Zeno of Elea
In the tradition of Parmenides of Elea, Zeno was a student of his who flourished in the mid 5th century BC. Much of Zeno’s thoughts comes down to us from Plato’s Parmenides, where there’s a dialogue between Parmenides, Zeno and Socrates. Laertius adds, as Aristotle did, that Zeno was “skilled to argue on both sides on any question…” He was an early, if not the earliest philosopher to use the dialectic method, and therefore an influence for a young Socrates and Plato later on. The meeting may be imaginary because it is not possible to verify Plato’s account, but it set up a challenge to Eleatic philosophy for posterity. There are texts that purport that Zeno was in Athens, was paid for his instruction and that Pericles heard Zeno discourse. In Plato’s account Zeno was described as 40 and Parmenides 65. At this time Socrates was supposed to be a “very young man.” In Plato’s Parmenides, Parmenides and Zeno are translated as and described as lovers. In another account, Parmenides adopted Zeno when they were younger. It’s for sure that many readers with a sense of humor will try to conflate both of those stories, but it’s hard to know what really happened because all these accounts are passed down over the years through intense memorization that few modern people could tolerate. It’s not like sending a documentarian back in a time machine to film the dialogue. The end of Zeno’s life also has different accounts like alternate storylines manufactured for sensation, which makes it more salient and therefore easier to remember, but may not be entirely true.
Diodorus of Sicily, for example, recounts his version. “When Zeno’s native city was being ground down by the tyranny of Nearchus, Zeno formed a conspiracy against the tyrant. But he was found out, and when he was asked by Nearchus, while suffering the agonies of the torture, who his fellow conspirators were, he replied, ‘Would that I were as much the master of my body as I am of my tongue!’ And when the tyrant made the torture more and more severe, Zeno still withstood it for a while; and then, being eager to be rid at last of the agony and at the same time to be revenged upon Nearchus, he devised the following plan. During the greatest intensity of the torture, pretending that his spirit was yielding to his bodily pains, he cried out, ‘Relax it! I will tell the whole truth.’ And when they did so, he asked Nearchus to come near and listen to him privately, asserting that many matters he was about to disclose would best be kept secret. When the tyrant came up to him readily and placed his ear close to Zeno’s lips, Zeno took the tyrant’s ear into his mouth and sank his teeth into it. And when the attendants quickly approached and applied every torment to make Zeno relax his hold, he held on all the tighter. Finally, being unable to shake the fortitude of the man, they stabbed him to death that they might in this way break the hold of his teeth. By this device Zeno got release from the agonies he was suffering and exacted on the tyrant the only punishment within his grasp.” But in another account that sounds like something out of a Scorsese movie, “Hermippus says, that [Zeno] was put into a mortar, and pounded to death.”
Kirk and Raven describe Zeno as being “like Parmenides…to have been originally a Pythagorean…His characteristic method was, to reduce his opponents’ hypotheses to absurdity by deducing from them the contradictory consequences. The hypotheses to which he especially turned his destructive talents were two, namely plurality and motion, which were unquestioningly accepted by all except the Eleatics themselves; but for all that, his arguments may well have been aimed particularly at the Pythagoreans.” The classic arguments for Zeno involve scenarios where perceptual measurement is difficult to reconcile with how we can zoom into matter endlessly without finding absolute demarcations in matter. We stop at the limit of our strength or technology and give up the search at one morsel, atom, or subatomic particle, and can’t go any further without new technological aids and advancements. For those familiar with past episodes on Buddhism and Nagarjuna, these arguments will be recognizable in the One vs. Many arguments.
Mindfulness: Nirvana: https://rumble.com/v1grcgx-mindfulness-nirvana.html
Thought and Meditation – Rob Burbea: https://rumble.com/v1gqufd-thought-and-meditation-rob-burbea.html
One example from Philoponus was that Zeno “rested his proof of this on the infinite divisibility of any continuum. For, he argued if what is were not one and indivisible, but were divided into plurality, nothing would be one in the proper sense (for, if the continuum were divided, it would be divisible ad infinitum)…” A similar argument was about Place. Simplicius recounts that “Zeno’s argument seemed to do away with place, putting the question as follows: if place exists, in what will it be? For every existent is in something; but what is in something is in a place. Place therefore will be in a place, and so on ad infinitum therefore place does not exist.”
Because there is a sense of space and place, there’s also a sense of movement. A famous example from Zeno was The Arrow where motion is treated more like displacement of space, where at no point does movement leave a vacuum behind. “The flying missile is at rest during its flight, if everything must either be in motion or at rest, but an object in flight always occupies a space equal to itself. But what always occupies a space equal to itself is not in motion, it is therefore at rest.” Zeno is focusing on how a reconfiguration of an infinite body is still interdependent.
