not realize where they got their theories from. They are Neoplatonic Philosophers and do not know it. The Neoplatonic Philosophers, the defenders of the Explanation of the World, go on from there. This theory is not only true for the evolution of living things, it is true for all the universe. Whoever wishes to understand and explain the universe has to intellectually reproduce the unfolding process, fold by fold, from the first egg. This is ex-plicatio. Only this is the real Explanation of the World.

2. Plato’s Unwritten Doctrine
Plato wrote Dialogues accessible, easy to read, for the public in general, illuminated by such beautiful and rich myths that even today they feed all those who want to learn Philosophy. But the dialogues are almost always inconclusive. Except for some dialogues written in his old age, Plato did not make clear and well-defined conclusions. The arguments in favor of one side are presented and discussed, then the arguments presented by the other side are discussed and evaluated. Okay, we know that this is the manner of dealing with thesis and antithesis. It is the game of opposites. Except that Plato almost never took his readers to the synthesis in which both poles are overcome and preserved. In the Dialogues, one does not find the conciliation of the opposite poles that characterizes the real dialectic synthesis.
Plato, a defender of the Negative Dialectics? Absolutely not. Plato thought the final synthesis, the Great Synthesis, would not be understood by beginners and those outside, far from the live, personal dialogue in which questions and answers face each other, with all the unpredictables; but also with all the richness that a live dialogue offers and allows. In writing, in the dialogues written for the beginners, Plato presented only the initial moment of Dialectics in which the opposite poles are articulated one against the other. For those initiated, those who have begun to understand, Plato offers in live dialogue, face to face, the treasure map. The Great Synthesis is the heart of Dialectics. Dialectics first of all means the method of the thesis, antithesis and synthesis, that is the game of opposites. Dialectics also means the conception that not only the world of things, but also the world of speech develops, fold by fold, from a first beginning.
Some Neoplatonic thinkers completely assimilated both constructive elements of Dialectics, the triadic method as well as the unfolding process of all things from the One. Plotinus, Proclus, Nicolaus Cusanus and Hegel need to be mentioned here. The triadic structure and the process of evolution passes like a backbone through the philosophical systems of the authors mentioned here. That is why Plotinus’s book is called Enéade. The name Enéade means nine, there are nine parts to the book. A Neoplatonic system is always made up of three parts that correspond to thesis, antithesis and synthesis. Since each of these parts is subdivided in three, we have a total of nine parts. That is where Plotinus’s Enéade, a book that has nine parts, comes from. This is the structure of the system in Proclus as well as in Hegel. In some other Neoplatonic thinkers the dialectic method with its triad sort of vanishes. It exits from the methodical thought and leaves only the process of development of everything starting from a unique beginning in the first plane. This is the case of Spinoza. Looking well, analyzing the authors carefully, we can see that they are, not excluding this variation, all definitely Neoplatonic. The philosophic roots of Lamarck, Erasmus and Charles Darwin, of Herbert Spencer and almost all the contemporary Biologists are Neoplatonic. Among the present day Biologists, the excellent work of Richard Dawkins, professor at Oxford, stands out. In Philosophy, Spinoza, Fichte, Schelling and Hegel were, in Modern times, those who best represented the Neoplatonic tradition. Among the poets, Goethe should be mentioned. Goethe, in an charmingly simple poem, suggests that we imagine God not as a being that is out of the world manipulating the orbit of things from outside, but as something that is within the process of the universe and from within moves all. This, and exactly this, is Dialectics, this is the Explanation of the World.
In the Dialogue The Sophist, Plato clearly shows that he is not a defender of Negative Dialectics, the Dialectics without Synthesis. He asks in this Dialogue which are the supreme classes. It is clear that they are opposite poles, a game of opposites. The two pairs of opposites that come about as the highest and most explanatory are rest - movement and the same - the other. Is the universe made up of these four elements? No, Plato says. The universe is firstly Being, synthesis of rest and movement, synthesis of the sameness and of the otherness. - Rest is not movement. Right. And movement is not rest. That is also right. But isn’t rest a being? If it were not a being, it would not exist; therefore, rest is a being. Isn’t movement a being? Of course it is. Then both rest as well as movement, although both are mutually excluding poles, thesis and antithesis, they come together as Being on a higher, nobler level. The same occurs with the sameness and alterity. Both mutually exclude each other, but both are Being. Being is the synthesis of the two pairs of opposites that rule the construction of the universe. The Being, synthetic, is the One that is the Whole and within which opposite poles unfold. Within the Being rest and movement, sameness and alterity are polarized. The Being is Synthesis, the Great Synthesis. And this Being is not only the Being that is the One and that is the Whole, Hen kai Pan, it is also the Good. The Unwritten Doctrine was compiled by his students in the form of a Dialogue On the Good, Peri tou Agathou. This dialogue, never written personally by Plato, was put forth in writing by his students. It is the merit of the School of Tübingen, in our century, continued today by the School of Milan, to have given emphasis to the Esoteric Doctrine and to have reconstructed the theory of the main work of Plato, the most important of all, in general lines. It is due to this that we understand what the Dialogues insinuate but do not clearly state, it is from where we derive the Neoplatonic tradition: the triadic process and the idea of universal evolution.

