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Awakened Great Zen Master Seung Sahn - is it possible he lost the state of Nibbana?
From my understanding of awakening (and also according to answers here like Is it possible to become UNenlightened?), it is an irreversible process. It makes sense in theory as, once one awakens, realises the way out of all the dukkha, it's such a wonderful state. Why would one replace it with anything else?
It is told that Great Zen Master Seung Sahn has reached awakening in 1949. However, later on in life, Master Sahn has had sexual relationships with students, which he publicly admitted and did two repentance ceremonies. Even though it seems that the affairs had not been hurtful to the students, the first thing which comes to my mind is: in order to engage in sexual relationship, one must have some lust - some unsatisfactoriness or dukkha - which contradicts the state of nibbana.
Does anyone have any thoughts on this matter? Some of possible explanations that I can think of:

Is it possible that engaging in sexual relationships was what the situation requested, that it was right-action? After all, precepts are guidelines and, if situation requires so, they are ought to be broken. If so, why did Mater Sahn do repentance ceremonies? Was it also right-action?
Perhaps different buddhist traditions lead to different state of nibbana. I am relatively new to buddhism and all the traditions so I don't quite understand if this is even possible? (though I doubt it)
It is possible to become "un-awaken" after all?

Perhaps different buddhist traditions lead to different state of nibbana
Even within one tradition there are different stages or degrees of enlightenment -- see for example Four stages of enlightenment.
I think that this answer implies that the "awakening" which you quoted, i.e. ...

According to his book Dropping Ashes on the Buddha, he came to the understanding that “the rocks, the river, everything he could see, everything he could hear, all this was his true self. All things are exactly as they are. The truth is just like this.” In 1949, at the age of twenty-two, he attained enlightenment. This was confirmed by the great Korean Zen Master Ko Bong, who gave Zen Master Seung Sahn “inka” or transmission of the dharma. Ko Bong’s transmission publicly certified and authenticated Zen Master Seung Sahn’s enlightenment experience, giving him the authority to teach and train students.
Following his enlightenment experience, Zen Master Seung Sahn spent three years in silence, strengthening his Zen practice. He then became active in etc.

... is not "complete enlightenment".
I think there are instances of misbehaviour -- a teacher having affairs with students is not unheard of -- some people (or groups) even claim that's a good thing, getting over inhibitions or something, maybe Tantric justification, I don't know. To quote one example (and maybe not the best example):

On this level, if we are capable of seeing something pure in every human being, our sexual lives can be tools to create enormous joy. If it happens on the level of purity, if we have respect for each other, if we experience ourselves and others on a beyond-personal level, then enlightened energies can move and we learn something in the process—it’s totally amazing!

Others (outside the group, or ex-group-members) may condemn it (e.g. as exploitative ... or perhaps as hedonistic). See also "Celibacy in the Vinaya" in this article, Celibacy in Buddhism.
I read once -- see here -- that there may be quite a difference between what different people or different schools perceive as enlightened or nearly-enlightened or perhaps blameless behaviour (but beware that summary may be wrong, based on a misunderstanding, not well-explained, etc.).
Also (to get back to the question) I think that different schools may have slightly different doctrines about what nibbana is and whether it is (once attained) permanent. Instead of speculating, or "going by reports", perhaps it's important to experience for yourself what is "skilful", effective (what are the results of this or that), and ethical.

Worth mentioning regarding Tantra and Vajrayana that Vajrayana is not a path of renunciation, thus practitioners are not forbidden from sexual intercourse in any way. Furthermore, Nyingma tradition even advise that true practitioner should at least have a wife, as it leads to greater liberation so on.

Only an enlightened being can truely comment on spiritual attainment of other being, so its not possible for people here to tell honestly what must have happened with the master.
From what I know, Nibbana is not reversible, it is permenant. If he fell back, then may be he did not actually attain enlightenment. People have all sorts of spiritual experiences which they confuse as enlightenment.
If he did repentance ceremony, then AFAIK I don't think he was enlightened.

Theravada Buddhist answer.

Is it possible that engaging in sexual relationships was what the situation requested, that it was right-action? After all, precepts are guidelines and, if situation requires so, they are ought to be broken. If so, why did Mater Sahn do repentance ceremonies? Was it also right-action?

I cannot give a satisfying answer to that question, other than if Master Sahn chose to do repentance ceremonies, he must have regarded some actions as being non-right actions.

Perhaps different buddhist traditions lead to different state of nibbana. I am relatively new to buddhism and all the traditions so I don't quite understand if this is even possible? (though I doubt it).

There is only one Nibbana. Nibbana is not made or created. It does not arise, perish or undergo transformation. It is uncaused, unconditioned and timeless.
Nibbana is an existing reality that yogis can discover by following the Noble Eight Fold Path, as expounded by the Buddha.

It is possible to become "un-awaken" after all?

It is not. Once the lower and higher fetters (chains, bonds) have been broken, they cannot return or reestablish themselves. They are gone for good.
If you pull garden weeds and remove all traces of the plant, roots etc., it cannot grow back.
The Buddha declared final knowledge thus:

"Destroyed is birth, the holy life has been lived, what had to be done has been done, there is no more for this state of being” (meaning; no more wandering in Samsara).
-- SN 153,8: Is There A Method?, p. 1214 - Bodhi, Trans.


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Are the Pali words "cause" ("hetu'), "condition" ("paccaya"), "nutriment" ("ahara") and "root" ("mula") synonyms?
Are the Pali words "cause" ("hetu'), "condition" ("paccaya"), "nutriment" ("ahara") and "root" ("mula") always synonyms?

before i try to submit an answer, given your track records, are you sincerely looking for an answer or you just want people to submit their answers for you to criticize and give grade?

See also Is causation (hetu) in SN 22.82 different to conditions (paccaya) in Dependent Origination? (and this topic).

The Pali words "cause" ("hetu') is NOT a synonym of "condition" ("paccaya"). To explain this, let me take the example in paticca samuppada (PS). The PS cycle that describes the “cause and effect” in Buddha Dhamma starts as: “avijja paccaya sankhara, sankhara paccaya vinnana, vinnana paccaya nama rupa, nama rupa paccaya salayatana,….”.
One may tend to think that “avijja paccaya sankhara” means “avijja causes sankhara” or “ignorance causes one to acts that generate bad kamma”, but it is not so. All of us ordinay people have avijja, but that does not mean that we always act accordingly. Most of the time we act appropriately or morally. However, if avijja is there, it is likely that at times one will act with avijja and do inappropriate or immoral things.
Thus PS does not refer to a “direct link”. Any effect must have a cause. But there can be possible causes without leading to any effects. Otherwise, Nibbana would not be possible. For causes to bring about corresponding effects, suitable conditions must be present. That is what ‘paccaya’ means.
Similarly the Pali words "nutriment" ("ahara") is NOT a synonym of "root" ("mula"). In Pali language, “mula” is a root, so that “mūlika héthu” means “root causes”. To explain this, let me take the example of a tree. The roots (mūlika hetu) are critical for the tree’s survival, but the “patta” also plays an important role for the tree’s growth. The “patta” are essential for the tree’s survival, just as the roots of the tree are. One could kill a tree simply by a process called “girdling” where those phloem cells are removed. Girdling, also called ring-barking is the complete removal of a strip of bark. from around the entire circumference of either a branch or trunk of a woody plant. Girdling results in the death of the area above the girdle over time. A branch completely girdled will fail and when the main trunk of a tree is girdled, the entire tree will die.
So, the tree’s survival depends on not only its roots, but also its “patta” containing those critical phloem cells. Thus, CONDITIONS are as important as ROOT CAUSES, and both these taken together is "nutriment" ("ahara") for the tree.

