Episode 12: The Eleatic School & the Way of Truthiness

December 20, 2021

After the Median invasion, the Ionian philosopher Xenophanes, a student of the Anaximander, was forced to flee to Elea in Magna Graecia and brought the philosophy of the Ionians to the Eleans. His student, Parmenides, then founded the Eleatic School which was skeptical of the senses, and argued that despite its appearance to the contrary, the Earth was round. Parmenides's student, Zeno, in turn developed his famous paradoxes to prove his teacher's assertion that motion was an illusion.


Good evening, and welcome to the Song of Urania, a podcast about the history of astronomy from antiquity to the present with new episodes every full moon. My name is Joe Antognini.

Before we begin I wanted to mention that if any of you dear listeners are going to be at the winter meeting of the American Astronomical Society coming up in January 2022 in Salt Lake City, you can hear me live, although I will not be talking much about the history of astronomy. I will be on a panel during the NSF Astronomy and Astrophysics Postdoctoral Fellowship session to provide what advice I can about getting a permanent job inside or outside astronomy. As I have never had a permanent job inside astronomy, my advice will mostly be focused on getting a permanent job outside astronomy, specifically in tech, machine learning, data science, that sort of thing. If that is something you would enjoy, I hope you will attend. I suspect we will all learn something.

Well, on to the show. Our last episode on Pythagoras and the Pythagoreans, or as Aristotle called them, the so-called Pythagoreans was a little divergent from the overall chronological narrative I’ve been developing as we’ve learned about the astronomy of ancient Greece. Pythagoras himself was contemporaneous with some of the philosophers of the Ionian School, in particular Anaximenes, who came after Anaximander and before Heraclitus. But the Pythagorean School persisted for several centuries, and thanks to the secrecy of the school, it is very difficult to determine when exactly different ideas came about. So most of our knowledge of the astronomy of the Pythagorean school comes to us through an author named Philolaus, who was active about a century after Pythagoras.

So now we are going to have to turn back the clock somewhat and revisit Greek philosophy around the time of Pythagoras once again. The episode on the Pythagoreans was also something of a digression from the main thread of Greek astronomy because the Pythagoreans really did stand apart from the other Greek philosophical schools. They were, as I tried to emphasize, highly secretive, and in many ways almost cult-like relative to other philosophical schools of the day. Of course, ancient philosophy was very different than modern-day philosophy in that there was a much stronger emphasis on how to live properly — what constituted a good life, well lived? Many modern philosophers regard this as being more the domain of self-help books than serious philosophy which is interested more in thorny questions about the nature of consciousness, language, ethics, and so forth. So, while we don’t see many contemporary philosophers providing their students with extensive instructions as to how they ought to live their lives, the ancient philosophers felt no such compunction. Nevertheless, even relative to that standard, the Pythagoreans certainly took it to another level.

But in this episode we will turn towards a school that was more in line with the typical philosophical schools of ancient Greece, the Eleatic School, so named because its two most notable members, Parmenides and Zeno, were both from the town of Elea in southern Italy, or, as it was known at the time, Magna Graecia. Now, as with the Ionian School, the name “the Eleatic School” was not a formal kind of school and is just a label that historians of philosophy have slapped on after the fact to try to group together some philosophers from a similar part of the world who were interested in similar questions. By contrast the Academy of Plato and the Lyceum of Aristotle developed into more formal institutions whose purpose was to provide a forum for philosophical discourse, both by lectures from senior members, and dialogues between members. But we are not there yet. At this point in Greek intellectual life, philosophy was a more informal affair, with philosophers attracting a group of students who would learn what they could at the feet of the master.

Now, I mentioned that the two most well known of the Eleatics were Parmenides and Zeno. But we will start with another philosopher who is closely associated with the Eleatics and had a pronounced influence on them, but is not always included in the group — this is a philosopher by the name of Xenophanes.

Xenophanes was almost exactly contemporaneous with Pythagoras, both were born around 570 BC, but Xenophanes lived about a decade longer than Pythagoras, dying around the age of 90, sometime between 480 and 475 BC. Xenophanes forms the point of connection between the earlier Ionian School and the later Eleatic School. Xenophanes was born in the city of Colophon in Ionia, which was just a little bit north of Miletus, just a few days travel. Like Miletus, Colophon was a wealthy town, and in those days was considered the literary capital of Ionia. In his youth he seems to have moved to Miletus and become a student of the great astronomer Anaximander, whom we talked about in Episode 9 on the Ionian School. But Anaximander died when Xenophanes was 24 years old, and the following year, 545 BC, was the year of the Median invasion of Ionia and Xenophanes was forced to flee his home and he never returned. Heraclitus writes that from that point on, the next 67 years “tossed his care-worn soul up and down the land of Hellas.”

Herodotus has an account of the Median invasion and the subsequent migration that it precipitated. The invasion was led by the Median general Harpagus. Now, Harpagus played a crucial role in the fall of the Median empire and the rise of the Persian empire. Now, you may remember a few episodes back to the Battle of the Eclipse, in which there was a total solar eclipse, supposedly predicted by Thales, that occurred during a battle between the Medians and the Lydians. These hostilities had been brought about because the Scythians had killed a Median boy and fed him to the Median king Cyaxares.

Well, a little bit after this battle, Cyaxares died and was succeeded by his son, King Astyages. Herodotus then tells a story about King Astyages that is somewhat reminiscent of the tale of Perseus’s birth. According to the story, King Astyages dreams that his daughter will bear a son who will destroy his empire. Naturally, after his daughter bears a son, Cyrus, who later becomes known to history as Cyrus the Great, which maybe foreshadows where this story will go, King Astyages orders his top general, Harpagus, to kill the child. But Harpagus recognized that the child was royalty, and did not wish to bring the wrath of the gods upon himself by killing a royal child, so he disobeyed his orders and found a shepherd whose wife had just given birth to a stillborn child. So he swapped the infant Cyrus with the stillborn child and presented the shepherd’s stillborn child to King Astyages to prove that he had killed Cyrus, and in reality Cyrus was raised by the shepherd.