3. The two First Principles
Plato derives everything, all the process of the unfolding of the universe, from the two First Principles, the Principle of Unity and the Principle of Duality or Plurality. The first principle says the all is the One, that everything started with the unity. The Being is the One. The Being is that which it is, firstly it is the One. The Being is the One; in the beginning there was only the One and this is the Whole that is all. The One is the Universe. The One and the Whole, Hen kai Pan. And where does the multiplicity of things come from? Don’t we live in a world of multiple things?
Multiplicity begins with Duality. The Two is the beginning of the Multiplicity. The One has always had the seed of multiplicity within itself: aoristos dyas, the undetermined multiplicity. The One is not just the One, because it has always been within itself also the Other. It is bipolar. This fundamental alterity has existed forever within itself. There is a pole that is itself, the One, but there always is also the other pole that is the Other-Being. The Same and the Other, the first pair of opposites, has always been inside the Being. That is why there is a triad. Thesis is the initial One, antithesis is the Other-Being that has always opposed the first pole, synthesis is the Being that is not only the One but also the Other. The Whole-that-is-Being, Totality, synthesis, includes two opposite poles inside itself. The first principle, the Principle of Identity, supplies unity to the universe, and is the source of all order. The second principle, the Principle of Multiplicity, is the source of Multiplicity, it is the chaos from which the diversity of things emerges. Later on in this paper, I add a third principle to these two principles of Plato. To better clarify the sequence and the interdependence between these principles, I unfold Plato’s Principle of Unity into two principles, one which is the Principle of Identity and comes before the Principle of Multiplicity, the other that comes later and gives order to the multiplicity that appeared. I will call this third principle the Principle of Coherence.

4. The Mystery of the Trinity
The Platonic and Neoplatonic dialectic triad goes deeply into the Christian tradition and the intellectual structure of that which the first Christian thinkers called the most important and highest religious mystery, the Holy Trinity. In the beginning there was only one God. There is only one God, but this God is at the same time trine. He is One and Trine at the same time. God is God the Father, the Son and the Holy Ghost. In the beginning of the Trinitarian creation there is the One-God. This One-God begets the Other, the Son. Father and Son are in opposition like opposite poles. The Father is not the Son or vice-versa. But, when the Father and the Son meet again, one loving the other, both conciliate into a higher synthesis that is then called the Holy Spirit. This eternal process of engendering is called the Holy Trinity. God, who is only one God, unfolds within himself into three persons. The One-God is also the Trine God.
As we can see, this central nucleus of Christian doctrine is clearly Neoplatonic. But most Christian thinkers today, like present day Biologists, many times do not realize where their roots came from. Until the XII century Christianity was always a rich and productive branch of the Neoplatonic doctrine. Only with Albertus Magnus and Thomas Aquinas did the west go back to reading and studying the Aristotelian system and its static conception of the world. From the XII century on, Christian thinkers were divided into Aristotelian and Neoplatonic, with the advantage always more clearly to the first. Aristotelianism in its thomist version will be declared in the XIX century the official Philosophy of Catholicism, putting the Neoplatonic thinking almost into oblivion. When, in the XX century, a theologician and philosopher like Teillard de Chardin appears and proposes the Neoplatonic doctrine again in a new form, nobody in the intellectual catholic world knows how to evaluate it and say exactly what is happening. Almost no one understands anything of what he wants to say, no one can contextualize his intellectual proposal, no one can insert it into the line of the old tradition.