Welcome back. While this answer contains no references to the Pali suttas, it is well reasoned. I like it. Regards

Your next two (”nutriment“ (”ahara“) and ”root“ (”mula") ) is a bit more difficult to point out.. but I will give it a good try. Thks for your compliment as I rarely get one from you. :)

Paccaya/hetu/āhāra = Whole Condition (Lead&Supporting Condition) in paṭiccasamuppāda.
Mūla = Lead Condition/Root Condition in paṭiccasamuppāda.
Mūla = "Root" in pāli language. Life is similar  to a tree, lobha&dosa&moha&whole unwholesome are the seed & root of life. When you want to kill this tree you have to destroy whole seed&root. Because if you destroy just the top of tree, new trees can grow up again and again by the left seeds&roots. This is the reason which pali often use mūla as Lead Condition. See the quote sutta below for more explanation.
HetuPaccaya is used by sāriputta-mahāsāvaka in paṭṭhāna-abhidhammapiṭaka because he have to avoid to conflict mūla with Sutta Pitaka Vol 4 : Sutta. Ma. Mū.  {285.1} (English translation). if he use mūla in this context instead of hetu, all other unwholesome saṅkhāra can't be mūla, so paṭṭhāna will conflict with that sutta. That's the reason why sāriputta chose hetu instead of mūla for paṭṭhāna.
Paccaya/hetu/āhāra = Whole Condition (Lead&Supporting Condition)
Playing as lead condition in paṭiccasamuppāda

Tasmātihānanda  eseva  hetu  etaṃ  nidānaṃ  esa  samudayo esa paccayo
upādānassa yadidaṃ taṇhā. --Sutta Pitaka Vol 2 : Sutta. Tī. Ma. {58.3} / (English translation)

Playing as supporting condition in paṭiccasamuppāda

tasmātihānanda eseva   hetu   etaṃ  nidānaṃ  esa  samudayo  esa  paccayo  vedanāya yadidaṃ phasso.  --Sutta Pitaka Vol 2 : Sutta. Tī. Ma. {58.3} / (English translation)
Kavaḷīkāro āhāro oḷāriko vā sukhumo vā phasso dutiyo manosañcetanā tatiyā viññāṇaṃ catutthaṃ . ime kho bhikkhave cattāro āhārā bhūtānaṃ vā sattānaṃ ṭhitiyā sambhavesīnaṃ vā anuggahāyāti. --Sutta Pitaka Vol 8 : Sutta. Saṃ. Ni. [31] / (English translation)

Mula = Lead Condition/Root Condition

{79.7}   Katamo   ca   sīha   pariyāyo   yena   maṃ  pariyāyena sammā    vadamāno    vadeyya   tapassī   samaṇo   gotamo   tapassitāya
dhammaṃ   deseti   tena   ca   sāvake   vinetīti   .   tapanīyāhaṃ
sīha pāpake     akusale     dhamme    vadāmi    kāyaduccaritaṃ
vacīduccaritaṃ manoduccaritaṃ     yassa    kho    sīha    tapanīyā
pāpakā    akusalā Dhammā     pahīnā    ucchinnamūlā    tālāvatthukatā
anabhāvaṃ    katā āyatiṃ     anuppādadhammā     tamahaṃ    tapassīti
vadāmi    tathāgatassa kho   sīha   tapanīyā   pāpakā   akusalā
dhammā   pahīnā  ucchinnamūlā tālāvatthukatā    anabhāvaṃ   katā
āyatiṃ   anuppādadhammā   ayaṃ   kho sīha   pariyāyo  yena  maṃ
pariyāyena  sammā  vadamāno  vadeyya  tapassī samaṇo gotamo
tapassitāya dhammaṃ deseti tena ca sāvake vinetīti.
{79.8}  Katamo  ca  sīha  pariyāyo  yena  maṃ  pariyāyena  sammā vadamāno   vadeyya   apagabbho   samaṇo   gotamo   apagabbhatāya
dhammaṃ deseti  tena  ca  sāvake  vinetīti  .  yassa kho sīha āyatiṃ
gabbhaseyyā punabbhavābhinibbatti    pahīnā    ucchinnamūlā
tālāvatthukatā    anabhāvaṃ katā   āyatiṃ   anuppādadhammā   tamahaṃ
apagabbhoti   vadāmi  tathāgatassa kho   sīha   āyatiṃ   gabbhaseyyā
punabbhavābhinibbatti  pahīnā  ucchinnamūlā tālāvatthukatā   anabhāvaṃ
katā   āyatiṃ  anuppādadhammā  ayaṃ  kho  sīha pariyāyo   yena   maṃ
pariyāyena  sammā  vadamāno  vadeyya  apagabbho samaṇo gotamo
apagabbhatāya dhammaṃ deseti tena ca sāvake vinetīti. -- Sutta Pitaka Vol 4 : Sutta. Ma. Mū.  {285.1} / (English translation)

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Buddhism And Dimension
What does the perception of Buddhism observe or speculate, about the limitations of our 4 dimensions of perceptual observation (three dimensions of space, giving us the material; and time being the fourth, affording us memory of events within the material that we can judge the present by)?
If Buddhism's pursuit is of enlightenment, could that goal lead to perception of five dimensions of observation (as that perception would afford a picture of the direction of time both ways, and give the observer a picture of every possible event leading from the 'choices' of each of the inhabitants of this world and every outcome of every choice chosen past present and future)?
Is this the enlightenment Buddhism is pursuing (as it would give the observer knowledge of the outcome of every choice, and in a sense the 'Judgement and sentence' of every action, but would detach them from any interaction within the four as a consequence of its perception, and the certainty which would trap any attempt to change the four's events because of the undeniable logic)?

What does the perception of Buddhism observe or speculate, about the
  limitations of our 4 dimensions of perceptual observation (three
  dimensions of space, giving us the material; and time being the
  fourth, affording us memory of events within the material that we can
  judge the present by)?

We can only find limitations for any number of dimensions of perception because all dimensions eventually collapse. Space is not self.Space does not give us material or time. Material is a separate element. It can be classified Earth element. Every element needs to be examined separately. Time is actually embedded with every element as every element must change or perish.

If Buddhism's pursuit is of enlightenment, could that goal lead to
  perception of five dimensions of observation (as that perception would
  afford a picture of the direction of time both ways, and give the
  observer a picture of every possible event leading from the 'choices'
  of each of the inhabitants of this world and every outcome of every
  choice chosen past present and future)?

No dimension can include all choices we make because sometimes there is free will. Free will by definition can not be predicted individually or statistically. In other words if you tell me through prediction what I will do in future then I sometimes have the free will to change it. For example if you predict that I will stop this sentence with a full stop then I won't

Is this the enlightenment Buddhism is pursuing (as it would give the
  observer knowledge of the outcome of every choice, and in a sense the
  'Judgement and sentence' of every action, but would detach them from
  any interaction within the four as a consequence of its perception,
  and the certainty which would trap any attempt to change the four's
  events because of the undeniable logic)?

I don't think so. Enlightenment is state which is unborn , uncreate. Nirvana can not be expressed in words because the One who attained Niravana can not be said to conscious or unconscious or choice driven or choiceless.

I agree with some of your statements but determinism does not allow a nature of change of events even when determinism has been concluded as it logically opposes the nature in its determination and conclusion. Free will is a concept that i think will be discussed for millennia even after science attempt to support it with a nature in the outcome of quantum being uncertain events that ultimately shape our classical perception. And my singular objection is the nature of definition of random or chaotic events and its antidote of certainty having no Truth full absolute without argument.

