Nagarjuna’s Tetralemma: Zen Math Will Never Add Up

Nagarjuna’s four propositions tell us that something may be what it is or it may not; it may be neither or it may be both. This is Zen math.

By Judy Roitman

Image via Alamy.

There is only one thing from the very beginning, infinitely bright and mysterious in nature. It was never born and never dies. It cannot be described or given a name.

But originally there is no thing, no light, no dark, no birth, no death, nothing to be named and no one to name it.

Yet 0 = 0, 1 = 1, 2 = 2, in daytime it is light, at night it is dark, my name is Judy, my husband’s name is Stan.

Formal dharma speeches in the Korean tradition often begin with three introductory comments, which generally fit into a form that can be traced back to the early first-millennium Buddhist sage from India, Nagarjuna, who deeply influenced all of north Asian Buddhism—Mahayana and Tibetan—with his relentless and meticulous philosophical exploration of shunyata, emptiness, and pratityasamutpada, or codependent origination. His arguments, rich with ethical implications, point us to a freedom beyond categories.

Nagarjuna’s method of liberation is threefold: to look carefully at language and thinking, completely deconstructing them so that nothing is left; to point to our original mind by exhausting the contradictions of our ordinary, thinking mind; and to reveal the inherent contradictions we face every time we try to speak. Every time we try to say something, we are making a big mistake—we are pointing away from truth. Nagarjuna’s method is to analyze things so closely that our discursive thought just vanishes. When, as he says, “emptiness is the relinquishing of all views,” what are we then left with?

There is a vast literature analyzing Nagarjuna’s thought. But how can we manifest Nagarjuna’s teaching directly? This is exactly the purpose of those quirky little stories that form Zen’s basic texts: to challenge us to respond right now, with no hesitation, neither forgetting the profound ethical possibilities of pratityasamutpada nor the falseness of any categories we use to analyze reality.

Central to Nagarjuna’s technique is the tetralemma—essentially, a dilemma with four options—otherwise known as the four propositions. The tetralemma traces back to ancient India and the sixth-century BCE Jain sage Sanjaya, possibly earlier. There are many ways to express the tetralemma. Here’s one:

X is Y, Y is X.
X is not Y, Y is not X.
No X, no Y.
X is X, Y is Y.

In case you were traumatized by your middle school algebra class (full disclosure: I’m a retired math professor), another way to understand this is by taking two arbitrary nouns—I’ll pick form and emptiness because that’s traditional—and substitute them for X and Y:

Form is emptiness, emptiness is form.
Form is not emptiness, emptiness is not form.
No form, no emptiness.
Form is form, emptiness is emptiness.

We can summarize the first line as 1, the second as not 1, the third as 0, and the fourth as 2.

Going back to the first three lines of my talk, then, we have:

There is only one thing from the very beginning, infinitely bright and mysterious in nature. It was never born and never dies. It cannot be described or given a name.

These first lines are also the opening lines of the great sixteenth-century Korean master So Sahn Hyu Jong’s Mirror of Zen. They point to 1.

But originally there is no thing, no light, no dark, no birth, no death, nothing to be named and no one to name it.

This negates everything from the first line, much as the Heart Sutra negates the classifications of the Abhidharma (the extensive Buddhist analysis of mind attributed to Buddha’s disciple Shariputra). This points to 0.

Yet 0 = 0, 1 = 1, 2 = 2, in daytime it is light, at night it is dark, my name is Judy, my husband’s name is Stan.

This negates the negation. As one version of what the Buddha said when he woke up has it, each thing is exactly what it is, complete in itself. This points to 2, which in this context means 2 or more.

Here we find the unmistakable stamp of Nagarjuna: three-fourths of the tetralemma shaping a rhetorical form that has lasted into the twenty-first century.

There is a story from the early Transmission of the Lamp records about the eighth-century Chinese master Shi Tou. In this story a young monk, Ya Shan, comes to Shi Tou and says, “I understand the Buddha’s teaching. But I heard that around here, you all just sit in silence. What does this mean?” And Shi Tou says, “This way won’t do. Not this way won’t do. Both this way and not this way won’t do. How about you?” (Hearing this story, Ta Hui’s great female dharma heir Miao Tsung awakened.)

