Greek Philosophy: Plato's Timaeus & Parmenides

THE TIMAEUS

Last time, as we examined Plato’s Republic, I mentioned that Plato’s later dialogues increasingly became monologues in which Socrates and other characters put forward Plato’s own philosophical views.  The Timaeus, which was considered by many early Platonists and Medieval Neoplatonists to be Plato’s most important work, puts forward Plato’s cosmology.  Indeed, for many years in Medieval Europe, the Timaeus was the only dialogue of Plato’s available for study in Latin, as well as one of the only texts on cosmology, physics and the workings of nature available to scholars until the Renaissance.

In the Republic, Plato used Socrates to put forward his theories on the proper form of the individual and society.  In the Timaeus, which is supposed to take place the day after the Republic, Plato uses Timaeus and others to put forward his theories on the form of the cosmos, which corresponds to the proper form of both healthy individual and just society.

Socrates gathers again with fellow aristocrats and says that he would like to hear about how an ideal state such as the republic discussed the previous day would interact with other societies.  While the police, the guardians of the city, protect everyone from enemies, this does not explain how the leaders of the city, the philosophers, would choose to engage in foreign relations.  

Critias tells Socrates of Solon’s journey to Egypt and what he learned from the priests there.  Solon, the famed Athenian lawmaker, was given dictatorial power over Athens because he was wise and capable of good rule at a time when tyrants were seizing power over other Greek city-states.  This would mean that the aristocrats came together and elected Solon to dictatorial power so that one of them could not seize power over all the others.  While some ancient sources of later periods say that Solon allowed common people into the assembly for the first time in history, modern scholars are skeptical of this today.  Solon’s reforms broadened the availability of positions of authority, but only to those wealthy enough to afford to arm themselves either as cavalry or infantry in times of war, a distinction common people such as farmers and craftspeople would have found quite unaffordable.

After Solon had instituted his government reforms, he immediately left Athens for a period of ten years such that he could not be convinced to change anything.  It was during this time that he may have gone to Egypt and met with the Pharaoh and discussed philosophy with Egyptian priests, which some sources say was his first stop after leaving Athens.  

Critias tells Socrates that, when Solon went to Egypt, he found at the apex of the Nile Delta, where the Nile divides in two, there is a place called Sais, and the priests there say that they have a special bond with the people of Athens and share the same patron goddess (Neith for the Egyptians, Athena for the Athenians).  After talking with the priests, Solon realized that the Athenians did not have much understanding of history.  One old priest tells Solon that, due to civilizations being eliminated by great floods and firestorms, the Greeks are children, and Greek historians are merely reciting nursery rhymes.  

The priest says that the Athenians do not remember, because they have just become educated and civilized, but the Egyptians know from their history records that nine thousand years ago the Athenians stopped the people of the island of Atlantis, who were threatening to take over the world, all of Europe, Asia and Africa (as represented on Anaximander’s map).  Atlantis was thought to be an island in the Atlantic Ocean, outside the mouth of the Mediterranean.  Plato’s Timaeus is indeed the first time that Atlantis is mentioned in history.  The story, which is now believed to have been an invention by Plato, is very similar to the Battle of Marathon, where the Athenians and Spartans repelled the Persians.  We now know that Egypt was not as many thousands of years old as Plato believed, but this does show Plato believed that they were civilized long before Athens.  Ironically, the old priest says that the ancient Athenians saved all of Egypt and Greece from slavery.

Note that Plato, through the old Egyptian priest, says that the long ancient Greeks were the greatest warriors, but the Egyptians were the great scholars who kept the records of history.  The priest also tells Solon that, in long ancient Egypt and Greece, the common goddess they share taught to separate the scholars from the warriors, and the warriors from the common people.  Plato is telling us that the order of the Republic, which is eternal and ideal, was taught by a goddess to Egypt and Greece equally, though the Greeks were too great in being warriors to have the scholars to have recorded this.