And even causality and classical physics leads you to a defensible argument with no precise truth in action and reaction that recursively makes its own argument invalid and inconclusive and results in truth being a factor of faith and subjective and unobjective fact.

There is indeed a rumour that Enlightenment may open freedom of travel in an extra dimension. If this were true, here is one way it could work:
For a human observer the extra dimension could look like parallel/alternative variants of reality, analogous to what's described in the endless works of fiction. Moving along this dimension would require ability to see the space of variants, which to the observer would look like (partially constrained) perceptual ambiguity. Picking one concrete perceptual interpretation among the variants would constitute moving along the extra dimension. In order to see the ambiguity of the extra dimension, one would need to learn to overcome the deeply ingrained habit of rigid interpretation. Altogether this could look rather similar to mastery of Emptiness as is taught in Mahayana Buddhism, particularly in Vajrayana and Zen.
The author of this answer had some first-hand experience with the above, enough to suspend his judgement and admit possibility thereof.
Another line of thinking interprets time as dimension that things evolve along, denying possibility of free will in the absolute sense and only leaving it as a perceptual illusion from the perspective of an individual observer. This seems to be logically consistent with the teaching of anatta, and is confirmed by historical Zen Masters either explicitly (Dogen) or implicitly.

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thanks for your retort but it seems to me that travel along the extra dimensions that we naturally have space and time ultimately revolve to a singular unchanging perception while the surroundings do not and there events cascade through determinable factors not of the knowledge of the the singular person because of the bubble they are in, this postulation still depends upon a nature of determinism which affords and is inseparable from the desire of dimensional travel and suffers a current limitation in the nature of our understanding of time as exterior to three dimensions.

What does the perception of Buddhism observe or speculate, about the limitations of our 4 dimensions of perceptual observation (three dimensions of space, giving us the material; and time being the fourth, affording us a memory of events within the material that we can judge the present by)?
If we understand dimension as a vector direction in which energy or information is expressed, then I will say Buddhism largely acknowledges the limitations of perceptual four dimensions. With my definition, you can say that each of the four Jhnanas are different dimensions of existence which are hidden from the ordinary experience. As a matter of fact, Buddhism says that there are 121 different states of consciousness, rendering each of them as a dimension of existence in turn.
If Buddhism's pursuit is of enlightenment, could that goal lead to the perception of five dimensions of observation?
You have limited your view to physicalist point. Enlightenment will entail witnessing everything, ability to look into the future is a trivial thing, IMHO the leaves in the hands of Buddha are fewer than the total leaves in the woods. The Rabbit hole is the abyss.
Is this the enlightenment Buddhism is pursuing.....?
What you say is the obvious byproduct, but that's not what is being pursued.

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Can you criticise or improve Ven. Bodhi's description of Mahayana
Here I summarised, and here I referenced, this little essay by Bhikkhu Bodhi: Dhamma and Non-duality (the first four paragraphs seem to be about Advaita Vedanta, the remainder about "Mahayana Buddhism").
The first time I referenced it was for a question about non-duality, and the second for a question asking whether "enlightenment" (which I took to include, "nearly enlightened behaviour") is the same for all schools of Buddhism -- because it seems to contrasting Mahayana with Theravada.
I guess it's likely that what Ven. Bodhi wrote is partly true, but written from a Theravada point of view.
I was wondering whether you could read and critique the essay (or if that's too much, especially the bits of it which I quote below); for example:

Is it (or are bits of it) misleading or wrong?
Are bits of it unclear, could be better expressed?
Does it focus on (put undue emphasis on) the wrong thing, e.g. "non-duality")? Or does it concentrate on atypical examples, or on outliers that it's better to ignore, e.g. "crazy wisdom"?

At least one or two people here thought it was wrong:

Bhikhu Bodhi views on Mahayana are false and denigrate Mahayana. In fact, emptiness in Mahayana is empty itself. Therefore in Virtue it doesn't reject rules, but only shows their conditional (empty) nature. In Meditation, it doesn't refute that causes lead to effects, it only shows their conditional (empty) nature, which helps to abandon them, for example, instead of keeping attempts to battle them. So Mahayana doesn't refute the truths of Buddha, it only shows better ways to their realization. In Wisdom, true reality is NOT the One. "The One" is just an illusory idea. Be careful.

I'm not sure I understand all of this comment/explanation though; for example, does it suggest that the rules of virtue are empty (conditional)? Does it say that causes are empty, or that effects are empty, or is it that Pratītyasamutpāda itself is empty, and what exactly should be abandoned? Does "abandon that which is empty" suggest that the rules of virtue too should or can be abandoned, and if so isn't that partly (or even mainly) what Ven. Bodhi seems to be complaining or puzzled about?

Here's a quote from Wings to Awakening by Thanissaro Bhikkhu:

The regularity of the Dhamma, here, denotes the causal principle that underlies all "fabricated" (saṅkhata) experience, i.e., experience made up of causal conditions and influences. Knowing this principle means mastering it: one can not only trace the course of causal processes but also escape from them by skillfully letting them disband. The knowledge of Unbinding is the realization of total freedom that comes when one has disbanded the causal processes of the realm of fabrication, leaving the freedom from causal influences that is termed the "Unfabricated."

I understand that to mean:

Observe (fabricated) phenomena
See the causal processes
Make choices which lead toward cessation

To that extent I thought that Pratītyasamutpāda itself isn't empty nor abandoned -- instead it's used. And the whole doctrine is dualistic -- things are skilful or unskillful, wise or unwise, right or wrong, attentive or inattentive, leading to cessation or not, etc.
So, for example, this time from Dhamma and non-duality again:

When we investigate our experience exactly as it presents itself, we find that it is permeated by a number of critically important dualities with profound implications for the spiritual quest. The Buddha's teaching, as recorded in the Pali Suttas, fixes our attention unflinchingly upon these dualities and treats their acknowledgment as the indispensable basis for any honest search for liberating wisdom. It is precisely these antitheses — of good and evil, suffering and happiness, wisdom and ignorance — that make the quest for enlightenment and deliverance such a vitally crucial concern.

The bits of the essay where he seems to me especially critical of (or misunderstanding of) what he perceives as a non-dual doctrine of Mahayana are:

Virtue:

Such distinctions, it is said, are valid only at the conventional level, not at the level of final realization; they are binding on the trainee, not on the adept. Thus we find that in their historical forms (particularly in Hindu and Buddhist Tantra), philosophies of non-duality hold that the conduct of the enlightened sage cannot be circumscribed by moral rules. The sage has transcended all conventional distinctions of good and evil. He acts spontaneously from his intuition of the Ultimate and therefore is no longer bound by the rules of morality valid for those still struggling toward the light. His behavior is an elusive, incomprehensible outflow of what has been called "crazy wisdom."

Meditation:

Since, for the non-dual systems, distinctions are ultimately unreal, meditation practice is not explicitly oriented toward the removal of mental defilements and the cultivation of virtuous states of mind.
The meditative themes that ripple through the non-dual currents of thought declare: "no defilement and no purity"; "the defilements are in essence the same as transcendent wisdom"; "it is by passion that passion is removed."

Wisdom:

In the non-dual systems the task of wisdom is to break through the diversified appearances (or the appearance of diversity) in order to discover the unifying reality that underlies them. [...] For such systems, liberation comes with the arrival at the fundamental unity in which opposites merge and distinctions evaporate like dew.
In the Ariyan Dhamma wisdom aims at seeing and knowing things as they really are (yathabhutananadassana). Hence, to know things as they are, wisdom must respect phenomena in their precise particularity. Wisdom leaves diversity and plurality untouched. It instead seeks to uncover the characteristics of phenomena, to gain insight into their qualities and structures. It moves, not in the direction of an all-embracing identification with the All, but toward disengagement and detachment, release from the All.

