Any real life examples these days of Tetralemma (Catuskoti) fourfold negation? What would be the fifth ('true') corner?

Exploring Theravāda's connections to other paths - what can we learn from other traditions, religions and philosophies?
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Re: Any real life examples these days of Tetralemma (Catuskoti) fourfold negation? What would be the fifth ('true') corn

Post by Coëmgenu »

If the OP wants to find a "fifth corner," IMO a questionable exercise that likely defeats the point of Madhyamaka, a place they ought to go looking is at the Chinese elaborations of the two truths by Vens Zhiyi (Zhizhe) and Jizang of the Tiantai and Sanlun schools respectively. Ven Jizang's "four middles" are how his school came to understand Madhyamaka. Ven Zhiyi understood it through the "threefold inclusive truth" of 1) emptiness, 2) conventionality, and 3) the middle. They arrive at these ideas through Madhyamaka as outlined in the Madhyamakaśāstra specifically. What is important to remember is that these exegetes did not conceive of themselves as finding the fifth corner. They were simply exegetes of Venerable Nāgārjuna's work. The connection between Ven Zhiyi and Madhyamaka is also downplayed by later Tiantai patriarchs who wish to reinvent him as practicing and theorizing in a vacuum and exclusively according to the Lotus Sūtra.

Of that threefold inclusivity, Ven Zhiyi says "All three truths are emptiness, all are the tathāgatagarbha, and all are the true aspect. Not three, they are three. Three, they are not three. They are neither combined nor separated, neither uncombined nor unseparated, neither the same nor different, and yet the same and different."

It's a heady business. I really like Ven Zhiyi as a Buddhist thinker and an exegete of the sūtras (as well as a meditation teacher by proxy via his school), but I can't get down with everything he says, especially his theories about the chronology of the Buddha's career.
It is because the valleys are empty that they echo. It is because the mirror is empty that it reflects. It is because the flute is empty that it affects sound. It is because the ears are empty that they can listen. It is because the eyes are empty that they can see. It is because the nose is empty that it can smell.

If these were of substance inside, then there would be obstruction in these.

(from the writings of Master Liè, Daoist text, ~370AD)
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Re: Any real life examples these days of Tetralemma (Catuskoti) fourfold negation? What would be the fifth ('true') corn

Post by DNS »

Here's a fun example for this topic:

The Liar's Paradox

Person x: "I am lying."

If Person x really is lying, then he's telling the truth, which means he just lied.

If "this sentence is false" is true, then it is false, but the sentence states that it is false, and if it is false, then it must be true, and so on.

https://en.wikipedia.org/wiki/Liar_paradox
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Re: Any real life examples these days of Tetralemma (Catuskoti) fourfold negation? What would be the fifth ('true') corn

Post by mikenz66 »

DNS wrote: Thu Jun 17, 2021 11:29 pm Here's a fun example for this topic:

The Liar's Paradox

Person x: "I am lying."

If Person x really is lying, then he's telling the truth, which means he just lied.

If "this sentence is false" is true, then it is false, but the sentence states that it is false, and if it is false, then it must be true, and so on.

https://en.wikipedia.org/wiki/Liar_paradox
This is a simple analog of Goedel's Incompleteness Theorem:
https://en.wikipedia.org/wiki/G%C3%B6de ... s_theorems
Gödel specifically cites Richard's paradox and the liar paradox as semantical analogues to his syntactical incompleteness result in the introductory section of "On Formally Undecidable Propositions in Principia Mathematica and Related Systems I". The liar paradox is the sentence "This sentence is false." An analysis of the liar sentence shows that it cannot be true (for then, as it asserts, it is false), nor can it be false (for then, it is true). A Gödel sentence G for a system F makes a similar assertion to the liar sentence, but with truth replaced by provability: G says "G is not provable in the system F." The analysis of the truth and provability of G is a formalized version of the analysis of the truth of the liar sentence.
I'm not expert on this stuff, but it's worth noting that Goedel's theorem exists, as otherwise one might mistakenly assume that (being rather rough about it) in a consistent formal system it is possible to prove all true statements or prove the consistency itself. I.e. don't be overconfident that your opinions about provability and consistency are correct.

