Catuskoti

[thilo]

Hello,
I hope this is the right place to post this.

I just read an interview with Graham Priest (https://tricycle.org/article/the-logic-of-paradox), a philosopher with a PhD in mathematical logic. Since I have a background in mathematics myself (once a mathematician, always a mathematician, right?), that alone was reason enough for me to dive into it.

Broadly speaking, the interview explores how we deal with contradictions and paradoxes, not only in general, but specifically within Buddhism, where they obviously show up quite frequently.

Western logic usually struggles to resolve these contradictions. Personally, I often find it difficult to handle such paradoxes in a "logically satisfying" way. That is why I found the concept of Catuskoti incredibly impactful (to avoid using the word "enlightening" here).

Put simply, the principle states that a proposition is not limited to being just true or false. It can also be both true and false at the same time, or neither true nor false. This entire concept can be elegantly mapped onto algebraic structures or set theory, which I find absolutely fascinating. While this mathematical approach might only be of limited help in finding ultimate "truth", it means I no longer feel like I just have to "endure" or tolerate a paradox.
I find this profoundly fascinating because it strips away the (often very subjective) label that Buddhist or Eastern philosophy is somehow "unlogical." Instead, it shows it is merely unlogical within our Western framework of logic (perhaps "metalogical" if you will) and that our boundaries are often just linguistic ones.

Do any of you have thoughts, comments, or perhaps book recommendations on this topic?

Gassho
sat/lah

[Hoshuku]

What an interesting post and pleasse ignore me if my response is off beam.

'A long time ago', I came to the conclusion that if you reach a point in which two contradictory things appear to be both true then you are nearer to any truth that we might hope to uncover - the two sign posts are both pointing the right way and it is our 'koan' to get them together in some way. I did this first with Christian ideas such as Jesus being both transcendant and immanent at the same time, the eucharist being both bread / wine and his body / blood at the same time, the Trinity being Three and One at the same time etc. Although, I've left those behind, the feeling of creeping closer to truth through contradiction has never left me.

As I said, my penny worth of musings.

Bows
Hoshuku
Satlah

[Seikan]

Hello,
I hope this is the right place to post this.

I just read an interview with Graham Priest (https://tricycle.org/article/the-logic-of-paradox), a philosopher with a PhD in mathematical logic. Since I have a background in mathematics myself (once a mathematician, always a mathematician, right?), that alone was reason enough for me to dive into it.

Broadly speaking, the interview explores how we deal with contradictions and paradoxes, not only in general, but specifically within Buddhism, where they obviously show up quite frequently.

Western logic usually struggles to resolve these contradictions. Personally, I often find it difficult to handle such paradoxes in a "logically satisfying" way. That is why I found the concept of Catuskoti incredibly impactful (to avoid using the word "enlightening" here).

Put simply, the principle states that a proposition is not limited to being just true or false. It can also be both true and false at the same time, or neither true nor false. This entire concept can be elegantly mapped onto algebraic structures or set theory, which I find absolutely fascinating. While this mathematical approach might only be of limited help in finding ultimate "truth", it means I no longer feel like I just have to "endure" or tolerate a paradox.
I find this profoundly fascinating because it strips away the (often very subjective) label that Buddhist or Eastern philosophy is somehow "unlogical." Instead, it shows it is merely unlogical within our Western framework of logic (perhaps "metalogical" if you will) and that our boundaries are often just linguistic ones.

Do any of you have thoughts, comments, or perhaps book recommendations on this topic?