Ven. Bodhi:

This is the claim that there is no ultimate difference between samsara
  and Nirvana, defilement and purity, ignorance and enlightenment.
  For the Mahayana, the enlightenment which the Buddhist path is
  designed to awaken consists precisely in the realization of this
  non-dualistic perspective. The validity of conventional dualities is
  denied because the ultimate nature of all phenomena is emptiness, the
  lack of any substantial or intrinsic reality, and hence in their
  emptiness all the diverse, apparently opposed phenomena posited by
  mainstream Buddhist doctrine finally coincide: "All dharmas have one
  nature, which is no-nature."

There is no such claim in Mahayana, that is incorrect understanding of non-duality.
If person skips pieces of Mūlamadhyamakakārikā dealing with concepts of identity (ekatva) and difference (nanatva) in chapters MMK22 (tathagata) and MMK24 (four truths) where Nagarjuna prepares us for MM25 and specifically MMK25.19-20, then one gets opaque and incorrect understanding of Nagarjuna's treatise. There are also vast concerns and disputes raised by scholars on correctness of Stcherbatsky's analysis and K. K. Inada's translation, but it is a topic for a different discussion.
On Buddhist school differences. Everyone that wants to reconcile Theravada and Mahayana should read some of Third Turning of the Wheel sutras for their purpose was to reconcile the two schools. These sutras are a fundament of Yogacara school which is present in Mahayana for the most part.
For instance, Samdhinirmocana Sutra:

Character of compound realm of the ultimate is a character devoid fo
  sameness and difference.  Those who impute sameness or difference are
  improperly oriented.
(...)
Suviśuddhamati, for instance, it is not easy to designate the
  whiteness of a conch as being a character that is different from the
  conch or as being a character that is not different from it. As it
  is with the whiteness of a conch, so it is with the yellowness of
  gold.

You cannot separate yellowness from gold, they are dependent on each other. So key point here is that, non-duality means that things are not one, but neither they are different - they are somehow composite. And this is the Middle way. Bad cannot exist on it's own, for the concept of Good has to exist, so they complement each other on the layer of dependency. Consciousness cannot exist on its own, for it to exist there must be all other Skandhas to form a sentient being;  it cannot be ripped apart and exist on its own as consciousness. And so on.
If we watch World Cup and cheer for one team watching a game, it is easy to generate ill-will towards players and fans of other team, but in truth, without Team B there wouldn't be a game of football. It is humanity playing a game in which it doesn't have to be Us against Them, let the better team win in fair play and everyone be merry. Here, Team A and B are different, but same as well, they are all football players and human beings. Non-duality generates compassion, for it takes into account totality and complexities of dependent origination and cause and effect.
Now, on getting touch with the reality and non-conceptuality:

Suviśuddhamati, if the character of the compounded and the character of the ultimate
  were different, then the ultimate character within all characters of
  compounded things would not be their general character.

Here, non-dual way is to look deeply into Emptiness as the realm of ultimate is the common characteristic of all things. It is the origin of all things. So our conceptual visualisations are typically not different from the ultimate truth, but they are not the same either. And this is the Middle way. Insight into ultimate takes us to the middle way between the two where we experience realm of suchness. The realm where we see past delusions of inherently existent phenomena.
Let's spin the Wheel:

One makes things into objects, so one can be a subject. I attach to signs. I see the mountains. First turning of the wheel.
One then understands how things are not fully expressed by mere concepts. I detach from signs. I don't see the mountains. Second turning of the wheel.
One understands that conceptual objects lack real representations of things and goes beyond them, reconciling ultimate with contextual. I see the mountains again. I attach to signs through lens of three natures: Signs have Imaginary nature. Signs have Dependent nature. Signs have Truly Existent nature. Third turning of the wheel.

Such non-conceptual (but conceptual also!) way is purest way of experiencing compassion by getting in touch with suchness. The ultimate of love, compassion and joy cannot be expressed with boxed and sliced compartments of signs and words. They need context and that is experienced by insight into Emptiness. There is essence beyond speech and thoughts and words and expressions cannot reach it. It is the things as they are.
If we understand, transcending limitations of fixed dual concepts and go can go forth through prejudices; we are neither same, nor different from each other. We are not different from the world. Example here: I need to be ecologist and take care of the planet because I consume nature's crops, resources, but also I am built of nature's elements; water and oxygen. Now everything depends upon me and my life has great purpose.

You say, “There is no such claim in Mahayana.”  Yes, there is. Specifically Verses 19 and 20 of chapter 25 of Nagarjuna’s Fundamental Treatise on the Middle Way. Venerable Bodhi’s paraphrase saying they are not ultimately different is fine even if the language is a bit imprecise. Also, the Third Turning is not definitive teaching. Nagarjuna’s treatise is the definitive teaching on emptiness and needs no reconciliation.

No, there is a phrase but not the teaching itself. Therefore there isn’t such claim. These aren’t one and the same without distinction as this is simply nihilism and Buddha taught middle way.

Every verse in the MMK has meaning and is important. I agree that samsara and nirvana aren’t the same without distinction. Nevertheless, ultimately speaking they are exactly the same without distinction. Why? Because they do not exist ultimately... that is neither can withstand ultimate analysis.

As for Third turning of the wheel is definite teaching for anyone that recognises Yogacara philosophy in any way. And it is pretty much omnipresent in Mahayana, though not some much in Vajrayana.

But again you talk ultimately, yes ultimately pretty much so, but we have concepts we have to validate against ultimate, therefore we can only come in the middle to become disillusioned and beyond conceptual.

I see nothing amiss with the words of Ven. Bodhi in the first paragraph. Mahayana is cautious about the phrase 'Middle Way'  It should not imply the reality of the two extremes. In an Ultimate sense the Middle Way view is a denial of the Middle Way. 'Middle Way' would be a Conventional phrase, relevant where we are opposing two views, metaphysical positions or concepts but meaningless when we are not. Nagarjuna proves that all distinctions are reducible. Samsara and Nirvana would be a classic case. His proof is complex but his result is very simple.         .  ,  .

Modern Mahayana as practiced today has several sub-schools which are not always in agreement about various points of doctrine. Moreover, you can find practitioners of these various traditions on this forum. Venerable Bodhi to his great credit acknowledges this right up front in his essay. With this in mind I'll try and give the critique from my specific school of the Tibetan Gelug viewpoint as I understand it. Mind you, I'm just a Buddhist patzer so please take with a grain of salt.
I have great respect for Venerable Bodhi and so I want to couch any critique of his essay with this disclaimer as well as note that it was written quite a few years ago. I would be highly surprised if Venerable Bodhi's position hasn't changed quite a bit since 1998. I believe he acknowledged as much in helping to give the Theravada viewpoint in Buddhism: One Teacher, Many Traditions.
Now, the first thing I would vehemently dispute is this:

The Mahayana schools, despite their great differences, concur in
  upholding a thesis that, from the Theravada point of view, borders on
  the outrageous. This is the claim that there is no ultimate difference
  between samsara and Nirvana, defilement and purity, ignorance and
  enlightenment. For the Mahayana, the enlightenment which the Buddhist
  path is designed to awaken consists precisely in the realization of
  this non-dualistic perspective. The validity of conventional dualities
  is denied because the ultimate nature of all phenomena is emptiness,
  the lack of any substantial or intrinsic reality, and hence in their
  emptiness all the diverse, apparently opposed phenomena posited by
  mainstream Buddhist doctrine finally coincide: "All dharmas have one
  nature, which is no-nature."