Now, Herodotus does not make clear how exactly this happens, but ten years later, the boy Cyrus was playing king of the hill, apparently just as much a game in the ancient world as it is today, and was discovered, somehow, to be the grandson of the king. When King Astyages learns of this, he, naturally, is not pleased. To punish Harpagus for disobeying his orders he prepares a banquet for Harpagus, kills Harpagus’s son, and then serves the son as the main course of the feast. So this is the second time that a cannibal feast shows up in the ancient Greek history of Media. And, in fact, these are not the only ones, yet another cannibal feast shows up in the myth of Thyestes. So, given these parallels, these details from Herodotus, who after all, was as much interested in spinning a good yarn as capturing accurate history, might be taken with a grain of salt. Well, in this particular story, the general Harpagus collects the remains of his son from the plates to be buried. King Astyages then has the question of what he should do about his still-living grandson Cyrus. So he consults his magi who tell him that because the child was discovered while playing king of the hill, he had already fulfilled the prophecy by becoming a king, so the child was now of no threat.

Harpagus, as you might imagine, is none too thrilled with King Astyages after he killed his son and cooked him for a feast. So while he remains in the court, he secretly starts to plot against the king, turning the favor of nobles against him and building his relationship with Cyrus. When Cyrus is old enough, Harpagus sends a message to Cyrus in the belly of a rabbit to encourage him to revolt against the king. Cyrus builds an army and attacks King Astyages, so King Astyages commands Harpagus to fend off the attack and destroy the upstart’s army. But in the battlefield, Harpagus defects, and orders his soldiers to join with the soldiers of Cyrus and kill the king.

From this betrayal, the Median Empire fell, fulfilling the prophecy, and the first Persian Empire, or the Achaemenid Empire, began. As you might recall, I discussed some of the later exploits of Cyrus at some length. After his conquest of the Median Empire he later conquered the Neo-Babylonian Empire and is generally very favorably received in the Hebrew Bible because after the destruction of the Neo-Babylonian Empire he restores the Israelites to their land, ending the Babylonian Exile.

But, as this long-winded story concerns the Greek philosopher Xenophanes, after Cyrus had defeated his grandfather and destroyed the Median Empire, but before he conquered the Neo-Babylonian Empire, he continued to push west into the Lydian empire, which he also conquered. Now, Lydia was just east of Ionia, basically encompassing the western part of modern day Turkey, whereas Ionia lay just along the western coast and some of the nearby islands. So naturally after conquering Lydia, Cyrus continued to push right to the coast into Ionia and attacked the city of Phocaea, which was very close to Colophon, Xenophanes’s native city. The city of Phocaea was well defended, but did not have the resources to fight back against the enormous armies of Cyrus the Great, so the city was put under siege. Nevertheless, Phocaea was on the coast and Cyrus had no control over the seas. So the inhabitants of the city vowed to abandon the city and flee west. They traveled in some 60 boats to the island of Chios a few miles off the coast and beseeched the inhabitants to allow them to purchase one of their uninhabited islands. The inhabitants of Chios refused, however, so after a time the Phocaeans returned to their city. But by this point Cyrus had already plundered the city and moved on, leaving only a small garrison which the Phocaeans were able to destroy. But here there was division among the people. Although they had sworn an oath to stay together as a people, almost half of them preferred to stay in their home city, but the other half felt that they were on borrowed time, and it was only a matter of time before Cyrus returned to conquer their city once again. So, based on an omen, half of the residents sailed west to the island of Corsica, and then, after treating their neighbors poorly, departed again for Magna Graecia where they founded the city of Elea.

So it may well have been the case that through this migration, Xenophanes traveled from Ionia to Elea. In fact, when recounting this story about the exile of the Phocaeans, Herodotus may have had Xenophanes in mind. At any rate, the main consequence of this event was that, although it permanently exiled Xenophanes, it ultimately brought the Ionian philosophical tradition to the inhabitants of Elea, which later developed into the Eleatic School.

While this might be some small consolation for Xenophanes, it was clear that he missed his native land. Towards the end of his life, at the age of 92, Xenophanes penned a poem, a fragment of which has survived:

Sixty-seven years it is now that the burden of life
I am dragging to and fro through the regions of Greece.
Counting the years from the day of my birth, I was then twenty-five
— If I still correctly remember

This is the stuff one best talks about by the fire in winter,
Comfortably inclined, sipping sweet wine and nibbling some nuts:
‘Tell me, who are you, my friend, and where do you come from?
How old are you, my dear, and what was your age
At the time of the Median invasion?

Well, as for the philosophy itself that Xenophanes brought to Elea, this, too, he wrote in verse. Some of it has survived, but only in fragments. His principal interests are what we today might call theology and epistemology. He is interested in the nature of the god — and, to be clear, he is interested in the nature of god, singular — and he is interested in the nature of knowledge. What does man know, how does man know it, what can man hope to know?

The theology of Xenophanes is really quite radical for its time and place. It sounds almost like it could have been written by the prophet Jeremiah. Xenophanes completely breaks from the polytheistic tradition of ancient Greece. Like any educated Greek he was intimately familiar with the poems and the implicit theology of the bards Hesiod and Homer. But he rejects this picture of divinity. After all, the gods and goddesses of the Greek pantheon are remarkably human. They are adulterers, they harbor jealousies, steal, and lie. The only reason they’re not killing each other is because they are immortal. Xenophanes attempted to bring an element of rationality into the religion of his day, but found that he could not reconcile any sort of rationality with the myths of ancient Greece, and as such they had to be rejected.

Instead he argued that the gods and goddesses depicted by Hesiod and Homer were simply tales about humans who had superhuman powers. He writes

The Aethiopians say that their gods are flat-nosed and black
While the Thracians say that theirs have blue eyes and red hair.
Yet if cattle or horses or lions had hands and could draw
And could sculpt like men, then the horses would draw their gods
Like horses, and cattle like cattle, and each would then shape
Bodies of gods in the likeness, each kind, of its own.