5. Where does Determined Multiplicity come from?
In its first steps the Explanation of the World is easy to understand. In the beginning there is the Onenes. From this comes the Other-Being, which is different from the One and opposes it as another. But both the One and the Other-Being are Being. Being is a higher unit in which the One-Being and the Other-Being are conciliated. Everything is quite clear up to this point.
This first One and this first Other-Being are alike. One is a mirror image of the other. And both are conciliated in the Wholeness that holds both one and the other. Up to now we are dealing with the engendering movement that the old ones called the Trinity. This is a movement that is internal to the first beginning. The first beginning is trine. Okay. This first differentiation between the two poles is an undetermined duality, aoristos dyas. The poles of this first unfolding are still poles that are exactly alike. One is a mirror image of the other, one is just the alterity of the other. This type of alterity is a yet undetermined duality. The opposite poles do not yet present themselves with different characteristics, each one with its own determinations and characteristics. But the things of our real world have their own determinations, each one is different from the others. Where then does this Determined Multiplicity come from? What is the root and the principle of the different determinations? Where does the variety come from?
Here there is a crossroads. Here the Neoplatonic doctrine separates into two currents. The first current says that all the Multiplicity that one sees today is completely preprogrammed within the first egg. All the Forms, from the beginning preprogrammed in their structure and their minutest details, are implicitly contained in the first beginning, in the initial egg. Then, like the whole bird is preprogrammed in the egg, so all the Forms of the universe are completely preprogrammed in the initial One. The Explanation of the World unfolds like it is really unfolding because all this factic evolution is implicit in the initial egg. To ex-plain is to unfold. One can only unfold what was previously folded. Implicare means make the folds and put them into the initial egg, like in a Japanese origami. All the Multiplicity that exists and is being unfolded by evolution has always implicitly been within the initial egg. One can only explain that which is implicatum. Everything, in all its minute details. From this strong nexus between explicatio and implicatio two consequences which are extremely important in the History of Philosophy derived, and, in my opinion, conducted this first offspring of Neoplatonism to errors: the necessitarianism of evolution in Ontology and the conceptual apriorism of the system design. The necessitarianism of the evolutive process is a logical consequence of the rigidity of the structure; one can only unfold that which in the beginning was folded into the initial egg. Here it is not important if it was a creating God that made the implication by folding the determinations inside, or if it were the Forms themselves that had always been folded inside there. In both cases the process of unfolding is subject to a rigid necessitarianism: Only what is already there pre-programmed can be unfolded. In an evolution process subject to such necessitarianism only what is predetermined happens. In such a philosophy there is no chaos, there is no contingency. Spinoza is the best example of a Neoplatonic system in this pattern. In Spinoza there is no contingency whatsoever. Everything happens necessarily as a logical consequence of the initial predetermination. Such a system, not permitting contingency, does not open space for alternatives that are equally possible. Consequently there is no freedom of choice, that is freewill. If there is no free choice, there is no responsibility. If there is no freedom nor responsibility, there is no Ethics nor Politics, much less Democracy. The second extremely negative consequence is that the thinkers that followed this rigid model of explicatio and implicatio intend to logically deduce all multiplicity of the things of the world starting from a first principle. Therefore, if all things ontologically derive from a first ontological principle, then Philosophy should logically reconstruct, a priori, all the propositions that make up the Explanation of the World in a rigorously deductive way. To deduct everything a priori then becomes an obsession - wrong of course - of these thinkers. Dieter Wandschneider and Vittorio Hoesle are some of the modern thinkers who defend such a conception of the world.
The first tendency, that of the Neoplatonic necessitarian philosophers, explains Multiplicity through a Predetermination, through the implicatio. The second tendency, that of the libertarian Neoplatonics, which I belong to, gives a different explanation and introduces the Principle of Chaos, the Principle of Difference, or, in modern language, the Emergence of the New. The first Principle, the Principle of Identity, says just A. It repeats the A, also saying A, A, A, A etc... It also says A=A. But with all of this we still didn’t leave A. We must deal with getting to something that is not A itself. What then? Is it not the case of saying Non-A? Of course, we can construct the Non-A by the anteposition of negation. But with this we still do not have determined multiplicity. How do we arrive, not at the undetermined alterity Non-A, but to a determined alterity like B, or C, or D etc.? This is the problem. This question can not be solved only by the Identity Principle, because this also just stays at A, in its iterations and its reflexive identity. It can also not be solved just by the anteposition of negation, because this does not supply an Other that is in itself determined. How then does Determined Multiplicity come into being? Where does it come from? It comes from itself, it creates itself, suddenly it is there and appears. This is the Emergence of the New, as the Biologists today say in the Theory of Systems. It emerges, it comes into being, without having been predetermined from the beginning. The determined alterity, the Other, unfolds in an explicatio, but it was not yet there folded within, it was not implicatum. The new fold is not just an unfolding of a previously folded fold that was put inside, but the making of a new fold. The One, in its evolution process makes folds that did not previously exist. The preprogramming made by the first principles only determined the general evolutive process, it did not determine the details. This is the Principle of Difference, this is the chaos that within itself creates the variations. This is why it is called Chaos. Because the variations that come into being and emerge are not predictable, they cannot be deduced. But does this not take us to total chaos? A logical anarchy? The destruction of science? No, it does not. Because as soon as the variations appear, without being preprogrammed, the third Principle, the Principle of Coherence appears. This makes order reestablish itself. If against pole A comes a pole B, then three things can happen. Either A eliminates B, or B eliminates A, or A and B show themselves as compatible and enter into coherence with each other. A and B in this case become constitutive parts of a Greater Totality. Then come C, D, F etc., always under the rule of the Principle of Coherence that puts order back into the evolution of the universe and the unfolding of things.
Plato had two principles, the Principle of Unity, to on, and the Principle of Undetermined Multiplicity, aoristos dyas. In this exposition, I unfolded Plato’s first principle in two, the Principle of Identity and the Principle of Coherence, in order to better explain how the Chaos that comes from the Principle of Multiplicity is not such a chaotic chaos, but a chaos that comes to be ordered by a principle of order, which is the Principle of Coherence. The most important thing in this exposition that I did is that the role is being conferred to Chaos in the Emergence of the New. The New, the Other-Being, the Determined Alterity are not preprogrammed. They are not able to be previously deduced. Initially we deal with a Chaos, initially we deal with a Principle of Difference that is a Principle of Chaos. But the variations that so appear are immediately regulated by the Principle of Coherence.
This second, libertarian branch of the Neoplatonic Doctrine offers an Explanation of the World that contains a chaotic moment. That is why it permits contingency, freedom, and historicity. There is space for multiple variations, there is space for the contingency of things and for various alternatives, there is space for liberty and responsibility. The system of Philosophy in this proposed model is a system open to History that permits us to track down the genesis of the things, like walking backward, saying how and when the variations occurred. But it does not presuppose that all these variations are preprogrammed and that for this reason they are necessary moments in the unfolding of Nature. Nature in this project contains chaos, it contains chance, it contains variations that could have been different. Chance, even though it is not the most important element, it is an indispensable element in the evolutive genesis of the universe. Nature has a History that was like that but could have been different. That is why it is called Natural History. History, when it refers to man, becomes the History of Free Men.