The keyword that deserves special emphasis in the above is, "there is no ultimate difference." This is undoubtedly taken from Nagarjuna's Fundamental Treatise and has been misunderstood. The point is that in terms of essence or inherent existence that Samsara and Nirvana are exactly the same: they both utterly lack essence. Nevertheless, Samsara and Nirvana are very, very, very different and Mahayana does not make the outrageous claim that they are exactly the same. To think otherwise is to have mishandled the snake of shunyata to disastrous effect. Furthermore, it is not at all true that Mahayana holds that the, "validity of conventional dualities is denied." Quite the opposite! Conventional dualities exist. They are important. Suffering and Happiness exist. To deny this is tantamount to denying refuge in the Buddha, Dharma and Sangha ie., it is a terrible fallacy. Nevertheless, conventional dualities are exactly that: conventional! They do not have any ultimate inherent existence. If they did, they would not be conventional dualities, but rather ultimate or inherent dualities.
Another big dispute I have with Venerable Bodhi's presentation is this:

The teaching of the Buddha as found in the Pali canon does not endorse
  a philosophy of non-dualism of any variety, nor, I would add, can a
  non-dualistic perspective be found lying implicit within the Buddha's
  discourses.

This is wrong. You can find in the pali canon teachings on the very same doctrine of emptiness that Nagarjuna expands upon in his Fundamental Treatise. Everything Nagarjuna asserts in the Mahayana has its core foundation in the suttas found in the pali canon.
Now, for something that I completely agree with from Venerable Bodhi's essay:

When we investigate our experience exactly as it presents itself, we
  find that it is permeated by a number of critically important
  dualities with profound implications for the spiritual quest. The
  Buddha's teaching, as recorded in the Pali Suttas, fixes our attention
  unflinchingly upon these dualities and treats their acknowledgment as
  the indispensable basis for any honest search for liberating wisdom.
  It is precisely these antitheses — of good and evil, suffering and
  happiness, wisdom and ignorance — that make the quest for
  enlightenment and deliverance such a vitally crucial concern.

Well said! This deserves extra emphasis and is entirely in keeping with the Mahayana perspective. Buddhism is the empirical practice of studying the problem of suffering and existence and finding an antidote. It is based upon reason and personal verification of truths that have been discovered. It is a path to be walked and finally completed. Denying the existence of these important dualities will lead to a dead end at best and the Avici hell at worst.
So if Buddhism is a practical empirical matter, then why does the Mahayana emphasize the doctrine of emptiness which seems to be an etherial metaphysical issue divorced from practical consequence? Precisely because the great Spiritual Heroes of the past have discovered through empirical practice and verification that the only way to uproot suffering is to directly realize the utter lack of inherent existence in all of those critically important conventional dualities mentioned above. Directly realizing the emptiness in all things is emphasized precisely because it is a practical necessity to completing the spiritual path for all of our soteriological aims.
Continuing on I would dispute this:

Such distinctions, it is said, are valid only at the conventional
  level, not at the level of final realization; they are binding on the
  trainee, not on the adept. Thus we find that in their historical forms
  (particularly in Hindu and Buddhist Tantra), philosophies of
  non-duality hold that the conduct of the enlightened sage cannot be
  circumscribed by moral rules. The sage has transcended all
  conventional distinctions of good and evil. He acts spontaneously from
  his intuition of the Ultimate and therefore is no longer bound by the
  rules of morality valid for those still struggling toward the light.
  His behavior is an elusive, incomprehensible outflow of what has been
  called "crazy wisdom."

This is wrong. What does it even mean to say that conventionally existent things are only binding on the trainee and not the adept?? This sounds again like someone has grasped the snake of emptiness incorrectly.
What is the foremost warning given repeatedly over and over and over in the Mahayana literature in the gravest possible language: that surmising emptiness to mean that conventional existents like karma, rebirth, virtuous conduct, etc are ultimately non-existent therefore it doesn't matter how you behave is completely wrong and indicates anyone surmising so has grasped the snake of shunyata incorrectly leading them directly to the Avici hell.
There is a reason this is emphasized and repeated over and over. It acts as a guidepost or a handrail against the very real danger of misunderstanding emptiness which sentient beings are prone to do. If you think emptiness means that those conventional existents are trivialities to be ignored by adepts, then you have reached an incorrect understanding friend and this way lies dragons. Turn back!!!
I'll leave it at that. I don't deny that there are practitioners of Mahayana who have - to profound sorrow and regret - mishandled the snake of emptiness just as Venerable Bodhi seems to be stating in his essay. What I'd dispute is that all Mahayana adherents who study emptiness arrive with this mistaken grasp on the snake of emptiness.
Moreover, I'd assert - contrary to the essay - that grasping the snake of emptiness correctly and directly realizing the lack of inherent existence in all phenomena is a matter of paramount practical necessity for entering into the complete and ultimate enlightenment.
Hope this helps!

Re. what you called your second "big dispute" -- the Pali canon does literally talk about "emptiness" more than once; but does it talk about "a non-dualistic perspective"? Does emptiness count as "a philosophy of non-dualism of any variety"? I'm confused, partly because you said that e.g. the fact that suffering and happiness are both empty doesn't make them the same (doesn't make them non-dual) ... which implies that emptiness and non-duality aren't the same thing?

I don’t use the phrase non-dual or dualistic, but the way Venerable Bodhi used them I assumed was analogous to what we refer to as ultimate existents vs conventional existents. Maybe he meant something else...

Thanks. Wikipedia suggests it's a term of broad meaning, different meanings in different religions. Perhaps I should assume that it's not only not used in the Pali canon, it's also not used in Mahayana (i.e. that there are only various other more specific terms used). But in comments like this you used "non-duality" as if it were an orthodox term ... maybe you meant to use a different word there.

Yeah, I meant emptiness sorry.

I don't see any issue from Ven. Bodhi's "Dhamma and NonDuality" essay. He simply stated the obvious and any serious Mahayanist would have to agree. Why? because even in Mahayana, there's a famous case study designed specifically to caution their practitioners about the danger of the double-edged NonDuality sword. It's called "Pai-Chang's Fox". Five hundreds lifetimes as a wild fox just because of one wrong view is a strong enough lesson for a high-ranking venerable to finally realize the meaning of "Suffering is the same as Nibbana"...:-):

Every time Baizhang, Zen Master Dahui, gave a dharma talk, a certain old man would come to listen. He usually left after the talk, but one day he remained. Baizhang asked, "Who is there?"
The man said, "I am not actually a human being. I lived and taught on this mountain at the time of Kashyapa Buddha. One day a student asked me, 'Does a person who practices with great devotion still fall into cause and effect?' I said to him, 'No, such a person doesn't.' Because I said this I was reborn as a wild fox for five hundred lifetimes. Reverend master, please say a turning word for me and free me from this wild fox body." Then he asked Baizhang, "Does a person who practices with great devotion still fall into cause and effect?"
Baizhang said, "Don't ignore cause and effect."
Immediately the man had great realization. Bowing, he said, "I am now liberated from the body of a wild fox. I will stay in the mountain behind the monastery. Master, could you perform the usual services for a deceased monk for me?"
Baizhang asked the head of the monks' hall to inform the assembly that funeral services for a monk would be held after the midday meal. The monks asked one another, "What's going on? Everyone is well; there is no one sick in the Nirvana Hall." After their meal, Baizhang led the assembly to a large rock behind the monastery and showed them a dead fox at the rock's base. Following the customary procedure, they cremated the body.