To Xenophanes, the divine had to transcend all this, and to him the only way this could happen was if there was a single true, omnipotent God without form that encompassed all things. He writes:

One God alone among gods and alone among men is the greatest.
Neither in mind nor in body does he resemble the mortals.
Always in one place he remains, without ever moving.
Nor is it fitting for him to wander now hereto now thereto.
Effortless over All he reigns by mere thought and intention.
All of him is sight all is knowledge; and all is hearing.

This sounds like it could have been written by one of the prophets of Israel or the early Church Fathers. It is a view of God that is more or less consistent with the monotheism of Judeo-Christian theology, and wholly inconsistent with ancient Greek theology.

Now, of all the pre-Socratic philosophers, Xenophanes does not have the strongest reputation. Later scholars thought that his Greek was somewhat simplistic and thought that some of his ideas were absurd, particularly with regard to his astronomy which we’ll talk about momentarily. But Xenophanes’s rejection of the very anthropomorphic, highly dramatic polytheism of his culture in favor of this abstracted monotheism should place him as one of the most original thinkers of all times. Although most westerners today regard monotheism as a fairly natural idea — almost everyone in the West today believes in either one God or none at all — it seems to be an exceedingly non-intuitive concept. It has rarely developed in human civilization. Essentially the only reason that the ancient Israelites were a civilization of any note was that, alone among civilizations, they whole-heartedly embraced monotheism — the idea that not only was their national god more powerful than the gods of their neighbors — which, to be sure, was likely the original conception — but that those other gods did not even exist. Without this idea the ancient Israelites today would probably be just as well remembered as the Canaanites, Kushites, Hittites, and all the other “-ites” that populated the land of the ancient Near East. But their unique idea of monotheism radically separated them from their neighbors — a separation which their texts make clear that they were very keen to retain — and allowed them to maintain a distinct identity to the present day, whereas the rest of these ethnic groups melded with each other and faded away as over time new ethnic identities gradually developed. But even for the ancient Israelites, this idea did not come to them overnight. Based on the dates at which various texts of the Hebrew Bible were written it is clear, too, that this idea developed over centuries, with the God of Israel initially being conceived of as a conglomeration of the local gods of various tribes within Israel, later becoming the most powerful of the Gods, still later becoming the only God, and finally, abstracting away the anthropomorphic representations. But here Xenophanes is independently coming up with it.

As I mentioned Xenophanes is also interested in epistemology, and here he presents another profound idea, seemingly for the first time. He writes:

But as for certain truth, no man has known it
Nor will he know it; neither of the gods
Nor yet of all the things of which I speak.
And even if by chance he were to utter
The perfect truth, he would himself not know it;
For all is but a woven web of guesses.

The crucial idea here is the distinction between an objective truth, which Xenophanes believes exists, and our certainty of having that truth. So he believes that an objective truth exists. But he does not believe that we can have certainty that what we believe is the truth. Even if it so happens that what we believe is true, we cannot know that it is true. For us humans there is always some uncertainty. But Xenophanes is not an epistemological pessimist. He writes in another fragment:

The gods did not reveal, from the beginning,
All things to the mortals; but in the course of time,
Through seeking they may get to know things better.

So, while we can never have objective truth, we can proceed to iteratively improve our knowledge and draw ever closer to that objective truth. The philosopher of science Karl Popper, who is best known for his idea that the basis of science is falsification — theories are scientific if they make predictions which can in principle be falsified by some experiment — (he also made these translations, incidentally), Popper argued that in the epistemology of Xenophanes we have the foundation for Western science. In fact, Popper makes quite a forceful argument for the importance of the pre-Socratic philosophers generally. He speculates that this may have begun with Xenophanes’s teacher Anaximander who perhaps encouraged Xenophanes not to accept his own ideas uncritically, but to think about them, challenge them, find fault with them, and propose his own. This process of critical evaluation and proposing new ideas to remedy the defects of former ideas is at the heart of the scientific process, far more so than experimentation because experimentation must always be done with an aim toward evaluating some theory. In practice it is not done aimlessly, according to Popper it’s done to test the predictions and consequences of different theories. This culture of vigorous debate of competing ideas developed in the Ionian School, transferred to the Eleatic School, and ultimately became a feature generally of the philosophy of ancient Greece, and then Western civilization more broadly. This was a feature which really made it unique relative to other cultures. Other cultures certainly had philosophers and what we might call philosophical schools where students learned from the master. But the purpose of the school was to transmit the ideas of the master down through the generations more or less unchanged. Members of different schools might debate with each other, but within a school, the philosophy was set by the master and the job of the students was to interpret the wisdom of the master. In this regard, the Pythagorean school was more like the sort of philosophical schools that existed outside of ancient Greece. The Pythagoreans, particularly the Acousmatics, were very interested in preserving the ideas of the master Pythagoras. But the culture of debate and the deluge of original ideas introduced through the Ionian and Eleatic Schools was why centuries and even millennia later scholars looked to ancient Greece and saw that something unique in the development of intellectual life had occurred.

Okay, so what of the astronomy of Xenophanes? Here there are two interpretations — one is a fairly straightforward reading of his cosmology as it is transmitted by Aristotle and Aëtius. The other is a more unorthodox reading from Karl Popper, although, I must admit, I personally find it more persuasive. Now, in the standard telling of Xenophanes’s cosmology, Xenophanes holds that the Earth is essentially infinite in extent. It is flat and extends in all directions off to infinity. Not only that, the Earth also extends downwards to infinity as well. Above the Earth, the atmosphere extends up infinitely. Now, because the Earth extends infinitely downwards, there is no need to explain why the Earth stays up. As Aristotle is wont to do, he ridicules this explanation, saying that Xenophanes did it “to save himself the trouble of looking for a reason.”