Thank you for sharing this Thilo. I find this fascinating as I also used to struggle greatly with logical paradoxes (I did my undergrad and graduate work in western Philosophy with a partial emphasis on logic). At the same time, that is when I first began to explore Zen and other eastern philosophies/practices. While I first found many of the paradoxical teachings of Zen and other eastern traditions to be unnerving, there was also something incredibly attractive and fascinating about them that continued to draw me in. Over the years, I've come to fully embrace the paradoxical nature of many of our teachings and actually find great comfort in them. They help to nudge me outside of the "comfort" of logical thinking and into a different sort of "comfort" of unknowing or potentiality (a positive experience for sure, not just one of acceptance or resignation). I still find it hard to describe exactly. I also find the language often lies at the heart of most paradoxes. Take away language in favor of direct experience, and many paradoxes seem to vanish (as there is no more language of "this or that" to generate conflict).
And please understand all of this as just my own personal experience/thoughts, not any sort of teaching.

Gassho,
Seikan
stlah

P.S. For the record, I opened this discussion naively thinking it was going to have something to do with "cats" (i.e., CATuskoti ), but I found it to be even better than expected.

[Maro]

Hello!
this post is just for the "fun of it all"

I remember my response at the age of 16 when I came across one of the very very very few books that existed in Greece at the time about Buddhism.
It was D.T. Suzuki's book and I remember that I was just infuriated with the koans and their nonsensical nature. (to get the idea: at that time in school my grade in Logic was the equivalent of the A+ ...)

For some unfathomable reason, I was also intrigued (which most probably made the furry more intense - ha ha). So it took quite a while to look at Zen with the appropriate respect so as to allow it to work on me.

Gassho
Maro
satlah

[michaelw]

Might be wide of the mark here but given the relationship between mathematics and philosophy it might be worth exploring the Kyoto School philosophers. Masao Abe was more orientated towards Zen and western thought.

Gassho
MichaelW

satlah

[Tenryu]

Danke fürs Teilen! I found the interview genuinely interesting, even though it led me in a somewhat different direction.

Maybe my perspective is shaped by the fact that mathematics has never felt particularly intuitive to me. I have dyscalculia, and while I'm fully aware that this is my own experience rather than a property of mathematics itself, mathematical logic often feels less "natural" to me than, say, language does. Which is probably a bit of a paradox in itself.

One sentence especially stayed with me:
"Personally, I often find it difficult to handle such paradoxes in a 'logically satisfying' way."

My first, slightly cheeky Zen reaction was: "Why bother? Go wash your bowl."

But after sitting with it for a day, I realized there is something I appreciate about that reaction.

To me, Zen—especially through koans—doesn't seem to suggest that paradoxes need a better logical framework. Rather, it sometimes seems to invite us to notice our own urge to resolve them in the first place.

When I encounter something paradoxical, what helps me most isn't usually finding a more sophisticated explanation. Instead, I try to pay attention to what the paradox is actually doing in my experience right now: the thoughts it triggers, the feeling of uncertainty, the body, the breath, the silence around it. Sometimes the practice seems less about answering the question than about fully inhabiting it.

That doesn't make philosophical explorations like the catuskoti any less fascinating. Quite the opposite—I can see why they are so compelling. I just wonder whether Zen is pointing in a slightly different direction. Not so much asking, "How can I make this paradox logically satisfying?" but perhaps, "What happens if I stop demanding that it be logically satisfying at all?"

I don't know if that's a fair reading, but it's where the interview (and your post) left me after reflecting on it for a day.

Gasshō,
Tenryū
sat&lah

[Seikan]

When I encounter something paradoxical, what helps me most isn't usually finding a more sophisticated explanation. Instead, I try to pay attention to what the paradox is actually doing in my experience right now: the thoughts it triggers, the feeling of uncertainty, the body, the breath, the silence around it. Sometimes the practice seems less about answering the question than about fully inhabiting it.

This! Just sitting/being with with the paradox can be a very insightful experience (no analytical resolution required!).

Gassho,
Seikan
stlah

[Maro]

Rather, it sometimes seems to invite us to notice our own urge to resolve them in the first place.