Hmm, I'd say Venerable Bodhi has correctly diagnosed how some Mahayana practitioners misunderstand non-duality to disastrous effect. The issue I take is that Venerable Bodhi does not acknowledge in his essay that it is possible to understand non-duality correctly. Indeed, that it is necessary to do so in order to attain enlightenment. See my answer. Do you agree?

I think the Pai-Chang's case study pretty much spoke for itself. If a high ranking Buddhist master still paid a dear price for misunderstanding Nonduality, how much more careful should us common folks be toward the concept. It's certainly not the teaching for novices and so I wouldn't even bother wrestling with it for now. Ven. Bodhi was right, we should stick to the tried-and-true 4NT, 8FNP and when the time is right, Nonduality will take care of itself automatically.

@YesheTenley - I feel your comment is spot on. I may add an answer later but for now my comment would be that I agree with your comment. The essay embodies some serious misunderstandings. To be honest I'm surprised at the extent of the misunderstanding, .

[EDIT: I won't change much of this answer but I see in hindsight it is too blunt and argumentative. The substantive points seem correct but the language is all wrong for the venue. I've deleted the first line for being inflammatory. Apologies.]
I started to copy extracts in order to discuss them but quickly gave up. Almost every paragraph exhibits a failure to understand non-dualism. I find the article unrigorous, partisan and almost willfully ill-informed. Such a shame these misleading essays are published.
I'll comment on some extracts.
My second remark would be to point out simply that non-dualistic spiritual traditions are far from consistent with each other, but comprise, rather, a wide variety of views profoundly different and inevitably colored by the broader conceptual contours of the philosophies which encompass them.
This is demonstrable nonsense. Non-dualism requires a neutral metaphysical theory for which all positive metaphysical positions are rejected. Once we adopt this neutral position serious disagreements are out of the question. Thus non-dualists are able to endorse Philosophical Taoism, Sufism, Middle Way Buddhism, Christian mysticism, advaita, Modern Druidism, Patanjali's Yoga, the teaching so Sri Ramana Maharshi and more. This is possible because non-dualism forces us to normalise on the same doctrine with very little room for argument.
The 'philosophies that encompass them' is non-dualism and because it encompasses them they do not disagree with each other. I read this paragraph as saying 'I have not studied this topic'.
The teaching of the Buddha as found in the Pali canon does not endorse a philosophy of non-dualism of any variety, nor, I would add, can a non-dualistic perspective be found lying implicit within the Buddha's discourses.
This is tosh. The Buddha's teachings depend utterly on the non-dual nature of Reality. If we know what to look for we find nothing in the sutras but an endorsement of the non-dual philosophy. Not everyone does, of course, but those who do not must be content to have no philosophical grounding at all. Then Buddhism ends up in the same boat as Whitehead's commonplace Christianity. 'a religion is search of a metaphysic'. The fact is that Buddhism is either grounded on the only philosophy that survives logical analysis, which is non-dualism, or is logically indefensible. This is what Nagarjuna proves and it has been well-proven by Western philosophy. The reason Western philosophers cannot comprehend philosophy is that they reject non-dualism. If we wish to render Buddhist doctrine incomprehensible then all we need do is reject it.
At the same time, however, I would not maintain that the Pali Suttas propose dualism, the positing of duality as a metaphysical hypothesis aimed at intellectual assent. I would characterize the Buddha's intent in the Canon as primarily pragmatic rather than speculative, though I would also qualify this by saying that this pragmatism does not operate in a philosophical void but finds its grounding in the nature of actuality as the Buddha penetrated it in his enlightenment.
Of course the Pali suttas do not endorse dualism. Rather, they endorse non-dualism. There is no reasonable third option.
It is surely obvious that Buddha's intent was pragmatic rather than speculative and that this pragmatism is informed by knowledge, viz. the knowledge that the true and Ultimate nature of Reality is non-dual. If it is otherwise then Buddhism must be taught in a philosophical vacuum just as if the Buddha did not understand metaphysics and as if nobody has done so since. This idea is profoundly absurd and demonstrably incorrect. I cannot grasp how anyone could so badly misunderstand philosophy or Buddhism.
In contrast to the non-dualistic systems, the Buddha's approach does not aim at the discovery of a unifying principle behind or beneath our experience of the world.
I can hardly believe I'm hearing a supposed Buddhist say this. Has he read the sutras? I suppose one could argue that the Buddha's approach does not aim at anything except the discovery of truth, but it is clear that what is discovered is the non-dual nature of Reality.
It would be precisely because of the non-dual nature of Reality that the Buddha was so reluctant to speak about metaphysics. To do so requires a language of paradox and contradiction that would merely confuse many of his listeners. The only other possibility would be that he did not understand metaphysics and this is not plausible.
Instead it takes the concrete fact of living experience, with all its buzzing confusion of contrasts and tensions, as its starting point and framework, within which it attempts to diagnose the central problem at the core of human existence and to offer a way to its solution. Hence the polestar of the Buddhist path is not a final unity but the extinction of suffering, which brings the resolution of the existential dilemma at its most fundamental level.
It is only because Reality is non-dual that all dilemmas may be resolved and suffering may be ended. If Reality is not non-dual then the Four Noble Truths could not be true. The 'polestar' of the path is the union with Reality made possible by its ultimate unity.
Does not the Buddha advise us to abandon all our extreme views? How much more clearly could he endorse the non-dual philosophy? If we abandon extreme views we arrive at non-dual Reality for which all extreme or positive views are false. This is a neutral metaphysical position as proved and endorsed by Nagarjuna. Even Kant could work out that all extreme views are logically unworkable, and even Russell and Carnap. So can we all with some work. This is basic philosophy.
These extracts appear early in article. I have no inclination to read further. I see no understanding of the non-dual doctrine in this article and am embarrassed for its author. If I knew so little about non-dualism I'd not dare say a word about it in public. Even a scholastic philosopher with no meditative experience should be able to understand it better than this.
I would want to delete the target article from the internet for doing serious damage to Buddhist teachings and to mysticism in general.
If this seems arrogant, as it will to some, then this is a misperception. Non-dualism is provable in philosophy by the use of logic and reason with no appeal to scripture or conjecture, as Nagarjuna demonstrates. It simply 'stands to reason', where no other doctrine does. No speculative opinions are necessary if we 'shut up and calculate' as would a mathematician, We cannot actually get to Heaven by this method but at least we can make a decent map.
In short, Chris, my answer would be yes, and very easily.

Three questions, if I may, about non-duality as you describe it here and what that means. # 1 "Skillful versus unskillful", "dukkha versus sukha", "right view versus wrong view" -- these feature prominently in the suttas as doctrine. Are these not what you'd call "dualities"? Are they compatible (not inconsistent) with your describing both Reality and the Dhamma as "non-dual"? How do these relate to "non-dual Reality"? # 2 What's the connection between "non-duality" and the "four noble truths" -- how are they related, how is reality's being non-dual essential to the truth of the 4NT?

# 3 Are you saying that Buddhism and Sufism are the same? No you're not but you're saying that a non-dualist is able to endorse both. I might have found "non-dual" explanations difficult to make sense of in the past, like, "LOL there's no real difference -- everything is everything and nothing" is kind of hard to grasp -- maybe "hard to grasp" is part of the point of it, but (most unlike the suttas, even contrary to the suttas) that seems not at bit prescriptive.

@ChrisW - 1 - All views are wrong in the end since truth cannot be captured or known as a view and Reality would be beyond conceptual fabrication. 2.If there is cessation of suffering then suffering must be unreal (in some sense). The trick of grasping this doctrine is (imho) understanding the distinction between Conventional and Ultimate truth, and thus the need for a contradictory language that confuses almost everyone. I cannot say much about it here but have written much elsewhere, including a dissertation. .I'd be honoured if you wanted to read some of my efforts.