Critias tells Socrates that, as he listen to Socrates describe his ideal republic, he was continuously reminded of the story of Solon in Egypt, and found the similarities remarkable.  Notice that Plato, who believes that the ideal form is known by all of us but forgotten, only to be recollected through wisdom, is telling us through so many characters that through questioning Socrates is able to reconstruct, also recollect, the ideal form of the human being and society, which is thousands of years old and taught by a goddess to humanity.  Thus, Socrates’ wish is fulfilled.  He wanted to hear about how his ideal would work in actual practice, and now finds out that it did indeed work as a foreign policy as the ancient Athenians were able to counter the Atlanteans and rescue the Egyptians and fellow Greeks.  Socrates tells Critias that he is delighted to learn that his form of the just society was not merely an idea, but history, and that it is quite appropriate that they are speaking of it on the feast day of the goddess Athena.

Critias says that, before he tells the whole history of Atlantis, which he proceeds to do in Plato’s dialogue The Critias, Socrates should hear Timaeus give a history of the cosmos from the beginning up until the birth of humankind.  This is somewhat like the ridiculous joke in the movie Airplane, when Johny of the airport control room is asked to explain what went wrong, and start from the beginning, and he replies, “Well first the Earth cooled...”.  Critias is suggesting to Socrates that they start with the birth of the cosmos, which has an ideal form that turns out to be very much that of Plato’s Republic, and then they trace the beginning of mankind to Atlantis, and then trace ancient times up to their own day, drawing a straight line from the beginning of the universe to themselves and Socrates’ “discovery” of the cosmic form through wisdom.

Timaeus, a name which means ‘honor’ in ancient Greek,  was a Pythagorean who lived and taught in the time of Socrates.  Like Pythagoras, and Parmenides, Timaeus begins by distinguishing the temporary world of opinions, the sensory world we can perceive, from the eternal world of knowledge, the ideal form we can remember/understand through reason and wisdom.  Now Socrates becomes the simple-minded ‘yes man’ interlocutor, and agrees each time Timaeus pauses in his monologue to ask if what he has said seems correct.

While the sensory world is made of many things, the eternal and ideal form is a supreme One.  This One, often capitalized by modern scholars to distinguish it as supreme, is the point out of which the Pythagorean cosmos unfolded.  The world below is constantly changing, is becoming, much as Heraclitus said.  The form above is unchanging, is being, much as Pythagoras, Parmenides and now Plato have said. Parmenides argued that the world below is an illusion, and Plato gave the metaphor of the shadows inside the cave which are false images of the real things themselves which are outside the cave.  Timaeus says that becoming is to being as opinion is to knowledge.  Timaeus also says:

“We must, then, in my judgment, first make this distinction: what is that which is always real and has no becoming, and what is that which is always becoming and is never real?  That which is apprehensible by thought with a rational account is the thing that is always unchangeably real, whereas that which is the object of belief together with unreasoning sensation is the thing that becomes and passes away, but never has real being.”

Note that opinions can be true and then not true, but knowledge is concerned with the eternal and universal, that which is always true and does not change in time or by location.  This quotation shows us a very dogmatic position, that there is only one truth that is rational, and it is eternal and universal.  Any perspective or relativity must not be genuine knowledge or what is comprehensible by true reason.  A more skeptical thinker such as Xenophanes and Heraclitus would say that this rules out all human understandings as irrational, and Zeno might agree.

Timaeus says that there is a hidden father and architect of the universe, who looked at the eternal model when making the temporary and changing world below.  While at first many would say that this father, also called ‘The Divine Craftsman’ and ‘The Architect’ is a monotheistic god, it is actually an underling, the Demiurge (Demiurgos, in the Greek).  The One sprouts and unfolds into the eternal order and ideal models of things, which we will see is trinitarian like Plato’s republic and constitution of the individual, and the Demiurge, the sky father being that corresponds to the fire at the mouth of Plato’s cave from the Republic, not the Sun itself, then produces copies of the models in the ever changing world of earth below.

The Demiurge is also identified with Logos, the word first mentioned by Heraclitus, and the One is identified with Nous, first mentioned by Anaxagoras.  This is parallel with the Republic, as the philosophers are the mind of the city, who come up with the ideal model, while the police are the spirit and courage, the breath of the city, who carry out the orders and impress the model on the population.  

Plato’s Nous is much like Anaxagoras’ Nous, but as previously mentioned it’s interaction with the world is layered.  Nous does not move, but the Demiurge does, looking at the model that unfolds from Nous.  Socrates in Plato’s dialogue The Phaedo says that at first he was fascinated by Anaxagoras’ Nous, but then found Anaxagoras did nothing with it, and Aristotle shared Plato’s criticism in labeling Anaxagoras’ Nous a ‘deus ex machina’.  