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Re: Any real life examples these days of Tetralemma (Catuskoti) fourfold negation? What would be the fifth ('true') corn

Post by chownah »

From the Kalama Sutta
So, as I said, Kalamas: 'Don't go by reports, by legends, by traditions, by scripture, by logical conjecture, ......etc.....
For examples of why logical conjectures are suspect take a look at sutta DN1.
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Re: Any real life examples these days of Tetralemma (Catuskoti) fourfold negation? What would be the fifth ('true') corn

Post by Coëmgenu »

A video on the aforementioned Incompleteness Theorum:

It is because the valleys are empty that they echo. It is because the mirror is empty that it reflects. It is because the flute is empty that it affects sound. It is because the ears are empty that they can listen. It is because the eyes are empty that they can see. It is because the nose is empty that it can smell.

If these were of substance inside, then there would be obstruction in these.

(from the writings of Master Liè, Daoist text, ~370AD)
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Re: Any real life examples these days of Tetralemma (Catuskoti) fourfold negation? What would be the fifth ('true') corn

Post by Dan74 »

mikenz66 wrote: Fri Jun 18, 2021 12:13 am
DNS wrote: Thu Jun 17, 2021 11:29 pm Here's a fun example for this topic:

The Liar's Paradox

Person x: "I am lying."

If Person x really is lying, then he's telling the truth, which means he just lied.

If "this sentence is false" is true, then it is false, but the sentence states that it is false, and if it is false, then it must be true, and so on.

https://en.wikipedia.org/wiki/Liar_paradox
This is a simple analog of Goedel's Incompleteness Theorem:
https://en.wikipedia.org/wiki/G%C3%B6de ... s_theorems
Gödel specifically cites Richard's paradox and the liar paradox as semantical analogues to his syntactical incompleteness result in the introductory section of "On Formally Undecidable Propositions in Principia Mathematica and Related Systems I". The liar paradox is the sentence "This sentence is false." An analysis of the liar sentence shows that it cannot be true (for then, as it asserts, it is false), nor can it be false (for then, it is true). A Gödel sentence G for a system F makes a similar assertion to the liar sentence, but with truth replaced by provability: G says "G is not provable in the system F." The analysis of the truth and provability of G is a formalized version of the analysis of the truth of the liar sentence.
I'm not expert on this stuff, but it's worth noting that Goedel's theorem exists, as otherwise one might mistakenly assume that (being rather rough about it) in a consistent formal system it is possible to prove all true statements or prove the consistency itself. I.e. don't be overconfident that your opinions about provability and consistency are correct.

:heart:
Mike
Right on, Mike.

In case you want to explore this further, there is an example of incompleteness called Goodstein's Theorem, which briefly, defines a sequence of natural numbers that depends on a starting number (seed), so different for each seed. The interesting thing about this sequence is that it always comes back to 0 and stays there, but you can't prove it. Unless you assume the existence of infinite ordinals. So even though the sequence is defined purely in terms of natural numbers, a key property of the sequence requires going outside the naturals, in order to prove it.





Coming back to the OP, I would only say that the key thing about the Tetralemma is to keep it real. Keep it grounded in your practice, in the here-and-now. Otherwise, it's just another wank.
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Tetralemma simplified

Post by chownah »

This is for those who have no training or understanding of formal logic, mathematics, etc.....so they find this discussion unhelpful:

The tetralemma comes from the very most basic part of what is known as a "truth table". A truth table (go look at wikipedia but it won't be a simple explanation!) starts with two statements or propositions or theorems or assertions (they are all the same for this discussion).....it takes two of them....they can be thought to each be true or false. They are usually labeld "p" and "q"....and so will I....

The two statements can be of any kind....they can be related to each other or they can be completely unrelated. The key thing is that we must accept that each of these two statements can be considered to be true or false (depending on what people think for instnce). So p and q can both be either true or false.

So, if p is true then q can be either true or false....so when p is true there are two possibilities those two being that 1) p is true and q is true and 2) p is true and q is false.

So, if p is false then q can be either true or false....so when p is false there are two possibilities those two being that 1) p is false and q is true and 2) p is false and q is false.

Putting the previous two paragraphs together we see that there are exactly four possible combinations of truth/false values that can occur when considering both statements together.....there are no other possibilities....if you don't believe me then try to come up with a different one...

If you look at the four possibilities you will see that all four of the positions of the tetralemma are defined in the basic truth table....

p... q
t... t
t... f
f... t
f... f


Time to go plant some beans......
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Re: Tetralemma simplified

Post by chownah »

chownah wrote: Sun Jun 20, 2021 6:13 am This is for those who have no training or understanding of formal logic, mathematics, etc.....so they find this discussion unhelpful:

The tetralemma comes from the very most basic part of what is known as a "truth table". A truth table (go look at wikipedia but it won't be a simple explanation!) starts with two statements or propositions or theorems or assertions (they are all the same for this discussion).....it takes two of them....they can be thought to each be true or false. They are usually labeld "p" and "q"....and so will I....

