Formal Logic & Three Types of Nirvana

Discussion
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This is something for @yeshe.tenley to chew on, though I thought there would be other parties interested in this sort of thing. :smiley:

In a recent post I was discussing the tension between Mahayana view of Nirvana vs. Theravāda view (broadly, though even within schools they differ).

I’ve thus come to find (at least) three distinct positions on Nirvana, and some of the schools that can be associated with such views (though not exclusively - everyone has all sorts of ideas!):

  1. Phenomenological Claim: Nirvana is an absence of experience (Sautrantika, Neo-Theravāda, etc.)
  2. Epistemological Position: No specific concept is ultimately true, including this one. (Madhyamaka)
  3. Ontological Stance: Nirvana is the non-dual awareness of all thing. (Yogācāra, Zen, also perhaps Thai Forest Tradition)

The aim of this thread is to analyse these positions from a formal logic perspective, to see if they’re self-consistent, and whether there’s any actual difference between these positions (in other words, if there’s a logical equivalence between these expressions).

My attempt and hope here is not to argue whether one thought is true and rest are rubbish. Rather the opposite - to try and see if there’s a true distinction between these positions, and in what ways they might all be referring to the same thing. :slight_smile:

Now I’ll try to put them in formal language clumsily :smiley:. My expression might also be eclectic using old school modal logic symbols with formal logic.

_

1. Nirvana as an absence of experience

This can be tackled in some ways. I’m inclined to go for second one because first one is too similar to the next one.

  • N = ¬∃x.P(x)
    There is no x such that P(x) is true.

  • N = [ ∀x.P(x) = ∅ ]
    For all cases of x, P(x) is null.

2. Nirvana as negation of ultimate concepts, including this one

This gets tricky, there’s a few different ways I can come up with to express this:

  • N = ¬∃x.□P(x)
    There is no x for which P(x) is necessarily true.

Alternatively:

  • N = ∀x.¬□P(x)
    For all cases of x, it isn’t the case that P(x) is true.

  • N = ¬(∃x.□P(x))
    It is not the case that there exists an x for which P(x) is necessarily true.

3. Nirvana as non-dual awareness

This is the nitty one! :smiley:

  • N = ∃ x . { □P(x) ∧ ¬∃y . [ □P(y) ∧ P(x)≠P(y) ] }
    There exists an x for which P(x) is necessarily true, and there is no y such that P(y) is necessarily true and P(x) is different from P(y).

So that’s the fire-starter. :smiley:

First we should clean up these expressions. Alternatively, I would very much appreciate other expressions. After that, we can discuss:

  • Does negation of all ultimate truths imply a non-distinction for all objects (2 → 3)?
  • Conversely, if it isn’t the case that objects are non-distinct, can we still talk about the absence of ultimate truths (¬3 → ¬2)
  • Does absence of any distinction also imply an absence of sensory input (3 → 1)?
  • Conversely, if we can’t talk about absence of sensory input, can we still talk about a true non-distinction (¬1 → ¬3)?
  • How do these ideas really diverge and converge in general?

:hearts: :lotus:

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One thing that bugs me that functions for (all three?) might be necessarily different. So while for #1, P(x) might denote input, for #2, it might denote something else. That’s probably the first thing that needs to be defined well beforehand. Mhmmh.

Also, personally I’ve always found #2 to be kind of weak. If even the claim that “No thing is ultimately true” isn’t ultimately true, then I feel like it should conclude that “Therefore some things might be ultimately true.” To avoid that, it would have to posit “Except for this position, there’s no position that is ultimately true”, which isn’t the position of Madhyamaka (or any other school I’ve read about).

For now I refer to MMK to draw out what I think Nagarjuna says about non-dual:

18.8
Everything is real; and is not real;
Both real and unreal;
Neither unreal nor real.
This is the Lord Buddha’s teaching.

18.9
Not dependent on another, peaceful and
Not fabricated by fabrications,
Not conceptualized, without distinctions:
That is the characteristic of things as they really are.

18.10
Whatever comes into being dependent on another
Is neither identical to that thing
Nor different from it.
Therefore it is neither annihilated nor permanent.

18.11
This is nectar—the doctrine of
The Buddhas, patrons of the world.
Without identity, without distinction,
Not annihilated, not permanent.