Now, this cosmology on its own is plausible enough. But things start to get strange when you have to explain how day and night work. Because we clearly see the Sun rise each morning and set each evening, which seems to be tension with the idea that the Earth is infinite in extent. So Xenophanes’s explanation here is that there is an infinite procession of Suns, Moons, and stars. Each Sun simply moves in a line from east to west. From our perspective here on Earth it just appears that the Sun is rising and setting as it gets nearer to us and then further away. Now it seems as though the fact that the pattern of the stars is identical from night to night even though it’s a completely different set of objects is quite a remarkable fact, but it’s the necessary consequence of his theory. In addition to this, Xenophanes claims that the Sun, Moon, and stars, are all balls of gas set alight, though the Moon is compressed air, which gives it its silvery color. At least as regards the Sun and the stars, this is not so far off from the truth.

So, that is the straightforward interpretation of Xenophanes’s cosmology. The Earth is flat and infinite in extent, both to the sides and down. But some have argued that this was a hatchet job. The physician Galen who later wrote during the second century AD accused other philosophers of misrepresenting Xenophanes, saying, “In a malicious and slanderous way some commentators on Xenophanes have lied about him…. For nowhere can Xenophanes be found to have said anything like that.” Galen almost certainly had texts from Xenophanes that have today been lost, so he would have been in a better position to compare the representation that other philosophers made of Xenophanes, perhaps Aristotle among them, to the writings of Xenophanes themselves.

Karl Popper, an enthusiastic fan of Xenophanes, and the Eleatics and pre-Socratics more generally, felt that this usual interpretation of the cosmology of Xenophanes was far too simplistic for a mind of his subtlety. An alternative interpretation is that Xenophanes’s cosmology is really no different from that of his teacher Anaximander. You may remember that Anaximander argued that the world was a cylinder floating in a void and did not move because it was equally distant from all things. And in Anaximander’s metaphysics, the arche, the essential matter that composed all things, was what he called the apeiron, the Infinite. This word is actually the first technical word that appears in the history of natural philosophy — a word that was invented specifically to describe a new physical concept. Well, when Xenophanes says that the Earth extends downward to infinity, he is using this same word, apeiron. So it could equally well be read that the Earth extends downward to the apeiron. So another, perhaps more reasonable interpretation of Xenophanes’s cosmology is that the Earth is a cylinder, just as in the cosmology of Anaximander, but that this cylinder is floating not in a void, but is floating in the apeiron. So, the Earth extends downward to this apeiron and to the sides is surrounded by apeiron, but this does not mean that the Earth itself is infinite in extent. Now, in this reading, we must also accept that the attribution to Xenophanes of this idea of an infinite procession of Suns, Moons, and stars was completely fabricated by later authors, who, perhaps were attempting to reconcile the idea of an Earth infinite in extent with the observational fact that the Sun rises in the east every day.

The last thing I will say about Xenophanes is with regard to his cosmogony, which is also unique in that it is the first to be backed up with some observational evidence. In some representations, Xenophanes holds that the arche, the essential substance of all things, was Earth, or at least mud. This then rounds out the four classical elements. Thales had water, Anaximenes had air, Heraclitus had fire, and now Xenophanes has Earth. In the beginning all things were a sort of mud, and from this dry Earth and water separated. Unlike the cosmogonies of other ancient Greek philosophers, Xenophanes supported his idea with the observation that sea shells could be found far inland, up in mountains and in quarries. To him, this provided evidence that at one time water and Earth must have been mixed together more thoroughly than they are today.

Well, there is more I could say about Xenophanes. Aëtius, for example, claims that Xenophanes described a solar eclipse that lasted a full month. The most charitable interpretation of this statement is that Aëtius may have been misunderstanding a description of the fact that if you’re within the Arctic Circle the Sun does not rise near the winter solstice, but this also contradicts either interpretation of Xenophanes’s cosmology since this idea only makes sense if the Earth is spherical. But Xenophanes lived a very long time and maybe in his old age was influenced by his student Parmenides to adopt the idea of a spherical Earth. At any rate it’s hard to say.

But we should move on to the philosopher who is said to have founded the Eleatic School: Parmenides. As I just mentioned Parmenides was a student of Xenophanes, or at least was likely to have been a student. One of the strange things about Parmenides is that there is a very wide discrepancy as to when he lived. This is, of course, par for the course for the earlier figures. We don’t even know if Homer was a real person, much less when he lived. But by the time we get to the fifth century BC, we have enough sources and cross-references that it’s generally possible to date individuals to within a few years or so.

Now, Plato says that Parmenides and Zeno visited Athens together when Parmenides was 65 years old and Zeno was 40 years old and there they conversed with Socrates, who was very young at the time. If we assume that this means that Socrates was roughly 20 years old, this would mean that Parmenides was born around 515 BC. However, Diogenes Laërtius writes that Parmenides was at the height of his influence in the year 505 BC. If he was born in 515 BC as implied by Plato, this would mean that Parmenides was at the height of his philosophical powers at 10 years of age. Now, child prodigies exist in music, mathematics, and chess, but they don’t exist in philosophy. More plausibly, if we assume that Parmenides was at the height of his influence around age 40, this would put his birth in the year 540 BC, about 25 years earlier than we would get from Plato. So, who are we to believe, Plato or Diogenes Laërtius? Now, on its face this is kind of a ludicrous question. One the one hand we have perhaps the greatest philosophers who ever lived, a man of such staggering intellectual influence that Alfred North Whitehead wrote that “all philosophy is footnotes to Plato.” And on the other hand we have Diogenes Laërtius, who, I have tried to repeatedly emphasize, was a completely uncritical source and frequently didn’t have any idea what he was talking about. That said, however, while Diogenes Laërtius is happy to pass on dubious information because it tells a good story, he’s not really doing that in this case. He’s just conveying the year in which Parmenides was most active, something he presumably would have known given what was known at the time. And Plato, while he is a thinker of immense depth, was also known to bend the details in service of an anecdote. In this case his aim was not to convey the facts about when Parmenides lived, but may have just been trying to contrive a situation in which he could describe a dialog between Socrates and Parmenides to make a philosophical point contrasting their two philosophies. So perhaps, incredibly, we might be more inclined to believe Diogenes Laërtius over Plato in this one instance.