The two statements can be of any kind....they can be related to each other or they can be completely unrelated. The key thing is that we must accept that each of these two statements can be considered to be true or false (depending on what people think for instnce). So p and q can both be either true or false.

So, if p is true then q can be either true or false....so when p is true there are two possibilities those two being that 1) p is true and q is true and 2) p is true and q is false.

So, if p is false then q can be either true or false....so when p is false there are two possibilities those two being that 1) p is false and q is true and 2) p is false and q is false.

Putting the previous two paragraphs together we see that there are exactly four possible combinations of truth/false values that can occur when considering both statements together.....there are no other possibilities....if you don't believe me then try to come up with a different one...

If you look at the four possibilities you will see that all four of the positions of the tetralemma are defined in the basic truth table....

p... q
t... t
t... f
f... t
f... f


Time to go plant some beans......
chownah
Beans are planted.
So....here is an example of a couple of unrelated statements so that people just learning about this stuff will see how common place and easy a BASIC truth table can be:
For p I will use the statement "the president of Harvard college has a white cat".....and for q I will use "I planted beans one week ago today".

With your limited knowledge you will probably not know for sure if these two statements are true or false but you can certainly see that they are unrelated. Since none of you know the truth/falsity of these statements you must guess and so some of you will guess true for p and q....some will guess false for p and q....some will guess true for p and false for q.....and some will guess false for p and true for q.>>>>that's all of the possibilities.....there is no other possible outcome except for these four just like I said above....if you don't believe it then try to find another possible outcome!!!!

So....I hope you can see that the BASIC truth table can be used to tabulate all of the possible outcomes from any two statements at all......EXCEPT there is one EXCEPTION in that a statement is not acceptable if assigning it to be true or false in the beginning changes its value in the end.....this exception is what keeps the "liar's paradox" which DNS brought above out of any truth table (sorry DNS but that is the rule!).....other than that I think any statement at all can be used......of course ridiculous statements like the one's I use don't really mean much and I am only showing this to show that for the BASIC truth table any kind of statements can be used.

It gets more interesting when more interesting statements are used.

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Re: Tetralemma simplified

Post by Sabbe_Dhamma_Anatta »

chownah wrote: Sun Jun 20, 2021 2:45 pm

p... q
t... t
t... f
f... t
f... f




Thanks for the explanation.


However, the example of the truth table does not seem to satisfy the issue of the OP.


p & q are two separate (& probably unrelated) variables, with two possible outcomes (true or false) for each one.


Tathagata is only one variable, with four "possible" outcomes [in the mind of the asker]; but Buddha taught "the fifth corner."


Off-topic: ...> The learning point (dhamma-wise / not logic-wise) in that four-fold negation is that the questions themselves are wrong. There is no such variable in the first place, i.e. there is no tathagata, only aggregates.


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Last edited by Sabbe_Dhamma_Anatta on Sun Jun 20, 2021 4:54 pm, edited 1 time in total.
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Re: Any real life examples these days of Tetralemma (Catuskoti) fourfold negation? What would be the fifth ('true') corn

Post by Coëmgenu »

According to how the Madhyamakas understood the teaching of the Buddha, the Buddha taught specifically that there is no "fifth corner." The four thesis are exhaustively refuted and the four theses contain within themselves all possible existential stances, leaving no room for speculation. In the MMK, the four theses and attempts to justify them via a fifth thesis are directly linked to prapañca. In the opening stanzas, Venerable Nāgārjuna explains how, via various fourfold and eightfold negations, the treatise is about "the breaking of prapañca," according to the wording of his commentator, Ven Vimalākṣa. More to come when I'm at a computer.
It is because the valleys are empty that they echo. It is because the mirror is empty that it reflects. It is because the flute is empty that it affects sound. It is because the ears are empty that they can listen. It is because the eyes are empty that they can see. It is because the nose is empty that it can smell.

If these were of substance inside, then there would be obstruction in these.

(from the writings of Master Liè, Daoist text, ~370AD)
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Re: Any real life examples these days of Tetralemma (Catuskoti) fourfold negation? What would be the fifth ('true') corn

Post by Sabbe_Dhamma_Anatta »

Coëmgenu wrote: Sun Jun 20, 2021 4:47 pm ... there is no "fifth corner." ...
Agreed, regarding the existence of Tathagata.