6. The Achilles Heel
One Goddess offered the warrior Achilles a balsam that would give him protection and make him invulnerable to the enemy weapons. The skin, bathed with the miraculous balsam, would become unpenetrable. Achilles, however, when he bathed himself with the balsam, had a leaf stuck to the heel of his left foot. In that place where the leaf was stuck, the balsam could not do its work. This is the Achilles heel, in this area Achilles was vulnerable. Wounded exactly in this place, his heel, Achilles was killed.
The Philosophy systems also have their Achilles heel. The Neoplatonic systems, the Philosophy of the Explicatio Mundi, has as its Achilles heel the question of necessaritainism and the intention of wanting to deduce everything a priori. Even the first Christian thinkers, the Greek and Latin Fathers, raised the ojection against the Neoplatonic Philosophers that such a system ended up eliminating the contingency of the world, and then also the freedom of choice and moral responsibility. Saint Augustin, who was Neoplatonic, spent all his life trying to conciliate the predetermination with freedom of choice. He was not able to do it. Johannes Scotus Eriugena, in the early Middle Ages, tried again. Nicolaus Cusanus during the Renascence tried once again. Spinoza, a thinker who loved Ethics and Political Philosophy so much, gave in to the rigorous necessitarianism and became an explicit necessitarian. According to Spinoza, contingency simply does not exist. Schelling and Hegel, imbued with the importance of freedom, tried again. Hegel tried to put contingency back in, inside Logics. He declares - the only one in the History of Philosophy - that the Absolute Necessity is the Absolute Contingency. But he is not able to take the idea to a good conclusion and got lost, in my way of thinking, in ambiguities. In Hegel we never know if Necessity is really necessary or if it is contingent. Deep, deep down, I think, Hegel presented a strong tendency for a Neoplatonic necessitarianism. Among the contemporanians, Vittorio Hosle, although he tries to resist, falls back on the necessitarianism.
And why not? No, why? Necessitarianism, on denying the existence of contingency in the course of the evolution of the world, eliminates the contingency of things. The things are like that and not different because they have to be like that. The world is a process totally determined by completely rigid laws. If, at the moment , we do not yet know all the laws, then there is a deficit in our subjective knowledge. The inexactness measured by the Physicists, the chance spoken of by the Biologists, all this is just a deficit in our knowledge. As soon as we discover the physical laws, we will be able to calculate the course of the universe. Calculate backwards, saying exactly what happened. And calculate forwards, saying what will happen in the future. It is obvious that such a system will allow for neither the existence of alternatives in the things, nor freedom of choice in man, nor democracy in the State. Because, if everything is predetermined from the beginning, we can only give ourselves in to destiny and its inexorable force. - But would it not be the case of abandoning all these things, that would be just illusions, and giving ourselves up to the force of Destiny?
The argument in favor of a non-necessitarian conception of the world, in a final analysis, consists of the principle that the simpler theory is the correct one. The Neoplatonic theory, which we called libertarianism above, introduces the Principle of Difference, Chaos, from the very beginning. It is consequent and explains everything without the necessity of additional theories. It allows for and explains the contingency of things in Philosophy. It allows us to understand the usage of the calculations of probabilities as the only adequate way for certain sectors of nature, the relation of uncertainity of Heisenberg, in Physics, the importance of chance in the genesis of mutations in Biology, the freedom of choice and responsibility in Political Philosophy and in Law. - On the other hand, the necessitarian conception does not allow us to explain any of this, except through extremely complicated hypotheses to be added to the main theory.
To this the question of the burden of proof is added. Who is it that has the burden of demonstration? The one that accepts contingency in certain things? Or the one that accepts the total necessity of everything? The burden of the proof, in my point of view, falls back on he who presupposes, without being able to prove it, that all things, in all aspects, are necessary. To raise such a proposition as the universal principle is more than foolhardy. It is enough to bring only one example of contingency to demonstrate the falseness of such a principle. And here the necessity of always having new additional hypotheses appears: We are not dealing with something really contingent, necessity is hidden there inside, etc. - And that is why I stay with the theory which is simpler, that is more suitable to reality, that does not need successive additional hypotheses. I stay with the Neoplatonic branch that I called libertarian above. Explanation of the World, yes, but also counting on the element of chance.