Plato’s Nous does unfold out of itself to become the eternal model, but other than that it does nothing.  The Demiurge, the secondary god, does everything.  The Shadow puppets are like common people, the farmers and workers.  They supply temporary things, the shadows on the cave wall being like fleeting temporary opinions and mortal objects of desire, just as desires supply us with temporary opinions and things.  For example, I say “I want a sandwich”, and then later after eating the mortal sandwich the desire is no more and the statement no longer true.  

The One is the Sun outside of Plato’s cave, the philosopher of Plato’s city, and the mind/nous of Plato’s individual, the highest element that is the ideal and the source of everything below it.  The Demiurge is the fire at the mouth of Plato’s cave, the police/guardians of Plato’s city, and the spirit and courage of Plato’s individual.  The temporary things of our sensible world are the shadow puppets in Plato’s cave, the farmers and craftspeople of Plato’s city, the desires of Plato’s individual.  Lastly, the opinions we have, projections of our desires, are the shadows on Plato’s cave wall, temporary beings that are never real.

Early Neoplatonist Christians sometimes identified Plato’s Demiurge with the Holy Spirit of the trinity, the link between God and Jesus, while Medieval Christian Neoplatonists sometimes identified the Demiurge with Jesus, who is the link between God and the Holy Spirit below that dwells on Earth.  Neoplatonic Gnostics of the ancient world, who shared much of their thought with the early Christians, saw the Demiurge as a deceiving demon, a fallen god that has trapped human beings in a false world.  Descartes, the French philosopher central in the beginning of modern European philosophy, disproved a deceiving demon as his Queen was attempting to rid France of Gnostic heretics whose understandings contradicted Catholic orthodoxy.  

Recently, “the Architect” found its way into the Matrix series as a computer program that creates the world but is not its own creator.  The Matrix movies follow the Gnostic conception, not the traditional Platonic and Catholic Neoplatonic conception (note the use of ‘Neo’ as central character of the movies as well).  The Slovenian philosopher Zizek, who is critical like Nietzsche of Plato’s simple division between the real and the illusion, puts himself into the original Matrix movie in the beginning of his critical documentary about cinema.  Facing Morpheus, he questions whether there is a genuine choice in taking the red pill or the blue pill, in choosing to wake up from the dream or fall back asleep.  Like Heraclitus, who says that there is no limit to waking up, Zizek says he wants a third pill, not a pill that shows the reality behind the illusion, but a pill that shows us reality AS illusion, that shows us how we share our projections and socially co-create reality together as ideology.

The whole cosmos, for Timaeus (a mask of Plato’s) is a living creature, with the heavens as soul and the Earth as body.  Timaeus says that human beings are a plant with their roots in the heavens.  The head, the part of us that contains the ideas, is rooted in the One and its ideal model it has conceived, and the rest of us branches downward.  The demiurge fashions reason in soul, and soul in body in individuals.  The demiurge then moves everything in a circle, bringing about the life and death in cycles of earth beings underneath the cycles of the heavens.

This is all done by the forces of sameness and difference, similar to the love and strife of Empedocles.  Sameness has the higher and encompassing role, difference being proportional downward.  Note that the supreme One is the ultimate sameness, eternal and universal and the source of all that is eternal and universal, which then becomes the source of all that is temporary and locational.  For Plato and later Neoplatonists for thousands of years, things are ordered with trinities within trinities, each thing being one of a group of three, and itself composed of three parts.

While there are four elements, Timaeus describes how this is formed from fire and earth, with a third element air formed between the two.  Note that these three correspond to the Nous, Logos and sensory world of the cosmos, the philosophers, police and common people of the city, and the mind, spirit and stomach of the individual.  Fire, as it was for Heraclitus and Empedocles, is the highest element and most primary.  

Timaeus says that a fourth element, water, had to be added to the first three because the world is a solid, not a surface.  This is confusing at first, but not when we remember that the Pythagoreans honored the tetractys, a pyramid of dots, and said that a point leads to a line which leads to a plane which leads to a solid.  A point is singular and most simple, with no dimension.  A line is one dimensional between two points.  The simplest two dimensional plane is a triangle, between three points.  The simplest three dimensional solid is a pyramid, between four points.  Note that a triangle with a point on top is absolutely the same at the apex, and spreads into difference at the base.  Similarly, a pyramid is a point, absolute similarity at the apex, and is a plane of difference at its base, not to mention a solid through its span.