Like Xenophanes, Parmenides also wrote a philosophical text and, like Xenophanes, he did so in verse. Fortunately, more of this work has survived than the fragments of Xenophanes. His principle work is today given the title On Nature, and it’s estimated that what we have of it represents about a quarter of the complete text.

Parmenides was less interested in theology than Xenophanes, but was every bit as interested in epistemology. Although On Nature describes some astronomy, the principal problem the work is wrestling with is one of epistemology. The work is a little bit strange, almost mystical. It describes a revelation that Parmenides received from a goddess, who is unnamed but usually understood to be Dike, the goddess of justice. In a story that is later echoed in Plato’s Myth of Er, which I’ll discuss in a future episode, Parmenides is transported by chariot to a liminal space where night meets day and here is given a revelation as to the truth of all things. But the revelation of the goddess comes in two parts. First she describes what Parmenides calls the Way of Truth, which is the way things actually are. Then afterwards, she describes what is usually translated as the Way of Opinion, which is the way things appear to be, but are not. This on its own is weird. You, a philosopher, are transported to this mysterious realm and then a goddess tells you the true nature of all things, the Way of Truth — this all sounds good so far! But then, after telling you the truth of all things, the goddess goes on to tell you a bunch of lies. What’s the point of that? But after reading the Way of Truth, it becomes somewhat clearer why the goddess has done this, because the Way of Truth, as some commentators have described it, appears to be a work of insanity. The Way of Opinion is, while still a little weird, definitely more comprehensible than the Way of Truth.

The Way of Truth is, in essence, this. All things are one. The world is complete, full, a solid, unchanging, spherical mass. Motion is impossible, there are no gaps between anything. The entire universe is completely static. In this way, Parmenides is perhaps the purest of the monists. While Thales thought that fundamentally all things had their origin in water, and Anaximenes believed that all things had their origin in air, and Heraclitus fire, Parmenides does not believe that all things have their origin in a single substance. He believes that all things simply are a single substance — and any appearance to the contrary is an illusion.

Now why does he take this viewpoint? In Parmenides’s poem, the goddess says:

Listen! And carry away my message when you have grasped it!
Note the only two ways of inquiry that can be thought of:
One is the way that it is; and that non-being cannot be being
That is the path of Persuasion, Truth’s handmaid; now to the other!
this path is that it is not; and that it may not be being.\ That path — take it from me! — is a path that just cannot be thought of.
For you can’t know what is not: it can’t be done; nor can you say it.

Now, the essential message might be lost in the poetry here, but what’s going on is that Parmenides is providing the beginnings of a rational defense of his preposterous idea. The underlying assumption behind this mode of argument is that the senses are deceptive. We cannot trust what we believe to be true from our senses. Instead we must fall back on rational deduction, the path of persuasion. Only through rational deduction can we be assured that we are arriving upon real, universal truths. In this way, Parmenides could well be considered a gnostic philosopher. Although gnosticism is most closely identified with the Christian heresy of the first few centuries AD, the gnostic impulse powerful in human thought and pops up across space and time in human culture. The essential idea behind gnostic thought is that this world is a sort of prison. Our souls are constantly deceived by our bodies and the world that is apparently around us, and our goal is, through hidden knowledge, to escape the confines of our bodies in this world of shadows, to the true, transcendent reality beyond. In its development by Gnostic Christians, the world had been created not by God the Father as in Orthodox Christianity, but by a lesser, malevolent deity called the demiurge. But the figure of Jesus Christ had come into this world to impart this secret knowledge to some of his disciples so that they could escape from this world into the transcendent world created by God the Father. Perhaps the best cinematic allegory of gnosticism is the movie The Matrix, in which the protagonist, Neo, learns that the world around him is a simulation created by a malevolent figure called the Architect, and through the hidden knowledge given to him through the red pill by the Christ figure Morpheus, he can escape the false reality into the real one.

Of all the philosophers in the Western tradition, Parmenides comes closest to gnosticism, though much later on Kant, and the existentialists, Heidegger in particular, also have gnostic elements.

Well, if we cannot rely on our senses to arrive at the truth, we have to rely on rational deduction. And here Parmenides’s argument is essentially this. Only that which is, is. That which is not, is not. The void — the absence of being — therefore is not. If there is no void, then there are no spaces between things. The world is full, the world is a block. Therefore motion is impossible.

Now, this is a counter-intuitive conclusion because we clearly see around ourselves that things move. But we must always remember that our senses are deceiving us — they cannot be trusted. We have logically proved that motion is impossible — who are you going to believe, Parmenides, or your lying eyes?

This is, understandably, not especially satisfying. If the world is a static, unchanging block, there is nothing to do about describing it. Yet we demand explanations for what we see. So Parmenides grudgingly provides us with a second way of understanding the world. This cannot be the truth — we already proved what the truth was, that all is one and nothing moves. But, it is a way of understanding the world, which, while wrong, is more comprehensible to us mere mortals and is at least less wrong than other ways of understanding the world. This is the Way of Opinion. The Greek word here is “doxa”. And while “opinion” is one translation for it, another connotation for this word that is used is “verisimilitude”. Perhaps a more modern translation might be “truthiness.” So we have the Way of Truth, which is not really comprehensible to us mere mortals, and we are left instead with the Way of Truthiness. Not true strictly speaking, but given what we can know, it has the feel of truth about it.

So, what is in the Way of Opinion, or the Way of Truthiness? Unfortunately not much of this part of the poem survives, so we have to go off of the few fragments that do and references in other texts. But it seems as though this is where Parmenides described his cosmology, at least the false cosmology as it appears to us humans.

