Special Guest Paradoxes!

Hello friends!  I’m on vacation after finishing a very long crunch period that produced, mirabile dictu, a first draft of The City’s Thirst, my next Choice of Game, which is about hunting water rights for Dresediel Lex in the years after the God Wars. Bit of Western, bit of Noir, bit of giant scorpions, a skeleton or three, a roving reporter—all sorts of fun.

Things are Afoot in the Wider Internet.  Specifically, a ring of book bloggers are running a readalong of Three Parts Dead!  Which is a lot of fun, and if any of you want to catch up, or just to see what some folks reading the book for the first time have to say, definitely go and give them a shot.  Here are some links to the first third of the readalong: Lynn’s Book BlogOver the Effing RainbowViolin in a VoidOn Starships & DragonwingsThe Bastard TitleLittle Lion Lynnet’s, and Dab of Darkness.  I’m a storyteller at heart, and I love the notion of people reading my books and then mulling over them.

But since I’m on Vacation this week, I don’t have an essay of my own to share with you.  To make up for it, I’m going to share an essay my friend Matt Michaelson wrote about paradox, authoritarianism, worldviews, and progress.  I hope you like it!


I would like to tell you some stories of long ago and far away, which have more power over us than we know. One is about a man named Gongsun Long. He can be said to have witnessed none of the things he hoped for. Another is about someone you may have heard of, named Zeno.

The best known story about Zeno is that he wrote something called “Zeno’s Paradox”, which in the story you know may not be described in detail. In fact according to other stories, Zeno is said to have written of more than 40 paradoxes, of which nine come down to us today secreted away inside the shells of harder-to-kill texts. Zeno was tall and fair-haired. He was a teacher and a student. Pericles sat at his lectures. In Plato, he argues Socrates to a standstill. He died trying to kill the Tyrant of Elea, his home.

If the name Zeno’s Paradox refers in popular consciousness to one in particular, it probably refers to The Dichotomy. More or less: To cross a distance, first you must cross half that distance. To cross half a distance, first you must cross half of that. And so on. How can you cross any distance at all? And yet of course you do.

This, along with Zeno’s other paradoxes, was said to be a defense of Zeno’s mentor (and perhaps lover) Parmenides. Many thinkers disputed Parmenides’ arguments about the nature of reality. But, wrote Zeno, if you believe all of what you’re saying then how can you refute The Dichotomy?

Over the centuries this challenge was taken up, Zeno’s paradoxes have been taken as jokes or an affront. Obviously wrong for this reason. Or for that. And anyway what is the point? It has no depth. It’s a trivial game of words. You cannot speak of infinity in the way Zeno does, wrote Aristotle. It is terribly wrong. The charitable might admit his paradoxes were mystical. But certainly there was a limit to what anyone could say about them.

Graham Priest:

An abhorrence of contradiction has been high orthodoxy in the West for more than 2,000 years. … As Avicenna, the father of Medieval Aristotelianism, declared:
“Anyone who denies the law of non-contradiction should be beaten and burned until he admits that to be beaten is not the same as not to be beaten, and to be burned is not the same as not to be burned.”

Zeno died having failed to persuade the world of Parmenides’ truth or to kill the man who despoiled his city. One story goes that he was the kind of man who, in failure, held back by the tyrant’s men, with nothing left, bit off his own tongue with his teeth, and spit it in his enemy’s face.

Some part of Zeno’s work, which no one knew how to understand, was never wholly lost. And since the development of calculus, and especially since mathematicians and philosophers developed transfinite math, analytic philosophy, and forms of logic Aristotle did not know — since then the learned of the west have started to think of Zeno’s paradoxes somewhat differently. Not just outdated or mystical ideas. Perhaps something useful; an intuition pump. 19th century mathematician Karl Weierstrass’ analytic methods, which form the basis for the math of real analysis, can propose a very serious “solution.” Georg Cantor was partly inspired by Zeno to develop his math of numbers larger than infinity. It is now possible to speak, with analytic rigor, of how a person crosses a distance. It is possible to speak of types of infinity. It is possible to say, thanks to scholars who stood on Zeno’s shoulders, what type of infinity is described in his paradoxes, and some of the things that type of infinity can and cannot do. The Dichotomy is now widely taught in the humanities, the arts, the sciences, and in math. By the 20th century some paradoxes had become tools.

The story of Zeno’s life and work is a story about beauty in an unexpected depth. There are further depths.

In Zeno’s day the philosophies of the non-Greek world were just as rich. I do not know enough about them. But I know that if you want to see the world differently, go to another country and learn to see the world as they do there. Even among the things you both share, certain ideas may be larger or smaller. The Law of the Excluded Middle was smaller in the ancient east, and Synthesis was larger. Kant’s noumenal was larger, and Zeno’s Paradox was smaller. It is a sad story why Zeno’s Paradox was smaller. It brings us back to the beginning, and to ancient China.

Gongsun Long lived in a time when war was common and few could read. Rome fought the Samnites. Ashoka conquered the lands of the Indus, the Ganges, and the Kalinga. Doomed Qi was hegemon in the far east.

Nobody now knows very much about Gongsun Long. He was a student of the rites, and the old kings. He was a traveler. He enjoyed the patronage of noble men. He was said to be a member of the School of Names and a follower of Master Mo. He spent his life creating word games and advocating an end to war. Some of Mo’s followers — Mohists — were the sort of people who, if conquerors would not lay down their arms, would arm the conqueror’s enemies and fight on the side of any who could not defend themselves. Gongsun Long likely did not fight or design weapons for the downtrodden. At the court of a local lord in a small northern kingdom, he argued for peace in his time. He thought. He took students. It is given to us that the products of Gongsun Long’s teaching were recorded, written by his hand or his students’.