Plato adopted atomism from philosophers such as Democritus, but gave the atoms Pythagorean shapes, and relates these shapes to us through the mouth of the Pythagorean Timaeus.  The highest element, fire, has particles that are shaped like four-sided pyramids, also called tetrahedrons.  The pyramid was understood in Egypt to be a representation of light spreading downward onto the earth, as sunlight does in breaks between clouds, as mentioned with Pythagoras, and both Pythagoras and Plato thought very highly of Egyptian cosmology.  Fire is the simplest element, with the least sides the least differentiated, and is the most like a point unfolding into the simplest planes as sides and solid as overall shape.  

Earth particles are six sided cubes, much as one might see looking at sand closely.  Earth is the only element with square sides, each of the other three elements having equilateral triangles as sides.  In Indian thought, earth was also represented as a square, and Buddhist temples throughout Asia display a square base at the lowest level representing earth, topped by domes that represent air, then cones to represent fire, displaying the cosmic order of the elements.  In the Indian and Asian tradition, fire is triangular, but a cone, not a pyramid, possibly because fire is also pointy in Asia but much farther from the Egyptian Pyramids.  

Air particles, a mixture of the forms of fire and earth particles, are octahedrons, two four-sided, square-based pyramids stuck together at the base, giving it triangular points with a square-sided middle.  It is as if air is fire glued together or congealed in the middle as earthy, much like Thales thought that earth is congealed out of water.

Finally, water particles are twenty-sided icosahedrons, twenty triangles together.  Strangely, while the sides of fire, earth, and air particles follow a series of four, six, and eight in their sides, water particles are not ten-sided but twenty-sided.  Timaeus gives no reason why this is the case, even though he is concerned with progressing step by step from the simplest to most complex shapes to understand the elements, assuming that the cosmos unfolds in levels of simplicity to complexity.  Compared with fire, water is the largest and thus heaviest particle, the least mobile, and fire is the smallest and lightest particle, the most mobile.

As for the human individual, Timaeus says that the Demiurge fashioned the immortal human mind, and then added two mortal parts of the soul, housing the three in the human body.  The immortal part of the soul was placed in the head.  The mortal parts of the soul, spirit and appetite, were housed in the lower body, and the two parts are separated by the neck.  The spirit is housed in the heart, which is involved with the lungs, and the appetite is housed in the stomach, which is involved with the liver and spleen.

After first creating the human form, the Demiurge moved on to fashioning plants and animals, which it did out of the human form.  Timaeus explains that plants do have soul, and thus are alive, but they only have appetite, and are thus merely mortal.  The animal kingdom came about through reincarnation of human individuals.  After creating the human form and then a number of males, those who were too cowardly to do good were reborn for a second time as women.  In response, men developed seed out of the marrow of their spines, the basic stuff of life, which explains why the penis behaves as if it has a mind of its own (Timaeus says this...I’m not making it up as a joke).  In women, the womb opened and developed an appetite for producing children, which if unfulfilled can cause the womb to wander about the body causing problems.

Birds developed as reincarnations of humans who were foolish enough to trust the eye more than the mind.  Land animals developed as reincarnations of people who did not have wisdom (Timaeus says, “who had no use for philosophy and paid no heed to the heavens”) who followed their spirit rather than mind, and so their heads were drawn downward to the earth and their skulls shrank.  Lastly, those who had neither wisdom nor spirit were reincarnated as fish, who have no use for air as they have no spirit.  Since this time, souls are raised or lowered through reincarnation depending on whether they are wise or foolish.  This creates an interesting question: If a clam has no wisdom or spirit, how can it act nobly and raise itself from its station?

If much of this sounds foolish, this is the cosmology of Christianity and Europe well through the middle ages, up to Newton and Leibniz, who read Islamic scholar’s commentaries on the Timaeus as well as inherited the scientific developments of the Islamic world and Asia that slowly increased our understandings.  The Medieval Christians had to retranslate Plato, with central interest in the cosmology of the Timaeus, into Latin from Arabic.  Muslims were translating Greek texts for hundreds of years before the Europeans were capable of doing so.