Even more difficult for Zeno is that if you compare matter to measurement, technically you can subdivide distances into fractions ad infinitum so you couldn’t ever arrive at an absolute distance with certainty. Measurements are practical approximations like you see on a ruler. Each measurement marker on an ruler has a certain diameter so we can see it, but IT can be subdivided endlessly as well. Simplicius summarized that “the argument is, in outline, that a moving body in completing any given distance would have to pass through an infinite number of half-way points; which is impossible, and therefore motion is impossible.” It’s possible in perception, but impossible in the absolute.
Even comparisons between greater and smaller adjust our perception when the comparisons change, yet to Zeno it’s simply a rearrangement of the same things that are also interdependent reconfigurations in an infinite body. “For if it should be added to something else that exists, it would not make it any bigger…Clearly the thing being added or subtracted is nothing.” You can then subdivide matter and end up with no absolute measurements either. “‘The many must be both limited and unlimited in number. Limited, because it is as many as it is; no more nor less. Unlimited, because two things are two only when they are separated; in order that they may be separated, there must be something between them; and so too between this intermediate and each of the two, and so ad infinitum.'” You’re left with an infinite one-ness because even shape requires a beginning middle and end. “For no such part of it will be last, nor will there be one part…not related to another.” Aristotle of course criticized these arguments, and many of Zeno’s arguments survive through his writings. He separated ideas of mathematics from seamless experience. “Time is not composed of indivisible instants any more than any other magnitude is composed of indivisibles.”
To summarize these Eleatic ideas in Plato’s account of the meeting, Socrates asks “how do you mean this, Zeno? If things that are, are many, they must therefore be both like and unlike, but this is impossible. For unlike things cannot be like nor can like things be unlike. Isn’t that what you are saying? Now if it is impossible for unlike things to be like and like things unlike, is it also possible for things to be many? For if they were many they would have impossible attributes.” Zeno’s take from Parmenides’s positive proof is a negative proof of: “One says ‘The One’ and one says ‘Not Many…'”
Socrates later responds to Parmenides and his admission that there is an IS, and allows the like and unlike to be One in the sense that the plural of IS is ARE. They ARE. Ontology is the study of being, and being can include levels of being that allow for variety. How they share and partake with each other is their interconnection while still retaining plurality. For those interested in Buddhism, it’s similar to FORM = EMPTINESS, EMPTINESS = FORM. Things may be interdependent, but you wouldn’t ignore human perception. “But tell me this: don’t you think that there exists, in itself, some form of Likeness, to which is opposed a different one, which is unlike, and that both you and I and the different things which we do in fact call ‘many’ come to partake of these two things which are?” Through comparison of categories, Socrates shows that what attributes can be in common, which would be IS in the particular, or Being in the general, are the most simple and encompassing. IS can be broken down into ARE and still Be. “When he seeks to show that I am many, he just mentions that my right is one thing and my left another, my front’s one thing and my back’s another, and likewise for upper and lower-for I do, I believe, partake of Multitude. But when he wants to show that I am one, he’ll say that out of the seven of us who are here, I myself am one man and partake of the One. So he can show that both are true.” By delineating between supra- and sub-categories, the perception is simply looking at the Universe and using larger or smaller categories out of everything. What is looked at can be One AND Many. Some of these categories can be more general, and apply to many things, and some more specific. You can expand the One to include infinite existence and then subdivide from perception thereon.
Parmenides goes into exploring Plato’s Forms of Greatness, Beauty, and Justice. “Although one and the same, then, its whole will be in many separate beings at the same time, and so it would be separated from itself.” Socrates then provides an example of the day that “although one and the same, is many places at once and is not at all separate from itself.” The word partake, is used a lot but in a more modern style, the word share I think would be easier to grasp. The day for example looks different as it goes on and it has an opposite, the night. One could also look at the day in terms of 24 hours so that the night shares a calendar day, depending on categories you choose to prioritize and focus on. Parmenides warns that “if you’ll partition Greatness itself, then each of the many great things will be great by means of a part that’s smaller than Greatness itself- doesn’t that appear illogical?” Even further what is considered small is great in comparison to a smaller part of the small. “Since it’s just a part, the Small will be greater than it.”