So this is a non-dual different from the one I’ve expressed above Neither identical to that thing, nor different. But if this is still an expression of conventional realm…

Also 18.8 is quite close to Jain perspective, funnily enough! :smiley: (which I appreciate, to be honest)

24.8
The Buddha’s teaching of the Dharma
Is based on two truths:
A truth of worldly convention,
And an ultimate truth.

24.9
Those who do not understand
The distinction between these two truths
Do not understand
The Buddha’s profound teaching.

24.10
Without depending on the conventional truth,
The meaning of the ultimate cannot be taught.
Without understanding the meaning of the ultimate,
Nirvana is not achieved.

I defer to @yeshe.tenley to educate me on all things Madhyamaka, hopefully. :slight_smile:

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For Yogācāra position, here’s Vasubandhu’s Triṃśikā-kārikā:

Relevant parties (after a description of defilements):

[21] The self-nature (svabhāva) of the Other-Dependent (paratantra) [= pratītya-samutpāda] is a construction (vikalpa) that arises [in dependence] upon conditions. However, the Perfected
(pariniṣpanna) is always free from the former [i.e. svabhāva].

[22] For this very reason, the Other-Dependent is neither other, nor not other than the Perfected. It is said to be like impermanence, etc. – when this [Other-Dependent] is not seen, that [Perfected] will not be seen [or vice versa?]

[23] The self-naturelessness (niḥsvabhāvatā) of all dharmas was taught in connection with the
threefold self-naturelessness of the threefold self-nature.

[24] The first is without self-nature (niḥsvabhāva) by its very character; the second is [by definition] without self-existence (na svayaṃbhāva); and the third is the very state of the absence of self-nature.

[25] The ultimate [nature] of [all] dharmas is also Suchness (tathatā), because its nature is always just as it is. It is just the state of cognition-only (vijñapti-mātra).

[26] As long as the mind does not abide in the state of cognition-only, the latent disposition
(anuśaya) of the twofold grasping (grāha-dvaya) will not cease.

[27] Placing something before one and saying: ‘Just this is cognition-only’, one does not abide in
cognition-only, because this is also seizing [an object].

[28] When that very vijñāna does not seize an object, then it remains in the state of cognitiononly, which is the non-existence of [an object] to be grasped due to non-grasping.

[29] This [state] is unthinkable (acitta), ungraspable (anupalambha), is supermundane (lokottara) knowledge, the revolution of the basis (āśrayasya parāvṛtti) due to the abandonment of the twofold impediment [i.e. kleśāvaraṇa and jñeyāvaraṇa].

[30] It is inconceivable (acintya), beneficent, the element (dhātu) without defilement (anāsrava), lasting (dhruva). This is the ‘body’ of liberation (vimukti-kāya), which is blissful, called the Dharma of the Mahāmuni.

Especially sections 27 & 28 seem to deny that this nibbāna is = ayatana of pure consciousness, because in that ayatana, there is still the object-awareness of “Just this cognition only”.

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I won’t be able to participate in this discussion because I don’t really know formal type logic but I’m curious: What is Neo-Theravada? Is that a catch-all for modern Theravada strands? Or how do you define it? :cherry_blossom:

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Kind of, to differentiate it from Classical Theravāda, which, for our discussion’s sake, classified Nibbāna generally as a classification of its own and not as a cessation.

Neo-Theravāda can be further classified between Contemporary Classical Theravāda (which has cessationalist views), Sutta-Vinaya only Theravāda (or Early Buddhist Texts movement, EBT in short) - they usually promote the pure cessationalist view.

There are some further divisions like Thai Forest Tradition, some weird cults like Dhammakaya, so on and so forth, who for this article’s sake, do not believe in a cessationalist view.

Sectarianism never ends! :sweat_smile:

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Hi, Dogen. :slight_smile:

Just to add nuance here, Zen cannot be reduced to one thing. There are differing opinions within the Chan tradition of China/Japan/Korea/etc. There are strands that are very Madhyamaka focused, others that are more Tathāgatagarbha focused.

Likewise, Yogācāra is not one solid thing, but a rich tradition with centuries of evolution and varying interpretation. It is very influential in East Asian Buddhism in general, including Zen. But how it is interpreted varies, based in part on the distinction above.