Again, we have three-fourths of the tetralemma, in a different form: X; not X; and neither X nor not X. The part left out is: X and not X.

The story of Shi Tou and Ya Shan brings us to the middle way (which is what Madhyamaka, the school Nagarjuna founded, means). This middle way is not about living your life between the extremes of asceticism and luxury; it is a philosophically technical stance with vast ethical ramifications. “Is” is false; “is not” is also false; “is and is not” is false; “neither is nor is not” is also false. You cannot assert any of them. You can’t assert anything. Each statement of the tetralemma is, respectively, false, false, false, and false again. This holds true for any form the tetralemma might take. It also holds true for any view you might hold.

The great Zen monk Mu Mun expressed this clearly in his response to the thirty-seventh case of The Gateless Gate. In this case, a monk comes to the great Zen master Zhao Zhou and asks, “Why did Bodhidharma come to China?” Zhao Zhou answers, “The cypress tree in the garden.” Mu Mun responds with this poem:

Words cannot show truth.
Speech cannot point into nature.
One who holds words is dead.
One who attaches to sentences is lost.

Does this seem a little extreme? It’s not. Look carefully at how sentences, any sentences, are constructed, and there is always a problem. “I am standing here. You are sitting there.” By the dictates of English grammar (and every language has its grammatical exigencies), we’ve got I, you, standing, sitting, here, there. The specific grammatical demands of Navajo or Bantu might be different, but they are there, guaranteed.

And grammar necessarily distorts things. Nagarjuna’s methodology is to point out the distortions. How can there be a “here” without a “there?” How can there be a “there” without a “here?” How can we distinguish here from there? Where does here begin, where does there end? And so on.

Consider, for example, the tenth chapter in the Mulamadhyamakakarika, “On Fire and Fuel.” Nagarjuna shows that fuel cannot be fire and fire cannot be fuel, but fuel cannot not be fire and fire cannot not be fuel. Fire cannot be dependent on or independent of fuel. Fuel cannot be dependent on or independent of fire. He writes:

I do not think that
Those who teach that the self
Is the same as or different from the entities
Understand the meaning of the doctrine.

Such seemingly dry logic has profound ethical consequences—this is Nagarjuna insisting on codependent origination, or dependent co-origination, or interbeing, or interpenetration, or whatever you want to call it. You can’t assert anything because assertions necessarily separate, and things are not separate. It is our actual perception—not intellectual analysis, but direct perception—of no separation that truly reveals and necessitates ethical behavior. Nagarjuna’s logic invites us past our own ideas and into that direct seeing.

Nagarjuna explores his logic in meticulous detail. He uses language to go deep into a substrate that is more fundamental than language or ideas. Everything in the universe—what we know and what we don’t know, what we’re aware of and what we’re not aware of—everything comes together like that, before speech, before thinking, no distinctions, impossible to name, impossible to describe—and yet you cannot call it nothing.

Or, as the Mirror of Zen, paraphrasing the The Sutra on the Questions of Brahmavisesacinti, says, “The Buddha did not appear in this world to save sentient beings. Rather, the Buddha appeared in order to liberate this world from the mistaken view that there is life and death, and nirvana or salvation.”

One can make the case that any kong-an (Jpn. koan) is designed exactly to help us navigate this middle way, rejecting “is,” “is not,” and all the rest of the tetralemma. In one famous example, a monk asks Zhao Zhou, “Does a dog have buddhanature?” Zhao Zhou replies, “Mu,” which means “no,” and this mu has rung down for over a millennium, itself an object of deep inquiry. But asking, “What is mu?” is different from asking, “Does a dog have buddhanature?”

How could you answer this second question? Here’s a hint: “Yes” won’t do. “No” won’t do. “Yes and no” won’t do. “Neither yes nor no” won’t do. As Shi Tou says: How about you? In that moment, asked that question, how can you respond?

Similarly, when asked, “Why did Bodhidharma come to China?” Zhao Zhou responded, “The cypress tree in the garden.” Bodhidharma was, in legend and possibly in fact, the Indian monk who brought Zen to China, but Zhao Zhou did not answer, “To spread Zen Buddhism!” This would have missed the point.