The four-fold questions themselves are wrong as described in my previous (edited) post. The four corners collapse, and accordingly the concept of fifth corner becomes defunct.

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Re: Any real life examples these days of Tetralemma (Catuskoti) fourfold negation? What would be the fifth ('true') corn

Post by Coëmgenu »

Sabbe_Dhamma_Anatta wrote: Sun Jun 20, 2021 5:00 pm
Coëmgenu wrote: Sun Jun 20, 2021 4:47 pm... there is no "fifth corner." ...
Agreed, regarding the existence of Tathagata.
And, in the MMK, two more things explicitly, and with regards to many more things implicitly. Not being at a computer right now, you are subject to my poor memory, but I believe it is in the Nirvāṇaparīkṣā, MMK XXV in the Korin Study Notes, that Ven Nāgārjuna explicitly applies the fourfold negation to two more subjects: "the world" and "nirvāṇa." "The world," explicitly, refers to "the world" as an object of clinging and associated prapañca. "The world," implicitly, according to the commenterial tradition I am most familiar with, refers to the skandhas, āyatanas, dhātus, and the dharmas. "Nirvāṇa," most controversially, refers to "nirvāṇa" as an existing dharma. In those same study notes, in the Saṃskṛtaparīkṣā at MMK VII, you find a Madhyamaka refutation of the three moments of arising, abiding, and ceasing, and this will contextualize the negation of "the world." Since you have the study notes (I think), you will be able to look at Garfield et al. and Kalupahana commenting on the passages to get a modern perspective.
It is because the valleys are empty that they echo. It is because the mirror is empty that it reflects. It is because the flute is empty that it affects sound. It is because the ears are empty that they can listen. It is because the eyes are empty that they can see. It is because the nose is empty that it can smell.

If these were of substance inside, then there would be obstruction in these.

(from the writings of Master Liè, Daoist text, ~370AD)
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Re: Any real life examples these days of Tetralemma (Catuskoti) fourfold negation? What would be the fifth ('true') corn

Post by waryoffolly »

Coëmgenu wrote: Sun Jun 20, 2021 5:39 pm
Sabbe_Dhamma_Anatta wrote: Sun Jun 20, 2021 5:00 pm
Coëmgenu wrote: Sun Jun 20, 2021 4:47 pm... there is no "fifth corner." ...
Agreed, regarding the existence of Tathagata.
And, in the MMK, two more things explicitly, and with regards to many more things implicitly. Not being at a computer right now, you are subject to my poor memory, but I believe it is in the Nirvāṇaparīkṣā, MMK XXV in the Korin Study Notes, that Ven Nāgārjuna explicitly applies the fourfold negation to two more subjects: "the world" and "nirvāṇa." "The world," explicitly, refers to "the world" as an object of clinging and associated prapañca. "The world," implicitly, according to the commenterial tradition I am most familiar with, refers to the skandhas, āyatanas, dhātus, and the dharmas. "Nirvāṇa," most controversially, refers to "nirvāṇa" as an existing dharma. In those same study notes, in the Saṃskṛtaparīkṣā at MMK VII, you find a Madhyamaka refutation of the three moments of arising, abiding, and ceasing, and this will contextualize the negation of "the world." Since you have the study notes (I think), you will be able to look at Garfield et al. and Kalupahana commenting on the passages to get a modern perspective.
Sounds to me like Nagajurna carefully read MN 1 with regards to Nibbana. The dhamma is praxis for crossing over, not for speculative views even those about Nibbana.
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Re: Any real life examples these days of Tetralemma (Catuskoti) fourfold negation? What would be the fifth ('true') corn

Post by Sabbe_Dhamma_Anatta »

Coëmgenu wrote: Sun Jun 20, 2021 5:39 pm ... Korin Study Notes, ...
Awesome work.

from Streng (some edits [...] ): (I hope there is no typo)
  • [CHAPTER 25 - An Analysis of Nirvana (nirvana) - 24 verses .

    #1. [An opponent says:] If all existence is empty, there is no origination nor destruction. Then whose nirvana through elimination [of suffering] and destruction [of illusion] would be postulated?

    #2. [Nagarjuna replies:] If all existence is non-empty, there is no origination nor destruction. Then whose nirvana through elimination [of suffering] and destruction [of illusion] would be postulated?

    #3. Nirvana has been said to be neither eliminated nor attained, neither annihilated nor eternal, Neither disappeared nor originated.

    #4. Nirvana is certainly not an existing thing, for then it would be characterized by old age and death. In consequence it would involve the error that an existing thing would not become old and be without death.