Today, there is a pentagonal crater on the moon named after Timaeus.  In the Japanese animated show Yugioh, there is a knight from Atlantis named Timaeus (which I found out through Google Image).  Of course, Timaeus is not from Atlantis.  It is Critias who speaks of Atlantis, and Timaeus speaks of the order of the cosmos, while Atlantis is first mentioned in Plato’s Timaeus.


THE PARMENIDES

It was mentioned with Plato’s later dialogues that Plato revered Parmenides as well as Pythagoras, but in giving a form of the good, he is much more Pythagorean than Parmenidean.  It is complicated, however, as Parmenides did say that Pythagoras was right about the form of the world, but that this form was an illusion.

Plato’s dialogue The Parmenides, in which a young Socrates encounters Parmenides and Zeno and debates with them about whether or not there are ideal forms or a distinct form of the good, is known to be one of Plato’s most challenging dialogues.  While Plato has Socrates argue that there is indeed a form of the good in other late dialogues, in the Parmenides Socrates is not able to counter Parmenides, and in the end is undecided as to whether or not the good has a distinct form.  Recall that Parmenides argued that the One, the only real and true thing, has no differentiation in it at all, all difference being an illusion.  Some scholars believe that the dialogue is incomplete, and that Socrates would have proceeded to prove to Parmenides that there was indeed a form of the good.

In the Timaeus, Plato argues through his character Timaeus that rationality arrives at the singularly real, which is eternal and unchanging.  The One, identified with nous/mind, unfolds into a model which the Demiurge, identified with logos/spirit, uses to actively create all the temporary things of the sensory and unreal world.  Ancient and modern scholars have debated for centuries whether Plato believed that the plan was more properly of the One or of the Demiurge.  If the One formed the plan in mind, and then spawned the Demiurge, then there is indeed differentiation in eternal static being, and Plato is more Pythagorean than Parmenidean.  If, on the other hand, it is the Demiurge and its logos/speech that is the locus of the differentiated form, then there is no difference in eternal static being, the Demiurge is itself part of the temporary and the unreal, and Plato is more Parmenidean than Pythagorean.  

Perhaps Plato saw it much as Parmenides, that Pythagoras was right, but only about the formation of the real and unreal as a pair, and so all particularity, including that of the forms and the Demiurge, are unreal and illusion.  If we view things from below, then Heraclitus is right about the lowest, the temporary and chaotic, and Pythagoras is right about the highest, the eternal and formative.  However, if we view things from the very top, then only Parmenides is right about the eternal beyond the motions of the formative.  Just as previous Greek philosophers subsumed the positions of those before them, showing how their positions were somewhat right but somewhat wrong, Plato may very well be stacking Parmenides atop Pythagoras, and Pythagoras atop Heraclitus.  Heraclitus rightly understands the shadows of the cave, Pythagoras rightly understands the fire at the mouth of the cave, but only Parmenides rightly understands the Sun.  

This, however, creates a new problem: How is it that there are forms above and beneath the fire, both the true forms of things and the shadow puppets?  Is it that, like Parmenides argued, that Pythagoras is right about the forms of things, but even the difference between the true things and their false copies is itself part of the shadows, part of the illusion?  What if the Demiurge, like Pythagoras, is unable to see the unity of the model and the things, of the eternal and the temporary.  Perhaps we can view reality as an illusion, like Heraclitus, as distinctly real and illusion, like Pythagoras, and as real and illusion without distinction, as this distinction would itself be unreal, like Parmenides argues?  All three of these thinkers believe the One to be eternal, and all three believe the sensory world to be illusion.

Is Parmenides the most foolish, who denies the truth and reality of everything we see, or is Parmenides the most wise, who encompasses the truth and illusion of illusion itself into the singular and eternally true?  Perhaps Zeno understood Parmenides best, and knew that Parmenides never hoped to free us from illusion with words and distinctions, but wanted to show us the underlying unity of illusion and truth, to show us the impossibility of distinguishing anything without contradiction and illusion.

Plato’s Parmenides begins with Socrates challenging Zeno.  Zeno argues that sameness can not be different, and difference can not be similar.  Socrates says that we can get over this contradiction by distinguishing the eternal forms from temporary things, the temporary things participating in the forms relatively.  Just as things are themselves one and many, being singular things with many parts, so too are the forms one and many, particular forms that themselves are unified in the One itself.