In response, Socrates introduces abstraction and separates our ideas of things from the phenomenon and points out our activity in perception. “But Parmenides, couldn’t it be that each of these forms is a thought and properly comes to be nowhere but in souls? Then each could in fact be one and would not still suffer the things you just mentioned.” Certainly the suffering is only happening in the human mind and samples of perception. Each perception-sample IS. It brought Parmenides to consider that “Each is one of our thoughts—[not] thoughts of nothing [but] of something that is or is not?” Socrates then explains the Forms in a way like a projection of how we can utilize them and how their characters appear to us. “These forms stand in nature like patterns. The different things resemble them and are likenesses, and so the different things’ participation in the forms turns out to be nothing else than to be made in their likeness!” These patterns are recognized in humans as being of more or less recognition according to ideal forms, which like mathematics, can only exist in the mind perfectly, but are only approximations with matter. The ideas turn into branches of objective knowledge. Most importantly “neither do we possess them nor could they be among us.” This creates a mathematical objective reality with a sense of human purpose within it. Parmenides asserts that “then what the Beautiful itself is and the Good and all the things that we do suppose to be ideas are unknown to us.” “I’m afraid so.” Parmenides then feared that this knowledge is that of a God that doesn’t interfere with us and we have to suss out these objective truths for ourselves, and the danger is a pervading ignorance and also a freedom to go into denial. Parmenides then advised Socrates to develop theories by comparing what IS and also what IS NOT, to polish a more objective Truth as humanity learns and moves out from ignorance. In this version of the Theory of Forms, laws of cause and effect make up the patterns we see, and then we extrapolate logical laws by watching the behavior of matter. Matter is imitating logical laws that have the power to direct.
The Italian scholar and Catholic priest Marsilio Ficino, in his translations of Plato into Latin, admired Parmenides lack of resentment and his generosity in helping Socrates flesh out his ideas. “Notice how Parmenides, at times when philosophic tenets are being torn to shreds, trains the young man to be careful in his replies and judicious in his discrimination.” For Ficino, he views the forms as a sign from God, and that humans are also made in the likeness of God, or Forms. It becomes a guide that separates the divine from the profane on Earth and sends a signal for us to move towards, like an intelligence meditation of pure ideas contemplated, and crude matter is renounced. “Being about to perceive the single best principle of the universe, we are obliged, first of all, to lay aside whatever is most at variance with it, that is, evil and multiplicity, and to use all our powers to be called back to our unparalleled and best quality, back to the simple and peaceful contemplation of sublime intelligence.” This is hinted at when Parmenides chides Socrates about the cleavage between Forms and what ends up being dross for both of them. “Well then, Socrates, what about those things that would seem to be laughable, such as Hair and Mud and Dirt or any different thing that’s very worthless and lowly? Are you at an impasse over whether it is or is not necessary to say that there is a separate form of each of these, something different than what we can lay our hands on?” “No, not at all!” Yet there’s still a mystery that Socrates feels in his idea of the forms, or as Plato speaks for Socrates. “In the Theaetetus, when Socrates was asked to refute those who posited a single motionless being, he did not undertake to do so himself but gave this answer: Although I honour Melissus and others, who say that there is one self-consistent totality, for it may seem immodest of me to cross them, yet I honour them less than I do Parmenides alone, for Parmenides, to use Homer’s words, strikes me as one who is sagacious and worthy of great honour. I once conversed with him when he was advanced in years and I was but a youth, and he struck me as having a wisdom that was profound and noble in all respects. This is why I fear that we do not have the slightest understanding of his sayings and expressions, and what he himself implied by his words is, I fear, even more of a closed book to us.”