The overall structure of his cosmology is very similar to Anaximander’s. You may recall that Anaximander had what I called his “wheel theory.” In this theory, the Earth was at the center of the Universe. The Sun and Moon were not isolated spots on the sky, but it was sort of like there was a wheel centered on the Earth. We on the Earth were at the center of the wheel, looking out along the spokes to the rim on the sky. This wheel was filled with a firey air, but had a circular vent in one spot, so we only saw the Sun or Moon in one spot on the sky — the rest of the wheel was apparently invisible. Now this is kind of an unintuitive theory, and when I described this theory in Episode 10 I didn’t do much in the way of motivating it. Now, to be clear, nothing in the surviving literature motivates this theory, so we don’t really know why Anaximander came up with this idea, but taking into consideration the rest of his cosmology, we can speculate as to the reason. You may recall that in the episode about the Ionian School I spent a fair amount of time harping on the importance of Anaximander’s idea of symmetry. He argued that the Earth was suspended in the middle of the Universe and didn’t move because it was equally distant from all things and so could not arbitrarily choose some direction in which to move. But, of course, if the Sun and Moon were really discrete bodies, this would not be true. Sometimes the Moon is on one side of the Earth and sometimes on the other, and so is the Sun. So the presence of these two bodies would break the symmetry that Anaximander is relying on and could cause the Earth to move. So a plausible motivation for his wheel theory is that if the Sun and Moon weren’t just discrete bodies, but instead were extended across the entire sky, but were just invisible everywhere except one spot, we would restore the symmetry that his theory relied on. The Earth would be equally distant from every part of the Sun’s wheel and Moon’s wheel and would be stationary in the center of the Universe.

Well, Parmenides adopted an essentially identical theory, except that he used the word “wreaths” instead of “wheels.” Incidentally, the similarity of Parmenides’s wreath theory to Anaximander’s wheel theory could perhaps be taken as evidence for the more unorthodox interpretation of Xenophanes’s cosmology that I described earlier. Since Parmenides studied from Xenophanes and Xenophanes studied from Anaximander and both Parmenides and Anaximander had substantially similar cosmologies, it should perhaps be expected that this was also the cosmology of Xenophanes, the philosopher between those two. Now, Parmenides distinguished between three kinds of wreaths. Some wreaths were filled with fire, others were filled with condensed matter, and a third kind was filled with a mixture of the two.

As to what kinds of wreaths correspond to which celestial bodies, things get somewhat unclear. But a plausible interpretation of the fragments we have is that there essentially five distinct shells. In the center of the Universe, of course, is the Earth, which is made of condensed matter. Above it is the atmosphere, which is made of the firey material. Beyond the atmosphere there are the wreaths corresponding to the different celestial bodies, the Sun, Moon, planets, Milky Way, and stars. These wreaths have a different proportion of fire to condensed matter which is why the Sun, Moon, and stars appear so different. Then beyond these wreaths, there is another firey shell, and immediately beyond that is a final shell of condensed matter which is called Outer Olympos and represents the edge of the Universe.

The key in interpreting the texts that describe this cosmology is a preposition that can apparently be translated either as around or under. So in one reading we have a firey shell around a shell made of condensed matter, and this is taken to be the atmosphere around the Earth. But in an alternative reading, this firey shell is under the Earth, in which case it may have been added to explain volcanoes and hot springs.

Now I passed over an important detail as I was describing this cosmology, but one feature of his cosmology was that he held the Earth to be spherical. From what we know, Parmenides probably had no observational reason to suppose that the Earth has this shape, but probably arrived at it through its symmetry. After all Anaximander’s cosmology is very elegant with the Earth suspended in the center of the Universe through its equidistant position with respect to the circular hoops of the other bodies of the universe. But a wart on this theory is that in this perfectly symmetric system, the actual shape of the Earth itself is a cylinder, which is far from being perfectly symmetric. By substituting a sphere for a cylinder, Parmenides removed the most asymmetric component of the theory.

The fact that the Earth appears flat to us standing on it and yet is in reality round — or at least in the reality of Parmenides’s Way of Truthiness — is really quite in keeping with his overall epistemology, that our senses deceive us and are not to be trusted. Our eyes tell us the world is flat, but it is not so.

Now, Parmenides is not the only ancient astronomer to be credited with being the first to claim that the Earth is round. Some sources also claim that Pythagoras was the first to make this discovery. But given how foundational this idea is to all of astronomy, it speaks to Parmenides’s standing as an astronomer that he was at least considered to be a contender in having first claim to the idea. And this isn’t the only foundational astronomical discovery that is disputed, but among which some sources credit to Parmenides. Some sources claim that he was the first to recognize that the morning star and evening star are the same object, namely Venus. And finally Aëtius says that Parmenides was the first to recognize that the phases of the Moon are due to the changing reflection of light from the Sun on the Moon.

Now, on the one hand this is an idea that is entirely in keeping with the philosophy of Parmenides. We see with our eyes the Moon change every night. It waxes into a full moon, and then wanes and disappears before starting the cycle over again. But according to Parmenides, nothing is really changing. Once again, our eyes our deceiving us. This phenomenon is just an illusion of light casting shadows on a sphere. At the same time, however, this idea does seem to contradict Parmenides’s wreath idea. In this wreath model, what we see as the Moon is just a vent in the overall wreath that exposes us to the mixture of fire and condensed matter within. So there is no surface on which to cast shadows. Given the sources we have it’s hard to reconcile these.

The last discovery of Parmenides that I’ll recount is the idea of the climatic zones of the Earth. This is really a consequence of Parmenides’s idea that the Earth is spherical. As a sphere, it must have a north pole and a south pole, along with an equator and Parmenides seems to have understood that the climates in those various locations would be very different from each other. In particular, he divided the globe into five zones, which we still have to this day. There are the two polar zones around the north and south poles also sometimes called the frigid zones, then there are the temperate latitudes, and in the middle are the tropics, which is also sometimes called the torrid zone. Now, the locations where Parmenides divided the globe were probably somewhat different than the modern day division. In his system it seems like the tropical zone was about twice as large as it is in the modern map. But the basic idea that the polar regions would be very cold and the tropics very hot was a direct prediction of his theory that the Earth was spherical turned out to be fundamentally correct.