Socrates says that he would be impressed if someone were to show that the forms themselves are contradictory and have contrary qualities.  Parmenides then proceeds to dominate the rest of the dialogue, and as with the Pythagorean Timaeus now Socrates becomes a ‘yes-man’ interlocutor who is instructed by one wiser than he.  Parmenides asks Socrates what forms he is endorsing, and Socrates replies that (like a Pythagorean) he believes that there are mathematical forms and ethical forms of virtue, but he is not sure whether or not all things, particularly mud and hair, have ideal forms.

Parmenides tells the young Socrates that, after he is older and wiser, he will have come to see the truth of the things that he asserts.  Parmenides then brings several arguments against the position that there are distinct forms of things that are simply real and eternal, arguments much like those we examined previously with the Eleatics.

First, Parmenides asks Socrates how many things can participate in a form at once.  If a form is present in many distinct things, then the form must be many, and not one.  Let us use the example of the form of horses to illustrate these arguments.  If there is a form of horses, which all horses on earth participate in equally, how can this similar equality be the same if each horse exists in a different location?  Parmenides uses the metaphor of a sail covering many people, arguing that the sail does not touch each person at the same point, but each person in a different place.  If no two horses exist in the same location, how can the form of horses not participate in each horse differently?

Socrates replies that it does seem that many things equally participate in a form.  Horses do all seem to share the same identical form, even if they are in different places.  Parmenides then asks Socrates if a form itself has a form, if it has its own form, participating in itself.  To use our illustrative example, is the form of horses itself shaped like a horse?  Recall that Parmenides and Zeno were known to argue for the contradictory nature of place, and that if a place has a place, then its place must have a place, which has a place, leading to an infinite regress.  Similarly, if the form of a horse has the form of a horse, then its having the form of a horse itself participates in the form of a horse, leading to an infinite regress that never resolves itself in a static and complete form of horses (which now includes the form of the form of horses).

Here there is an interesting parallel with Russell’s Theory of Types, which he hoped would resolve a contradiction he found in Frege’s Set Theory but instead resulted in an additional contradiction.  Frege believed that he could give mathematics a pure foundation dealing only in sets of ideal abstract objects, quantities without qualities.  Russell showed that “the set of all things that are not members of themselves” created a paradox.  If it was not a member of itself, then it was, and if it was, then it wasn’t.  Russell proposed that sets of sets should not be called ‘sets’, but ‘types’, and so the contradiction would be resolved, as the set of sets that are not members of themselves would be a type, not a set.  However, as critics of Russell’s pointed out, this creates a further contradiction, as a set of sets is not a set, both a set and not a set.  Similarly, Parmenides is arguing that a form has its own form, and if we say that a form does not have its own form, how can it have its form so that it gives this form to other things?  

Aristotle believed, like Parmenides, that Plato’s forms would have to have forms of forms, ad infinitum, resulting in an infinite regress.  This became known as his “Third Man Argument”.  Why a third man?  Recall that Plato, like Aristotle and many other Greek philosophers, believed in a teleological universe, and that the heavens were alive with purpose.  Just as Timaeus argues that the universe is a living organism, in which there are many living organisms, Plato’s form of a man is itself an ideal man, a living being.  If this ideal man himself has the form of a man, this creates a “third man”, and so on, ad infinitum.

Parmenides follows a similar course as he continues to question Socrates, asking Socrates if thoughts themselves think, if the ideas themselves have higher ideas.  Considering the form of Plato’s cave and cosmos, the One is the great mind/nous that conceives of the Demiurge and ideas/forms, which then themselves conceive of the temporary sensory things below.  Conversely, we then from below participate in the ideas and in the One.  Parmenides argues that, just as a place must have a place, which leads to an infinite regress, and a form must have a form, which leads to an infinite regress, an idea must have a higher idea, which leads not to a static One, a highest conceiver/idea, but to an infinite regress.  