    #5. And if nirvana is an existing thing, nirvana would be a constructed product (samskrta), Since never ever has an existing thing been found to be a non-constructed-product (asamskrta).

    #6. But if nirvana is an existing thing, how could [nirvana] exist without dependence [on something else]? Certainly nirvana does not exist as something without dependence.

    #7. If nirvana is not an existing thing, will nirvana become a non-existing thing? Wherever there is no existing thing, neither is there a non-existing thing.

    #8. But if nirvana is a non-existing thing, how could [nirvana] exist without dependence [on something else]? Certainly nirvana is not a non-existing thing which exists without dependence.

    #9. That state which is the rushing in and out [of existence] when dependent or conditioned --- This [state], when not dependent or not conditioned, is seen to be nirvana.

    #10. The teacher [Gautama] has taught that a "becoming" and a "non-becoming" (vibhava) are destroyed; Therefore it obtains that: Nirvana is neither an existent thing nor a non-existent thing. .

    #11. If nirvana were both an existent and a non-existent thing, Final release (moksa) would be [both] an existent and a non-existent thing; but that is not possible.

    #12. If nirvana were both an existent and a non-existent thing, There would be no nirvana without conditions, for these both [operate with] conditions.

    #13. How can nirvana exist as both an existent thing and a non-existent thing, For nirvana is a non-composite-product (asamskrta), while both an existent thing and a non-existent thing are composite products (samskrta).

    #14. How can nirvana exist as both an existent and a non-existent thing? There is no existence of both at one and the same place, as in the case of both darkness and light.

    #15. The assertion: "Nirvana is neither an existent thing nor a non-existent thing" Is proved if [the assertion]: "It is an existent thing and a non-existent thing" were proved.

    #16. If nirvana is neither an existent thing nor a non-existent thing, Who can really arrive at [the assertion]: "neither an existent thing nor a non-existent thing"?

    #17. It is not expressed if the Glorious One [the Buddha] exists (1) after his death, Or does not exist (2), or both (3) or neither (4).

    #18. Also, it is not expressed if the Glorious One exists (1) while remaining [in the world], Or does not exist (2), or both (3) or neither (4).

    #19. There is nothing whatever which differentiates the existence-in-flux (samsara) from nirvana; And there is nothing whatever which differentiates nirvana from existence-in-flux.

    #20. The extreme limit (koti) of nirvana is also the extreme limit of existence-in-flux; There is not the slightest bit of difference between these two.

    #21. The views [regarding] whether that which is beyond death is limited by a beginning or an end or some other alternative Depend on a nirvana limited by a beginning (purvanta) and an end (aparanta), .

    #22. [***] Since all dharmas are empty, what is finite? What is infinite? What is both finite and infinite? What is neither finite nor infinite?

    #23. [***] Is there anything which is this or something else, which is permanent or impermanent, Which is both permanent and impermanent, or which is neither?

    #24. The cessation of accepting everything [as real] is a salutary (siva) cessation of phenomenal development (prapanca); No dharma anywhere has been taught by the Buddha of anything.

    .
Some source include "An opponent says" in the verse 1 only. Does that mean all the remaining 23 verses are by Ven. Nagarjuna?

============
edited:
[***] = hypothetical questions posed by Ven Nagarjuna in the voice of his interlocutor

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Last edited by Sabbe_Dhamma_Anatta on Mon Jun 21, 2021 4:56 pm, edited 1 time in total.
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Re: Any real life examples these days of Tetralemma (Catuskoti) fourfold negation? What would be the fifth ('true') corn

Post by Coëmgenu »

The first verse is spoken by the interlocutor, the rest by Ven Nagarjuna. The twenty-second to twenty-third verses are hypothetical questions posed by Ven Nagarjuna in the voice of his interlocutor. He answers these rhetorical questions with the opening of verse 24, but then also introduces a typical Madhyamaka "twist ending:"

MMK XXV.24
諸法不可得
滅一切戲論
無人亦無處
佛亦無所說
All phenomena being inconceivable
is the cessation of all of the frivolous ponderings.
To no person and in no place
has the Buddha ever spoken.


戲論 = prapañca = "frivolous ponderings" in this Sinocentric translation.
It is because the valleys are empty that they echo. It is because the mirror is empty that it reflects. It is because the flute is empty that it affects sound. It is because the ears are empty that they can listen. It is because the eyes are empty that they can see. It is because the nose is empty that it can smell.

If these were of substance inside, then there would be obstruction in these.

(from the writings of Master Liè, Daoist text, ~370AD)
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