Well, there is one other philosopher of the Eleatic School whom I’ll talk about — Zeno of Elea. Now, of all the Eleatic philosophers, Zeno is by far the most famous. Today most students of physics have heard of Zeno’s Paradoxes, but strictly speaking, Zeno does not really belong in a podcast about the history of astronomy because unlike Parmenides, he did not really have anything to say about astronomy. However, his paradoxes were so influential on the development of calculus and physics, which, in turn, later impacted astronomy, that I feel like it is appropriate to spend a little time on him here.

Now you may recall from earlier when we were talking about when Parmenides lived that Plato had told a story when Parmenides and Zeno visited Athens and conversed with a young Socrates. Plato tells us that at the time Parmenides was 65 and Zeno was 40. So if Plato’s account is historical, and that’s a big if, this would put Zeno’s birth at around 490 BC, though, as I mentioned, this dating conflicts with some of the information given to us by Diogenes Laërtius, so it may be off by as much as thirty years.

As is usually the case, Diogenes Laërtius gives us some entertaining stories about Zenos’s life, though who can say how accurate they are. In Diogenes Laërtius’s telling, Zeno entered into a conspiracy to overthrow the tyrant of Elea. Unfortunately Zeno was captured and tortured to reveal the names of his co-conspirators. He eventually relented and told the tyrant that the conspiracy had been organized in such a way that he did not know they names of the other members of the conspiracy. But he nevertheless had information that would be useful to catch the other conspirators. Zeno then became quiet, as though he was losing his power of speech. When the tyrant leaned in to hear what secret Zeno had to tell, Zeno bit the tyrant’s ear off. In a much later source, an author tells this story in a way reminiscent of the story of the Pythagoreans Mylias and Timycha. In order to prevent himself from revealing the names of his co-conspirators, Zeno bites off his own tongue and spits it out before the tyrant.

Well, as I mentioned, Zeno is by far best known for his paradoxes. These mostly come to us through Aristotle’s Physics. There are a number of paradoxes, and it’s probably the case that not all of them survive to today, but three in particular are the most well known and have had the most influence on the development of calculus and physics. The first of these is what is sometimes called the Stadium Paradox, or the Paradox of the Dichotomy. The idea is this. Suppose that you are running from one end of a stadium to another. Zeno claims that this is impossible. Because if you are going to run from one end to the other, this means that you need to first traverse through the halfway point. Then when you are at the halfway point, you need to go halfway from where you currently are to the end. Then when you are at that point, you still need to go through a point halfway from where you currently are to the end. And so on ad infinitum. You must complete an infinite number of steps in order to get to the end, and because this cannot be done, you can never reach the end of the stadium. But of course, going from one end of the stadium to the other is an arbitrary choice. The two points you want to go between could equally well be arbitrarily close together. Since you cannot go from one point to another, all motion is impossible.

Zeno makes a similar point with another paradox, Achilles and the Tortoise. The scenario is that Achilles, the fastest runner in the world, is in a footrace against a tortoise. The tortoise, however, has been given a head start. Zeno claims that Achilles can never catch up to the tortoise. Because when Achilles starts running, he must first run to the point where the tortoise was when he first started running. But by the time he arrives at that point, the tortoise has advanced somewhat. So now he must run to that somewhat more distant point. But by the time he gets there, he finds that the tortoise has advanced still further. So he must continue running until he gets to that point, by which point the tortoise has moved still further ahead and so on. No matter how many times this process is repeated, Achilles finds that the tortoise is always slightly ahead of him.

The final paradox I’ll mention is what is called the Arrow Paradox. Consider an archer who has shot an arrow through the air. Zeno claims that the arrow is not moving. For consider the arrow at some instant in time. It is simply suspended at one location in the air. Now consider it at some other instant in time. It is now suspended in that location in the air. At any instant in time, there is no motion, for the appearance of the arrow is identical to that of an arrow which is not in motion. The arrow is simply suspended motionless at different locations in different points of time. Somehow the motion is occurring between instants, which by definition, are at no points in time. Therefore motion is impossible.

Now, these paradoxes were really the first serious attempt by philosophers and mathematicians to grapple with the concept of infinity, and it took centuries to work them out. It wasn’t until the development of calculus in the 17th and 18th centuries AD that mathematicians started to feel like they had a reasonable resolution to these paradoxes, and even then, problems about the nature of infinity continued to bedevil mathematicians and logicians well into the 20th century. But, from the modern mathematical perspective, Zeno’s paradoxes in particular are no longer considered to be a problem. In the case of the Stadium Paradox, the modern mathematician simply says that although you are passing through an infinite number of halfway points, each time you do this takes half the time of the previous step. So the total time it takes is the sum of 1/2 plus 1/4 plus 1/8 and so on to infinity. But this series converges to the number two. So even though there are an infinite number of terms in the series, the sum is nevertheless finite, and there’s no problem here. The paradox of Achilles and the Tortoise has a similar resolution.

In the case of the Paradox of the Arrow, the modern physicist would say that the velocity of the arrow is defined to be the distance traveled by the arrow divided by the time it takes to travel that distance in the limit that the distance goes to zero. In other words, it is perfectly well defined to have two objects with the same position at some point in time, but different velocities.