I'm not suggesting Buddhism and Sufism are exactly the same, by the way, but that they both depend on the same metaphysical position and the Unity of All. I see no reason why a Buddhist would need to argue with Rumi or Al-Halaj. I would include them both under 'Perennial philosophy'. ,

@PeterJ Taoism agrees on the unity of reality under the name 'Tao'. But (and this nuance makes a huge difference), the Tao Te King tell us that both the nameless Tao and the Tao that can be named are part of the same elemental nature. It is not that one is real and the other wrong/false. The TTK says that concepts are "flashes" of the actual reality, but these flashes might indicate to that source nonetheless. I think this kind of non-dualism is more coherent with the suttas than what Mahayana sutras provide. Kind regards!

You are right about Rumi and many Sufis that lived hundreds of years ago. In Sufism there is the knowledge of Enlightenment Stages that in my opinion same with Buddhism.(I don't know the English informations but you can search this words: "Şeriat, Tarikat, Marifet, Hakikat". ("Şeriat" -Sharia don't have the same meaning of Quran's Sharia). I think "Tarikat, Marifet and Hakikat" means Stream Entry, Sakadagami and Arahant. But I think that most of the modern Sufis have nothing in common with Rumi but they are following a belief system that really don't have any commonalities with Buddhism.

So I think that real Sufism today almost dissapeared from earth. People use the word "Sofu" that I think that word originates from Sufi. And Sofu means fundamentalist of Islam LOL. Also related traditions like Alevism, Bektashism are just folkloric traditions today that don't have any real connections to the Sufi traditions that existed hundreds of years ago. And these traditions are also assimilated by the belief system that certainly don't lead people to direction of Nibbana LOL

@Murathan1 - You may be right about this. if so I'd be depressed. But I wonder if it is just that extremism today makes an open expression of the Sufi view too dangerous. It's always been dangerous but nowadays it might be suicidal. Where monotheism rules it's always been dangerous to talk about Truth and Knowledge. I'll do a bit of research on this to see where Sufism is nowadays. . .

@BrianDíazFlores - I'm not sure how you reach your view when Nagarjuna so clearly endorses the non-dual doctrine. But each to his own. If we wished to get to the bottom of our differences we'd need a different venue. .

@PeterJ I'm completely ignorant of Nagarjuna's arguments, so I cannot speak about that topic. My reply was written from my shallow experience and study of Taoism, which seems to propose some kind of non-dualism, but different in conclusion to Nagarjuna's. According to the TTK, the Tao encompasses everything -the Tao is everything- while at the same time accepting that apperances and concepts are part of that Tao, but not the essencial Tao. While everything is part of the same unity, that does not mean that concepts are useless and completely meaningless.

@PeterJ After all, our brains and minds evolved to understand at least partially the physical phenomena around use. Otherwise, we would had gone extinct as a species a long time ago. If our current mathematical expressions of the laws of physics allow us to predict events, then that must mean that concepts can at least partially understand reality. Concepts, therefore, are not entirely wrong, while at the same time are not reality itself. Kind regards!

At the first approximation, I am with PeterJ on this topic - although I usually try to express it in more reconciling terms rather than argue. @BrianDiazFlores - in my understanding of Tibetan tradition of interpretation of Nagarjuna, they are 100% aligned with the idea that "the illusory" is an actual aspect of "the real" - so the two truths are not in opposition. This assertion is made quite often by Tibetan commentators. Anyway, I generally agree that Ven. Bodhi seems to be almost willfully ignorant/sectarian, a position I can't appreciate.

@AndreiVolkov Oh! That's good to know! Then I think I had the wrong impression because of PeterJ's statement that "all views are wrong in the end since truth cannot be captured or known as a view". Thanks for the clarification! Kind regards!

@BrianDíazFlores - Andrei is right to point out that my approach is rather brutal. This is deliberate but sometimes inappropriate. As he notes, the 'illusory' would be an aspect of the Real and derive its own reality from that source. The absolute would encompass the relative rather than negate it. It's just that for a fundamental analysis the relative would have to seen as contingent and having only a dependent existence. The words 'illusory' and 'unreal' cause a lot of problems for this view, but they are used in a very particular sense.

@BrianDíazFlores - PS - The point about 'views' is a profound one and perhaps doesn't help here. The idea is simply that we cannot conceptualise Reality or capture it in a conceptual view. It's a tricky issue and causes some confusion.  .

@PeterJ I get it and I agree, and I think this deserves a discussion of its own. Thanks for the explanations! Kind regards!

Usually people, esp. from non-highly civilized origins, tend to kneel before authorities. When dealing with titles such as Venerable (in this case Bhikkhu Bodhi), The Holiest (followed by two more D capital letters), or the oldies Your Majesty (queen/king), they just bend for it, bargaining their intelligence and moral for gains (favour, popularity, even security, etc.). It's remarkable to exclaim: "What a terrible article" !!!

@Mishu米殊 - It is a terrible article but I regret the language I used in this answer and deserve to be told off for it. Mine is an answer from a philosopher rather than a Buddhist. Philosophically speaking the article is all over the place. I read it as a hatchet-job on Mahayana designed to mislead. It makes no difference to me what titles piople use. Regardless, I should speak less argumentatively and I'll be more careful in future ( I hope). I may add an edit.   .

I believe that non-duality exists in the Pali Canon based on the various not-self teachings. For example, the Pañcavaggi Sutta elaborates on how the self cannot be found in various phenomenon.

"Form, monks, is not self. If form were the self, this form would not lend itself to dis-ease. It would be possible [to say] with regard to form, 'Let this form be thus. Let this form not be thus.' But precisely because form is not self, form lends itself to dis-ease. And it is not possible [to say] with regard to form, 'Let this form be thus. Let this form not be thus.'
...
"What do you think, monks — Is form constant or inconstant?"
"Inconstant, lord."
"And is that which is inconstant easeful or stressful?"
  "Stressful, lord."
"And is it fitting to regard what is inconstant, stressful, subject to change as: 'This is mine. This is my self. This is what I am'?"
"No, lord."

I admit that is not explicitly stated in this sutra, but I believe that this is where non-duality naturally arises. Because duality requires a frame of reference on the world that generates such distinctions. This "frame of reference" is a type of misapprehended self. For example, declaring some form as mine or yours is the most obvious. But this is true of the claim that something is pure of defiled. One that identifies as disliking ketchup would consider French fries with ketchup as defiled, another would consider them "purified" by ketchup (please forgive the overextended metaphor).
Once one removes themselves from such fixed views, then one opens the door to dispassion and the end of grasping. For grasping can also only occur when one infers a self that either posses something or lacks something, and the resulting feelings lead to passion.

"Seeing thus, the well-instructed disciple of the noble ones grows disenchanted with form, disenchanted with feeling, disenchanted with perception, disenchanted with fabrications, disenchanted with consciousness. Disenchanted, he becomes dispassionate. Through dispassion, he is fully released. With full release, there is the knowledge, 'Fully released.' He discerns that 'Birth is ended, the holy life fulfilled, the task done. There is nothing further for this world.'"


text:
Describe the Mahayana path
This comment writes, reasonably enough:

Worth mentioning regarding Tantra and Vajrayana that Vajrayana is not a path of renunciation

So I was wondering what it is, if it isn't that.
I remembered that I've read that there are, but know very nearly nothing about, Five paths -- starting with the "path of accumulation".