Likewise, it seems that to talk about a type of awareness is phenomenological. This doesn’t really seem to be an ontological vs. phenomenological distinction.

Be well!

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Hello Venerable! :smiley:

Indeed, my categorisations were very broad strokes, just a general idea. Perhaps it’s wise to mention that.

Rather than making assumpings that “This is indeed the doctrine of this school” I’m just attempting to analyse general claims from various schools. :slight_smile:

Quite so! This is one of my investigations - is there actually any distinction found in various phrasings and formulations of these different schools, despite the appearance of a disagreement?

I’m always fascinated by the idea that it’s generally our grammar is the source of our disputes, and when boiled down to it, wisdom of sages are more or less the same.

Whether it’s too much “more” or “less”? :smiley:

Thank you, Bhante. :slight_smile:

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For what it is worth, I will throw some milk duds from the back of the peanut gallery and see if any stick to the screen.

This seems to imply that Nirvana cannot be experienced or known. What is nirvana? Is it a fiction? Is it undefined? Is it an experience that cannot be put into words? Is it a meaningless experience? My position is that it is a profoundly peaceful meaningless experience.

When you say “is ultimately true”, do you mean nirvana is a proposition that is true or false? Maybe it is a proposition whose truth value is undecidable or unknowable? Or do you mean there are no predicates that apply to it?

When you say “all things”, do you mean sensory input? If so, it seems to be input that cannot be parsed by the means available to us.

As written, N is true, false, undecidable, or unknowable.

When you say P(x) is null, do you mean the set of predicates for which P(x) is true is empty? As written, ∅ does not make sense. The proposition is true, false, undecidable, or unknowable.

I don’t think it makes sense to go further until clarifications are made.

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There is a more natural way of formulating #2 in logical terms and it just so happens that this natural way has been proven true and was in logical circles as devastating (even more so) for logicians and mathematicians as Einstein’s special relativity was for physics.

I’m of course talking about Kurt Godel’s celebrated proofs of the incompleteness of logic:

For any formal logical system of sufficient expressive power:

  1. There are necessarily true things that nonetheless can’t be proven true by that system
  2. It can not prove its own consistency

I think this is more or less what your #2 should be along with the fact that every logical system is also completely reliant on shared assumptions that cannot be proven from within the system.

FWIW, this might very well be an example of what is meant as ‘beyond reason’ in various ancient sources not that those ancient sources knew Godel’s proofs.

:pray:

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I think philosophers have known for a long time that concepts/words break down at some point. If I remove one blank at a time from a ship and replace it, at what point does it cease to be the same ship?

My question is: how does knowing that concepts breakdown lead to nibanna? Are you saying that there are some experiences such that no proposition can describe them and those ineffable experiences or some subset are nibanna?

Is this known through direct experience or is there a proof of it and why would you care if there was if the concepts breakdown anyway?

I

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Hi Raftafarian. :slight_smile:

First of all, thanks for your detailed response. I hope to tackle them at greater length when I have sufficient time.

Let me offer these in the meanwhile:

There have been quite a few schools and sages who’ve suggested the first point, indeed. Nibbāna would be dissolution of such concepts with regards to all experiences in some views (as well as mine).

Very good question. I believe that dissolution of conceptual thinking leads to an experience that can’t be said to be an experience, an awareness that can’t be called awareness, because those ideas are discarded to begin with. Poetically, we can call this state, continuum (or discontinuity) “peaceful”, for it is uninclined and unbothered with appearances.

Once the concepts are shakes off, one sees as it really is (yathābhūta).

It’s hard to argue for this peace with logic. :slight_smile: One would have to decide for themselves whether being involved with symbols, shapes and discussions is preferable to Shikantaza - just sitting.

Again, I would say this what we call poetically sukha is a direct experience.

Also another wise question. :slight_smile: It is probably impossible to assert that “Dropping off concepts is peaceful”. It’s a personal judgment, not quite something that can be proved logically.

What I am interested in is if once we break down the syntax of several schools all apparently having different definitions of nibbāna, if we end up with semantically equivalent statements after all.