Now, this solution is not entirely satisfactory, because in Zeno’s telling, we are only allowed to consider the arrow at a single instant in time. How can we tell that it is moving in that particular time? If we cannot tell that it is moving at any particular instant of time, we cannot tell that it is moving at any time at all, since time is composed of nothing more than a sequence of instants. For those listeners who have had some calculus, the question is essentially, is it possible to have two functions, which have the same values at all points, but different derivatives everywhere? One way of dealing with this problem in modern mathematics is with the concept of the surreal numbers. The surreal numbers actually harken back to a concept that was originally developed during the invention of calculus and later discarded as calculus became more formalized in the 19th century. This is the idea of the infinitesimal. In casual use, an infinitesimal just refers to a very small number, but in a strictly mathematical sense, an infinitesimal has a very specific meaning. An infinitesimal is the smallest positive number. In other words, it’s the next number after zero. Now, this is not a valid concept in the standard system of real numbers, because there is always a real number between any two real numbers. So if you were to pick some real number and declare it to be the smallest possible positive number, I could come back to you and give you that number divided by two. That is also a positive number and it’s smaller than yours. So the infinitesimals are not real numbers but are an extension of the real number system. By augmenting the real numbers with the infinitesimals along with infinity as a well defined number in its own right, we end up with the surreal numbers, or depending on the details of how we do this, the hyperreals. The picture is essentially that every real number is flanked by a pair of infinitesimals, one infinitesimally lower and one infinitesimally larger. Then we can answer Zeno by defining motion to be how the position of the arrow changes infinitesimally across an infinitesimal amount of time. These infinitesimal changes, are, in a loose sense, in a different dimension that ordinary changes in time since they’re not happening across real numbers. So, that is another way that a modern mathematician might answer Zeno about his arrow.

These kinds of resolutions are, I think, how most scientifically minded people who have encountered Zeno’s paradoxes treat them. Useful for the development of calculus, but are now solved. However, notwithstanding the useful impact these paradoxes did in fact have on the development of calculus, this treatment does, I believe, actually miss the underlying philosophical point that Zeno was making. Even if the mathematical and physical issues have been resolved, the philosophical issues are just as open as they were in the 5th century BC.

First of all, Zeno almost certainly developed his paradoxes in defense of Parmenides’s philosophy of the Way of Truth. Remember that Parmenides had argued that all change that we see is an illusion. All things are one, and all movement is impossible. Other philosophers had disputed this conclusion and tried to demonstrate its absurdity through paradoxes that would emerge if no motion occurred. So Zeno developed a series of paradoxes of his own to show that the concept of motion is a logical impossibility. Although our eyes appear to show us motion, it is necessarily an illusion.

This conclusion is not only a defence of Parmenides’s philosophy of the unity of being, but it’s also a refutation of the Pythagoreans, who remember, believed that all things were number and that from the number one proceeded all subsequent numbers. In the broadest terms, Zeno’s paradoxes show the logical inconsistency of moving from the one to the many. The Stadium paradox and Achilles and the Tortoise demonstrate the impossibility of going from many to one — how is it possible to compose a single quantity of an infinite number of constituents? And the Arrow paradox demonstrates the impossibility of going from one to many. We can have a single instant. But there is no purely logical derivation that can go from an instant to the concept of motion, which spans a continuum of instants. At their logical core, Zeno is essentially expressing a tautology. One is one. Many is many. Many is not one and one is not many. It is therefore impossible to go from one to many or from many to one. If the universe begins as one, it cannot become many.

One approach in handling the metaphysical implications of Zeno’s paradoxes in modern philosophy is with the concept of the supertask, developed by James Thomson in the 1950s AD. A supertask is an infinite series of events within a finite period of time. So in this sense, in the Stadium paradox, running across a stadium is a supertask, because one must traverse an infinite number of halfway marks in an finite period of time. Now, Zeno, being an Eleatic argued that such a task was impossible to complete, and therefore concluded that the concept of motion produced a logical contradiction and was an illusion. Few people today, even among philosophers, who are known to believe some wacky things, believe Zeno on this point. But that does not mean that all supertasks are possible. James Thomson proposed a philosophical experiment known now as Thomson’s lamp. The idea is that there is a lamp with a light switch. At the beginning of the experiment someone switches the lamp on. After one minute, they switch the lamp off. Then half a minute later, they switch the lamp back on. Then a quarter of a minute later the switch it back off, and so on. The lamp is switched on and off exponentially faster. Finally the experiment ends after two minutes. Is the lamp on or off? Now you might object that such an experiment is physically impossible, no one can toggle light switches this quickly, that it violates the laws of quantum physics or relativity, but this misses the philosophical point. In a philosophical thought experiment, you have to grant the philosopher the premise of their argument. This is not making a point about physics, it’s making a point about metaphysics. What would have to be true regardless of the physics of our universe? We can conceive of this experiment as being possible, so what would happen if it were? Thomson argued that even if the laws of physics in principle permitted us to perform such a supertask, it would yield a logical contradiction. Thomson writes:

It cannot be on, because I did not ever turn it on without at once turning it off. It cannot be off, because I did in the first place turn it on, and thereafter I never turned it off without at once turning it on. But the lamp must be either on or off. This is a contradiction.

From this Thomson concludes that such a supertask is impossible, even in principle. But if motion, which is apparently also a supertask, is logically possible — despite Zeno’s objections — then which supertasks are possible and which supertasks are impossible?

Well, as is the danger with Zeno, we are starting to drift a little far from astronomy. Now, of course, no one today really believes the Way of Truth proposed by the Eleatic philosophers, that all things are one and that the variety of objects and changes we observe are nothing but an illusion. But even in the time of the ancient Greeks, this idea was regarded skeptically. But one of the reactions against this idea led to one of the most profound scientific ideas of all time.

Two philosophers by the names of Leucippus and Democritus looked at the logic of Parmenides’s argument that all things were one. Remember that it went like this: what is, is. What is not, is not. By definition, the void is not. Therefore the void does not exist. Therefore the world is a block and motion is impossible. Leucippus and Democritus turned this argument on its head. The started from the observational fact that motion does exits. Therefore the world is not a block. There must be void between matter to enable motion. Therefore, matter comes in discrete units. Therefore, matter consists of atoms. So from this apparently preposterous argument from Parmenides, we ultimately end up with atomic theory.

But, this is a tale for another full moon. I hope you’ll join me then. Until the next full moon, good night, and clear skies.

Additional references

  • Popper, Karl: The World of Parmenides, 1998
  • Papa-Grimaldi, Alba: Why Mathematical Solutions of Zeno’s Paradoxes Miss the Point, 1996