Statues overturn and the things bright people build disappear. Of his books, six short scraps of characters survive attached to his name, buried in fakes and attempted reconstructions by medieval scholars a thousand years after his death. That was another dangerous age, and there were more after it. Today those medieval savants’ copies are themselves incomplete.

Like other Mohists, Gongsun Long wrote about argument and about logic. Of the remains, however, only perhaps two or three short items are truly his. They are mentioned in the Chinese canon in much the way Zeno is mentioned in Aristotle. A thorn in the palm, to be pulled. So many, many scholars attempted the removal, but the more who tried, the less likely they were to succeed in forgetting him. Master Zhuang mocked Gongsun Long along with other Mohists. In Master Zhuang, of course, to be mocked and to be upheld are not necessarily dissimilar.

Before the establishment of the Empire of All Under Heaven, Mohists and Confucians competed for influence in the courts of the Nine Countries (though nine was merely a traditional number, and the true number varied). After the establishment of the empire, books were burned and thinking was consolidated, and the organs of the state sided with the Confucians.

Bulgakov said that manuscripts do not burn. Shakespeare himself noted, however, that time would come and take his love away.

Much was forgotten of Mohists, perhaps more than any the other Hundred Schools. More than Zeno in the west, their work was said to be trivial, sophistic, or simply useless in the construction of ideologies of power. People decided to say such things, to forget the words, or to burn the work and cut out tongues. Even before unification, it is written that the men of Jixia Academy in doomed Qi did not approve of Gongsun Long. No less a great player of the game of kings than Lord Shang Yang, who dreamed of totalitarianism long ages before the word was first spoken, who built the war machine that ended the 800-year Zhou Dynasty, who designed new punishments for the masses and said none would be above them and was executed in his own fashion along with everyone he ever loved — he took from the Mohists the idea of collective responsibility and made it a tool for the state to control people. He was worse in his way than the Eastern Han ministers of the left and the right who sided with the Confucians, and burned Mohist books. I do not know their names. They did not entirely succeed. But Shang Yang is still quoted in the halls of Chinese power to this very day. He took what the Mohists made to be a defense against conquerors and used it to conquer things they held dear.

Today of the writings and deeds of the Mohists there remains very little, and there remains of Gongsun Long more or less only one paradox, which is called the Discourse of the White Horse. A white horse is not a horse, it says.

???: ??????????
[A]: Can it be that a white horse is not a horse?

[B]: It can.

[A]: How so?

[B]: “Horse” is how the shape is named; “white” is how the color is named. That which names color does not name shape. Thus I say: “a white horse is not a horse”.

For a long time the wrongness of this was a given and arguments attempted to brick over it. Or perhaps it was a joke or an insult. You may have the same reaction. But to you and all the scholars of dead dynasties who turned away I say: there is beauty in unexpected depths.

Recently, some scholars in the west have applied new types of logic or analytic philosophy to the white horse who is not a horse. Mathematicians who study what it means for things to be equal — scholars of isomorphism — have become interested again. Like infinity, sameness comes in different kinds, and there is much work to be done to study how it works in different fields. I wish I knew more about it, just like I wish I knew more about the Buddha.

Graham Priest again:

When Western philosophers look East, they find things they do not understand – not least the fact that the Asian traditions seem to accept, and even endorse, contradictions. Thus we find the great second-century Buddhist philosopher Nagarjuna saying:

The nature of things is to have no nature; it is their non-nature that is their nature. For they have only one nature: no-nature.

The Buddha argues that existence does not end, that there is no self, that suffering exists but is an illusion. There is much to be said of this beyond what I can write here. It is enough to say that Buddha’s is a vast country.

Many of the learned in the west have called the philosophies of the east “illogical.” Some have said philosophy as such is a product of the west and the west alone. Heidegger said that only Greek and German were languages sufficient for philosophic thought. Over time, translations were made. By Russel and Cantor’s time, serious responses were being made, and admixtures. Deep relationships were formed. Schopenhauer obsessed over the Upanishads. Jung loved the Yi Jing. Perhaps you expected the depth here.

I want to ask you something now. Do you know who Nagarjuna is? Do you know why the world is on fire? Do you know whether a white horse is a horse? Do you know of every great paradox humans once thought they knew?

Sometimes it is said that we in our age have a poor understanding of what progress is. It cannot simply be that money or volume or even a scalar index of human health can capture the essential thing about what is happening as time passes. Are we richer? Are we warmer? Are there more of us? Are we more happy? More free? Messrs. Zeno and Gongsun Long share a number of things in common, from a certain point of view.  They were each relatives of a movement that failed, and thoughtful men with principles. They died failures, and their work was hounded across the world. They are of course different, and well that it is so. Gongsun Long reminds me very much of Bertrand Russel as well, in a rhyming sort of way. If there is such a thing as progress, is that what progress is? Could it be exactly that which makes it so that Bertrand Russel’s pacifism and paradoxes were not abhorred but studied? I can write to you all of Master Mo and Gongsun Long and no political event in my imagining could lead to my being killed for this. I can think to myself that, as ridiculous as it sounds, I am not at all put out that the NSA might collect my tired ramblings to use for some purpose no one yet knows. I do not know.

I feel optimistic, however, because it seems that some beautiful ideas can survive against ignorance, contempt, or misuse.

One Response to “Special Guest Paradoxes!”

  1. nrlymrtl

    Thanks for the mention of the read along! Some fascinating world building going on in the first 3rd of the book – and great discussions.


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