When I encounter something paradoxical, what helps me most isn't usually finding a more sophisticated explanation. Instead, I try to pay attention to what the paradox is actually doing in my experience right now: the thoughts it triggers, the feeling of uncertainty, the body, the breath, the silence around it. Sometimes the practice seems less about answering the question than about fully inhabiting it.

Aye! This is what I find most interesting and precious. So well expressed Tenryu

Gassho
Maro
satlah

[Jundo]

I am going to dispute some of the article. Much of what he describes as "paradox" or "contradiction" is not that at all in Buddhist view.

It is much like saying that "I am a dad" and "I am a car driver" and "I am a resident of Japan." Each and all are true, and present no paradox or contradiction, being simply different views on who I am.

So it is in Zen Buddhism. For example, take reality being both bound by time, filled with separate provisional and time-bound selves, while also being timeless and free of separate selves. Both are true at once, simply varied views on our identity, without paradox or contradiction.

The best way to understand this is, for example, by using the simile of "ocean" and "waves." A flowing ocean may represent something that exists before, after, and during the finite times that waves rise and fall on the ocean. The waves come and go, but the ocean flows on and on. The waves may represent seemingly individual things and beings, but the sea is all the waters, with nothing added or taken away from the ocean when the waves rise or when they fall. Since the waves are just the ocean, water of these waters, they are the ocean including its properties of being timeless and beyond individual identity. Therefore the waves come and go in time but, as they are also the ocean they remain present and free of time too. The waves rise and fall, are born and die losing their specific identity, but to the extent they are thoroughly the ocean waters flowing on and on, nothing is lost and they do not come or go. There is no contradiction, just different ways to see the waves.

Likewise for statements such as “catching a bus and missing it,” or “being in China and not being in China" ... all possible in Buddhist view without contradiction or paradox. How?

Well, for example, we may return to our ocean and its waves: In the interpretation of some schools of the Mahayana, since the waves are each the ocean, and since ocean is ocean, then the waves are each other in other guise. It is something like saying that "the dad is me, and the car driver is me, so the dad is the car driver." Also, the dad is the car driver when driving the car, the car driver is the dad when heading down the highway, all without paradox or contradiction. At the same time, a "car driver" is a unique thing, different from a "dad." Thus, I might say that, for example, the bird is the fish flying in the sky, the fish is the bird swimming in the sea, yet not ... with each just itself ... and so it is for you and me, all beings and things, and the whole thing! No contradiction, no paradox!

Some views are even more radical, such as in Hua-yan vision, finding that each drop of ocean water is not only the ocean, but fully manifests, contains and is identical with the whole ocean.

Thus, I am both not in China nor on a bus (right now, I am in Japan in my house), yet I am also every person and grain of sand in China and on the bus too because I am them and they are me.

Much of this simply depends on our seeing ourselves and all things in wider ways, with more spacious definitions of who we are. No contradiction.

Gassho, Jundo (aka the bird and the fish and the ocean and Chinese bus rider and you too)
stlah

PS - I posted this as a comment to the article, contradicting the description of contradictions.

[thilo]

Hey everyone,

Thank you so much for the wonderful responses and the effort you put into this thread.
It is fascinating to see the different angles here. On one hand, looking at it through the spacious definitions Jundo mentioned (like the ocean and its waves) really helped lift the fog and showed me that what feels like a contradiction is often just a matter of perspective. On the other hand, the reminder to just inhabit the uncertainty rather than fixing it intellectually resonates deeply.

I suspect I still have a long way to go and my mathematical mind will probably keep bumping into these linguistic limits for a while. But I no longer feel the urge to force a "logically satisfying" answer onto everything.

So, with that in mind, I’ll follow Tenryu’s excellent (and not-cheeky) advice, stop worrying so much, and simply go wash my bowl.

Gassho,
Thilo
sat/lah

[Jishin]

The mathematician explores.
The philosopher analyzes.
The practitioner wonders.
The old monk washes his bowl.

Tea grows cold.

Everyone sits.

自心 ⭕️

ST