Which brings us to the way in which Zen deals directly with Nagarjuna. Doing so involves a bit more math in the form of the “one hundred negations,” but we needn’t spend much time on it. (According to Shunryu Suzuki, we arrive at one hundred negations by negating the singular, plural, existing, and nonexisting versions of all four logical forms from the tetralemma, multiplying by three for past, present, and future, then multiplying by two—nuomenal and phenomenal—and adding the original four: 4 x 4 x 3 x 2 + 4 = 100.)

Every time we try to say something, we are making a big mistake — we are pointing away from truth.

Consider the twenty-fifth case of The Gateless Gate. In a dream, Yang Shan goes to see Maitreya Buddha. Everyone is already seated in meditation, and Yang Shan is directed to the third seat. This is a very high seat, the third seat. It’s not the first, not the second, but still, it’s pretty good. So he sits in the third seat and an announcement is made: “The talk today will be given by the monk of the third seat.” Unfazed, Yang Shan gets up, hits the table with the gavel, and says, “The dharma of the Mahayana goes beyond the four propositions and transcends the one hundred negations; listen carefully, listen carefully.” The four propositions and the one hundred negations—that’s a direct reference to Nagarjuna.

Consider also the seventy-third case of the Blue Cliff Record. In this case, a monk says to Ma Tsu, “I’m not asking you about the four propositions and the one hundred negations. But please tell me why Bodhidharma came to China.” Ma Tsu answers, “I’m tired today and can’t explain it to you. Go ask Xi Tang.” So the monk goes to Xi Tang, who says to him, “Why didn’t you ask Ma Tsu?” The monk says, “I did! But he told me to ask you.” Xi Tang says, “I have a headache today and can’t explain it. Go ask Bai Shang.” So the monk goes to Bai Shang who says, “I don’t have anything to say about this.” The monk goes back to Ma Tsu, tells him the whole story, and Ma Tsu says, “Xi Tang has white hair and Bai Shang has black hair.”

Yang Shan, in his dream, says, “The dharma of the Mahayana goes beyond the four propositions and the one hundred negations.” Going beyond the four propositions and the one hundred negations is exactly what Ma Tsu does when he says, “Xi Tang has white hair and Bai Shang has black hair.” In fact, he went beyond them earlier when he said he was tired, as did Xi Tang when he said he had a headache, as did Bai Shang when he said he had nothing to say.

Like those Chan monks and masters up in the Chinese hills a thousand years ago, Nagarjuna did not always live in abstractions. He was a famous guy after all, an advisor to kings. In one famous letter to a patron, he wrote in graphic detail about the suffering or pleasure that results from negative or positive rebirth. But it is his abstractions that have the power to change our lives.

Since I discovered the Mulamadhyakakarika, it has been my companion on solo retreats. When obsessions, fears, distractions take over—and over weeks or months they will, guaranteed—to be reminded that “is” is not, “not is” is not, “is and is not” is not, “not (is and is not)” is not, this is liberation, this is the way out of the hells we so easily fall into. “Oh, it isn’t like that.” Whatever it is, it isn’t like that. And when you think it’s something else, it isn’t that either. My teacher, Zen Master Seung Sahn, called this don’t know: “Just keep this don’t know mind!” Then, like Ma Tsu, we can see that Xi Tang has white hair and Bai Shang has black hair. We know when to step forward and when to step backward. We know when to reach out a hand and how to use it. Subject and object no longer blind us; the interpenetration of all beings becomes completely ordinary. Everyone has moments like this. And then everyone forgets. Nagarjuna reminds us, with all his negations: oh, yes, this.

Judy Roitman

Judy Roitman

Judy Roitman (Zen Master Bon Hae) began practicing Zen in 1976 with Zen Master Seung Sahn at the Cambridge Zen Center. Two years later, she helped found the Kansas Zen Center with, among others, her husband Stan Lombardo. She was granted authorization as a teacher (inka) in the Kwan Um School of Zen in 1998 and received dharma transmission in 2013. She has also had a long and distinguished career as a professor of mathematics (although now retired from academic life) and as a poet.