7. The Crossroads
In the beginning of Classical Philosophy there is a great crossroads. With Plato and Aristotle Philosophy divides into two great branches, the Explanation of the World and the Analysis of the World, Neoplatonism and Aristotelianism. From Plato come Plotinus, Proclus, Saint Augustine, Johannes Scotus Eriugena, the medieval thinkers until the XII century, Nicolaus Cusanus, Giordano Bruno, Ficino, Spinoza, Fichte, Schelling, Hegel, Karl Marx. From Aristotle come Theophrastus, Albertus Magnus, Thomas Aquinas, William of Occham, Descartes, Kant, Frege, Bertrand Russel, Wittgenstein, Apel, Habermas, and all the Analytic Philosophy of today.
The second crossroads is inside the Neoplatonc thinking. Is the system of the Explanation of the World totally necessary or does it contain contingency? Plotinus and Proclus are strongly inclined to necessitarianism, Spinoza is definitely a necessarianist. Hegel wants to contemplate contingency, Hegel wants to find a way to save contingency and put it back into the system, but in my point of view, he cannot and he gets lost, in what concerns this problem, in ambiguities. Karl Marx is strongly inclined to necessitarianism; and that is why, in my point of view, Stalinism is not just an accident along the way, but a logical consequence of the system. Among the contemporaries, Wandschneider and Hösle lean towards necessitarianism. Hans Jonas on the contrary defends an Explanation of the World with contingency and freedom like that which I am proposing. This Explanation of the World with chance and contingency surprisingly coincides exactly with the General Theory of Evolution that is being proposed by the Biologists like Stephen Jay Gould and Richard Dawkins.