Parmenides openly asks Socrates that if we are conceived by ideas, which are conceived by God or the One, then who conceives of God?  We know that Parmenides does assert the existence, indeed the exclusive existence, of the One which is a singular monotheistic being, but he is showing Socrates that if there is any difference between ourselves and the ideas and the One, then this results in contradictions and infinite regress.  Thus, there can be no distinct ideal forms.  Later Neoplatonists argued that we conceive of the One, and the One conceives of us, in a reciprocal relationship, closing the loop such that it is both infinite, without end, and finite, closed and reciprocal, though Parmenides would argue that this understanding is contradictory and would not permit multiple and ideal static forms.

Finally, Parmenides confronts Socrates with what he calls the “greatest difficulty”.  If we only know things by knowing their forms, then we only know the forms by knowing the form of the forms.  If the forms of forms leads to an infinite regress, then we cannot know the forms.  On the other hand, if the form of forms is the One itself, as Plato has suggested in the Timaeus, and the One itself does not have a form, does not have a conception of itself higher than itself, then we cannot know the forms, as we cannot know the form of the forms.  Either way, with an infinite regress or a terminus in the One, there is no ability for human knowledge to completely grasp the forms of things, and so there is no ability for human knowledge to completely grasp the temporary things themselves.  Even worse, to the horror of Socrates, this would also mean that the forms cannot completely know us or any of the temporary things, and the One cannot know either us or itself completely.

While Socrates says that saying God does not know things is “monstrous”, Parmenides tells him that he is not able to argue and understand because he is young and not yet trained properly.  Later Neoplatonists such as Eriugena argued that God, the One, does and does not know itself, just as Hyperousia, Superbeing, is both being and nonbeing together as one, just as in Plato’s dialogues that are supposed to happen later, an older and wiser Socrates divinely knows that he does not know.  Knowing and not-knowing are not distinct, the difference being an illusion, a shadow projected by the Sun that is one and the same as the Sun itself.

Parmenides proceeds to show Socrates, by debating dialectically with Aristoteles (not to be confused with Aristotle, Plato’s student, who we will study next).  Parmenides leads Aristoteles through a set of exercises concerning the difference and identity of “the One and the many”, the central problem of Neoplatonism and the core of the Eleatic paradoxes.  Like and older and wiser Socrates leads Meno’s slave boy and the interlocutors of the Republic through questions, Parmenides leads Aristoteles to many contradictory conclusions about the One:

The One is both one and many.
The One does and does not exist.
The One is the object of knowledge and is not the object of knowledge.
The One comes to be and does not come to be.
The One passes away and does not pass away.
The One is in time and outside of time.
The One is in the many and not in the many.
The One has and does not have contrary properties.

Ancient and modern scholars have come to no complete agreement as to the meaning of these paradoxes, somewhat unified and somewhat disunified in their interpretations.  Medieval Christian Neoplatonists, such as Eriugena, Nicholas of Cusa and Ficino of the Renaissance in Florence, believed the Parmenides to be the ultimate expression of philosophy, Plato’s deepest text which springs from the well of the One itself.  

Hegel, one of the most influential of modern European philosophers, attempted to synthesize these contradictions in a system that would be the ultimate and complete philosophy, a unification of humanity and science with the mind of God, mediated by spirit which works in stages through history and culture.  This, of course, would be another trinitarian formation of mind, spirit, and desire, an attempt to complete the work of the Republic and Timaeus by resolving the contradictions of the Parmenides in the One.  Much of the European Continental tradition of philosophy has continued until today to wrestle with Hegel and his dialectical system, accepting many of his insights but rejecting any final resolution of a complete system.

Lacan, the influential French psychoanalyst, argued that the Real, the true whole underlying our superficial ‘reality’, is completely contradictory and our understandings are incapable of capturing it to one side or the other along any dimension.  Thus, any conception, any understanding, even the whole of scientific theory, is a mere image, a projection like the shadows on the wall of Plato’s cave.  The basic condition of humanity is narcissism, our insecurity resulting in attachment to images of ourselves, of things we desire and of our understandings of things we desire, a basic inability to be open to the whole and the process.

With the Timaeus, I mentioned that Zizek, one of the more respected continental philosophers today and a devoted follower of both Hegel and Lacan, wanted a “third pill”, not one that distinguishes reality from illusion but shows reality as illusion, shows reality as ideology.  This is similar to Plato’s Parmenides, who led Zeno, Socrates and Aristoteles through contradictions to show them that truth and illusion, reality and fantasy, can never be fully distinguished.