To review the arguments once again, Parmenides, in his old age, decided to debate a younger less experienced Aristotle, not the famous philosopher, to conserve his energy. Their arguments fleshed out a One that cannot be made of parts, because a Whole cannot have Parts. It cannot have a beginning, middle, or end. It has to be limitless with no shape. It can’t have a location, change or move if it were partless. Even things we see in motion are simply parts displacing each other in limited human perception, but the One itself is not moving. These are our perceptions and memories. At any one time perceptions are seeing shapes, locations, movements, and objects displacing each other in space and time. Even measurement cannot subdivide this One without our own participation in such labels. This is why age and time cannot be anything other than what humans introduce because even moments of time are smaller perception-memories that can be subdivided ad infinitum. We need memories of older and younger to make that comparison. Without the comparison we are back to just an indefinable IS. The One has no becoming or hereafter. The problem with these exercises is that they lack a sense of utility that humans crave. Even Ficino sees Parmenides as “the pursuer of Being, which is detached from sensory perception…”
That is the rub for Plato, the discounting of perception, and Socrates’s argument cleaves this One into two by finding common ground with Parmenides and Pythagoras that there is an IS, and the starting point is always two, not One, because of our perception. Our perception can notice opposites and through that knowledge, it can use imagination to develop precise ideas from those comparisons. We need comparison to learn conventional truth, which is an abstraction that allows us to count matter and develop mathematical abstractions from perception into seamless formulas. Then we can shape matter as close as possible to the idealistic potentials pointed to in those formulas for our benefit. Eg. An Architect. “…Each of these pieces hold fast to the One and Being, and the very least piece comes to consist, in turn, of two pieces, and, according to the same speech, it is always this way. Namely, whatever piece comes to be, it always holds fast to these two pieces; for the One always holds fast to Being and Being to the One. The result is that, since it always becomes two, it necessarily is never one.” The superstructure is the One Everything, and the substructure is IS. The Being is One, but we experience in human perception the multitude of the Being of IS and ARE. The Pythagorean method is then re-introduced by using number as a way to measure multitude, because we can count quantities in the repeated qualities found in perception. “And so if all number partakes of beinghood, would each piece of number also partake of it?” The numbers and being can be logical because general categories can house subcategories and “as long as it is, it must always, by necessity, be one thing; it’s impossible that it be nothing…For Being neither lacks the One nor the One Being; rather, since they are two, they are always, in every case, equal.” This allows the perception of movement, time, subject, object, shape and space. Perception already is a measurement out of the whole and what makes us human and capable of making some sense out of our existence.
The Presocratics: Pythagoras: https://rumble.com/v1gsugl-the-presocratics-pythagoras.html
The discussion reaches the limits of human perception and one has to resort to memory-instants, demarcation, and outlines to describe what is at rest or in motion. It again allows for a form of suffering and death, coming and going, where the One doesn’t lose it’s One-ness, but there’s an acceptance that “the One would suffer all these experiences, if it is.” An unlimited whole turns into a “limitless multitude.” The conversation expanded into Parmenides’s IS-NOT as a form of knowledge that people can attain because the knowledge of what IS NOT, IS knowledge. Plato’s theory of the Forms are like polished ideas that separate from imperfect perception. It’s like heavenly intelligence vs. deficient matter. In Plato’s Parmenides, Samuel Scolnicov uses the example of Beauty. “Sensible things are what they are because they participate in or imitate other entities, which are what they are in themselves. The beautiful itself is beautiful in and by itself; other beautiful things are beautiful because they stand in a certain relation to the beautiful itself, and only in certain respects but not in others…They are dependent, and this is why they are deficient…” Here we can look at matter imitating laws of the universe that we are able to formulate more perfectly than how matter actually behaves. Of course, the trick is to see deviances in behavior so we can update formulas to predict future behavior. There’s also a hostility because of that struggle to live in matter and to make matter conform to our perfectionist ideas. The irony is that both philosophers are taking perceptual experience in matter and extrapolating an unknowable One that can be understood, but not perceived, or Forms that are understood but imperfectly aligned with behavior in matter.
Zeno of Elea – Lee, H. D. P.: https://www.isbns.net/isbn/9781107480278/
Zeno’s Paradoxes – Wesley C. Salmon: https://www.isbns.net/isbn/9780872205604/
Plato’s Parmenides – Mitchell Miller: https://www.isbns.net/isbn/9780691629926/
Plato’s Parmenides – Albert Keith Whitaker: https://www.isbns.net/isbn/9780941051965/
Plato and Parmenides – Francis MacDonald Cornford: https://www.isbns.net/isbn/9780415613897/
Plato’s Parmenides: Text, Translation & Introductory Essay – Arnold Hermann: https://www.isbns.net/isbn/9781930972711/
Plato’s Parmenides – Samuel Scolnicov: https://www.isbns.net/isbn/9780520224032/
The Presocratic Philosophers – G.S. Kirk: https://www.isbns.net/isbn/9780521274555/
A Presocratic Reader – Richard McKirahan: https://www.isbns.net/isbn/9781603843058/
Lives of Eminent Philosophers – Diogenes Laertius Books 6-10: https://www.isbns.net/isbn/9780674992047/
The Library of History – Diodorus of Sicily: https://penelope.uchicago.edu/Thayer/E/Roman/Texts/Diodorus_Siculus/10*.html
Evermore Shall Be So – Marsilio Ficino: https://www.isbns.net/isbn/9780856832567/
Troubling Play – Kelsey Wood: https://www.isbns.net/isbn/9780791465202/
Philosophy: https://psychreviews.org/category/philosophy03/