8. The Great Question
The Great Question, the most important question in Modern Philosophy was put forward when the late Schelling in his Munich Lecture on Contemporary Philosophy, criticized the system of his friend Hegel because it was lacking contingency. Hegel’s error had origin and History, it was the same error of Spinoza, Proclus and Plotinus: Contingency was missing in the system. From that time on the job has been exactly this: How to put contingency back inside the system of the Explanation of the World? This is one of the two main questions of this book. We remember that this was also the task the young Hegel was trying to accomplish: How to conciliate the free Subject of Kant with the necessary Substance of Spinoza? This question refers to, as one can see, the crossroads that devides the two branches in the Neoplatonic School.
The second question refers to the crossroads between Platonism and Aristotelism. It is connected to the first question, but is not identical to it. How do we conciliate the game of opposites with the Principle of Non-Contradiction? How do we use contradiction as an instrument of construction and not of destruction? Is this possible? How can we play with thesis and antithesis without doing anything foolish?

II. W H A T I S D I A L E C T I C S ?

1. The Logical Square

1. The Great Confusion
Dialecticians and Analytics speak to each other but do not understand one another. They do not grasp the meaning of the words the other say. Aristotle said, criticizing Plato, that Dialectics was not a method of Philosophy, but only an intellectual exercise to sharpen the mind. A type of intellectual aerobics, we could say today. In the Middle Ages, Albertus Magnus and Thomas Aquinas adopted equally negative positions about Dialectics. thinkers. Plotinus, Proclus, Cusanus, Spinoza, Schelling and Hegel thought exactly like that. The only big question that remained open is about the existence or not of contingency in the pith of the process. Is there contingency? Is there chance? Does God throw the dice? Spinoza says no. Hegel is in doubt. I think there is contingency, that God does throw the dice, and I think that this is the space of equally possible alternatives which allows for liberty, moral responsibility and political democracy. Dialectics, yes, but Dialectics with contingency. Contingency and Historicity are, after Schelling, Kierkegaard, Nietzsche, Heidegger, and Gadamer, indispensable elements for any thought that one wants to be critical. He who does not take this into account falls in the hole of necessitarianism. And the Thracian Slave starts laughing.

3. THE THREE PRINCIPLES

3.1. The Necessary Translation
The traditional exposition of the triadic movement of thesis, antithesis and synthesis, as is done by Plato, Cusanus and Hegel, and as was reproduced by me in the previous chapter, is something as uncomprehensible as Greek for the Analytic Philosophers. It is pure Greek. One can not understand anything, they say. It is even worse, they add. Everything indicates that the Principle of Non-Contradiction, the first and fundamental stone in the construction of rational discourse, is disrespected there. How can thesis and antithesis be false at the same time? How can it be that Dictum as well as Contradictum are both false? Isn’t this acting against the Principle of Non-Contradiction? Isn’t this saying, and at the same time unsaying? Isn’t this foolishness? These are the classic as well as Analytic Logic.

3.4. Reflex Identity (in Logics) and Species (in Nature)
Reflex identity says that the second A (as well as the third, the fourth etc.) is the same as the first A, A=A. Here appears a phenomenon which has made us think hard since ancient times. In order to say the identity of A, it is necessary to say it or write it twice; first on the left, then on the right of the equal sign. Only then - through the explicit position of this first difference - can we clearly say the identity of A. The difference, the alterity, or simply the other, is what sticks out and begins to emerge here. We are still dealing with the same thing, that which is identical to itself, but the emerging difference begins to be seen. One perceives that there is a process in course here in which the identical comes out of itself to, later on, return to itself. This circular movement is the characteristic element of the basic structure of many important things that appear later on in evolution, like life, that is its autopoietic structure, or thought and free action, or spirit. But we have not arrived there yet, the difference is just a rough draft.
This reflex identity in Logics corresponds in living beings to the species. The species is that identity in which two or more individual living beings become the same without losing their identity with themselves. In the species it is not the singularity which is expressed ( the this to which we point with our finger), but the specific particularity, the species, or rather, that which is common to many individuals. The plan of construction of a certain species, engraved in the genes of all the individuals which compose it, makes up the typical structure of the species during ontogenesis. In that way, from a chick