My investigation here is less about proving one of these positions as correct (and others as false), but to determine to what extent they’re talking about the same thing or if they’re altogether different concepts. :slight_smile:

I hope this answers your questions, and I’ll be eager to engage with your lengthier post soon. :slight_smile:

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The first problem with this kind of logical statement is that you do not define what “experience” means. Depending on what you deem “experience” means the statement can turn true or false. Feel free to define it further.

Regardless, let’s take a look of how we could define “experience” to attempt to make the statement true according to a sutta source.
Suppose we’d defined “experience” as “experiencing rūpa, vedanā, saññā, saṅkhāra, viññāṇa by which one might be described” (Now, notice the careful phrasing added “by which one might be described” - in other words we are excluding 5GA by which one is not described - will get back to this point later why)

Now, given this definition, we could check MN72:

“In the same way, Vaccha, any rūpa by which a realized one might be described has been given up, cut off at the root, made like a palm stump, obliterated, and unable to arise in the future.
A realized one is freed from reckoning in terms of rūpa. They’re deep, immeasurable, and hard to fathom,
Any vedanā … saññā … saṅkhāra … viññāṇa by which a realized one might be described has been given up, cut off at the root, made like a palm stump, obliterated, and unable to arise in the future.
A realized one is freed from reckoning in terms of viññāṇa. They’re deep, immeasurable, and hard to fathom, like the ocean.

Thus, if we take statement
1. Nirvana as an absence of experience
expand the “experience”:
1. Nirvana as an absence of experiencing rūpa, vedanā, saññā, saṅkhāra, viññāṇa by which one might be described

We can observe that it matches what is stated in MN72. Notice, that if we did not append the statement “by which one might be described” we would not be able to prove it via MN72 as it states only that 5GA by which one might be described has been given up.

Thus, if MN72 is correct, the translation & interpretation of it is correct and our logical deduction is correct then statement 1. seems to be logically true.

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I think we have to differentiate between the experience of name and form and the experience of not (name and form). What it is to be an organism in the world is name and form. Nibbana/anatta is the experience of not being an organism in the world.

Added later:
Name
Form
Name and form
Not (name and form)
A tetra lemma if you like.

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The absence of experience is not an experience - it can’t be experienced, it’s not a phenomenon. So I would argue that it’s not a phenomenological claim, it’s more of an annihilationist claim.

A phenomenological claim would have been made in terms of the presence or absence of certain phenomena.

Here is an example of an actual phenomenological claim - from NIBBĀNA by Ven. Ñāṇavīra:

In the Udāna (viii,3 <Ud.80>) nibbāna is spoken of by the Buddha in these terms: Atthi bhikkhave ajātam abhūtam akatam asankhatam, no ce tam bhikkhave abhavissa ajātam abhūtam akatam asankhatam na yidha jātassa bhūtassa katassa sankhatassa nissaranam paññāyetha. (‘There is, monks, a non-born, non-become, non-made, non-determined; for if, monks, there were not that non-born, non-become, non-made, non-determined, an escape here from the born, become, made, determined, would not be manifest.’) ‘Such a positive assertion of the existence of the Unconditioned’ it is sometimes urged ‘must surely imply that nibbāna is not simply annihilation.’ Nibbāna , certainly, is not ‘simply annihilation’—or rather, it is not annihilation at all: extinction, cessation of being, is by no means the same thing as the (supposed) annihilation of an eternal ‘self’ or soul. (See Majjhima xi,2, above.) And the assertion of the existence of nibbāna is positive enough—but what, precisely, is asserted? In the Asankhata Samyutta (i,1 & ii,23 <S.iv,359&371>) we read Yo bhikkhave rāgakkhayo dosakkhayo mohakkhayo, idam vuccati bhikkhave asankhatam/nibbānam; (‘The destruction, monks, of lust, of hate, of delusion—this, monks, is called (the) non-determined/extinction.’) and we see that, if we do not go beyond the Suttas, we cannot derive more than the positive assertion of the existence here of the destruction of lust, hate, and delusion. And this is simply a statement that to get rid, in this very life, of lust, hate, and delusion, is possible (if it were not, there would be no escape from them, and therefore—Anguttara X,viii,6 <A.v,144>—no escape from birth, ageing, and death). And the arahat has, in fact, done so.

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