Is this doctrine ("five paths") for/from all (or most) forms of Mahayana, including East Asian and Zen for example, or is it more just Tibetan?
This wiki entry says,

It is called the path of accumulation because it is the stage at which one makes a special effort to gather the accumulation of merit, and also because it marks the beginning of many incalculable aeons of gathering the accumulations.
On the lesser path of accumulation it is uncertain when one will reach the path of joining. On the intermediate path of accumulation it is certain that one will reach the path of joining in the very next lifetime. On the greater path of accumulation it is certain that one will reach the path of joining within that very same lifetime.

There seems to be some controversy about whether (in "Theravada" for example) the doctrine is applicable "this very life" or whether it's understood as happening over multiple lifetimes.
Can you comment on that from a Mahayana view?

I'm not sure that I see the path[s] described in the Pali canon even as a "path of renunciation", though it's true that Nekkhamma is translated as "renunciation".
In formal Christian doctrine I think the word "renounce" is used in the context of "renouncing evil" or "renouncing the devil", and that the word "renounce" comes from a Latin word meaning "to protest".
I think that more informally/conventionally, though, the word is maybe used to imply something like, "try to do without what you like, at least temporarily" -- a person might try to renounce cigarette smoking, for example, or to eat less chocolate, or perhaps vow to stay with only one sexual partner.
I thought that Nekkhamma isn't quite like this informal meaning -- instead it involves clearly seeing the disadvantage of something, and therefore deciding that you don't even want it.
And so I think it might be more accurately described as a "path to cessation" rather than a "path of renunciation" -- cessation of suffering, of hindrances and afflictions etc. So:

Are any/various forms of Mahayana too a "path to cessation", or not exactly?

The definition of a path is: A virtuous mind conjoined with renunciation.
As it says in Maitreya/Asanga's Ornament of Clear Realization:

A path is a virtuous mind conjoined with spontaneous renunciation.
  Boundaries are from the path of accumulation through the buddha
  ground. The synonyms of path are: knower, exalted wisdom, exalted
  knower and clear realization.

Thus, all paths are 'paths of renunciation' in this sense, although I have never come across the expression 'path of renunciation' before.
A Mahayana path is a virtuous mind conjoined with bodhicitta (which renunciation). For instance, generosity in the continuum of a bodhisattva is a Mahayana path. Generosity in the continuum of someone who is on a so-called Hinayana path is a path.
Traditionally, we say that tantra must be practiced in dependence upon the three principles of the path.

Renunciation
The wisdom of emptiness
Bodhicitta

Therefore, it is aimed at bodhisattvas that are at least on the path of preparation, having realized emptiness by way of an inferential cognizer.
There are five paths:

The path of accumulation, where one becomes a bodhisattva by way of generating the spontaneous mind of enlightenment (bodhicitta)
The path of preparation. One enters this path by way of a first inferential (not direct) realization of emptiness, that is a union of samata and vipassana realizing emptiness.
The path of seeing. One enters the path of seeing by way of a first direct realization of emptiness, whereby all dualistic appearances vanish. This wisdom directly realizing emptiness acts as an antidote to the grossest levels of afflictions, therefore it is called the first true path. It is also an arya path. It is the first ground (which continues on to the path of meditation). We say that the ultimate Dharma jewel is true cessation and true path in the continuum of an arya being. This echoes your statements with respect to "path to cessation". Here, the first true cessation occurs upon entering the path of seeing. The buddha-ground or 'path of no-more-learning' is the final true cessation. There are various true cessations before.
The path of meditation. It has the ten grounds (bhumis) but there are also divisions into 11, 13, and 16. At the level of the 8th ground, a bodhisattva is free from all afflictions (just like a so-called Hinayana arhat). He still has to abandon "knowledge obscurations" which are the imprints of the afflictions (like the scent left by the garlic even after it's been removed from a container).
The path of no-more-learning or "buddha ground". One enters it when he is free from the two obscurations: afflictive and knowledge obscurations. From there, one obtains the four kayas (which can also be divided into 2, 3, and 5).

The Mahayana path is called 'path of perfection' because we perfect the perfections (paramitas) on each of the grounds.
From a tantric viewpoint, Tantra could be practiced from the generation of the three principles of the path, or as late as the last moment of ten bhumi. From a tantric point of view, one cannot achieve enlightenment (abandoning knowledge obscurations) without tantra.
The five paths are common to Mahayana traditions, including Zen, Tiantai, etc. It is classic Mahayana Abhidharma.
For instance:

The Blue Cliff Record mentions the 'path of buddhahood', 'path of meditation', etc.
Dogen mentions the 'path of seeing', the ten grounds, including the 'buddha ground' (佛地 butchi).
Wonhyo alludes to the 'path of cultivation' (accumulation), 'path of seeing', 'path of meditation', etc.
Chinul mentions the 'path of meditation', the ten bhumis, etc.
In the Mahaparinirvana sutra, that is commented upon widely, there is mention of the five paths. In 'A study of the unfolding of sinitic mahayana motifs', Wai-lun Lan alludes to 'path of perfection' and 'path of meditation'.
Zhiyi (founder of the Tiantai tradition) also speaks of the five paths and the ten grounds.

Non-renunciation means that Vajrayana might freely use defilements and desires rather than dispelling them or considering them to be renounced.
Vajrayana also uses sense objects in their meditation skilfully, like Guru Yoga or Deity yoga. Mahayana does not use such objects in such way (however, one exemption might be Pure Land Buddhism).
The analogy often given here is snake venom used to create antidotes. And obviously, the end result is renunciation itself! But by different means.
In the end it aims to transform these into skilful thing and positive (i.e. karma) instead of rejecting such attachments. The practitioner might utilise objects of pleasure and desire for the purpose of transforming poison into medicine - like compassionate energy, all, obviously, within reasonable code of conduct.
In Tantra desire is the ornament of enlightenment. Here is a comparison of sutric and tantric approach, some points are arguable, but it is the general picture.
And to summarise, Tsongkhapa:

There is no spiritual path without renunciation as the very definition
  of a spiritual path is an exalted awareness conjoined with
  non-fabricated renunciation, so of course the Vajrayana is a path of
  renunciation - it's a supramundane path if practised properly.
Objects are not contaminated from their own side, so if you remember
  emptiness, your enjoyment is not a cause of samsara.

As for ChrisW's request, here's the excerpt from the book Introduction to Tantra, The Transformation of Desire – Thubten Yeshe:

Tantra’s approach is very different. Instead of viewing pleasure and
  desire as something to be avoided at all costs, tantra recognizes the
  powerful energy aroused by our desires to be an indispensable resource
  for the spiritual path. Because the goal is nothing less than the
  realization of our highest human potential, tantra seeks to transform
  every experience — no matter how “unreligious” it may appear — into
  the path of fulfillment. It is precisely because our present life is
  so inseparably linked with desire that we must make use of desire’s
  tremendous energy if we wish to transform our life into something
  transcendental.
Thus the logic of tantra is really very simple: our experience of
  ordinary pleasure can be used as the resource for attaining the
  supremely pleasurable experience of totality, or enlightenment. It is
  natural that qualities of the mind, when cultivated, produce something
  similar, not opposite, to themselves. This is true for both positive
  and negative states of mind. In the same way that dissatisfaction
  itself can never become satisfaction, misery does not naturally evolve
  into happiness. According to tantra, we cannot hope to attain our goal
  of universal and complete happiness by systematically making ourselves
  more and more miserable. This is contrary to the way things actually
  work. It is only by cultivating small experiences of calm and
  satisfaction now that we will be able to achieve our ultimate goal of
  peace and tranquility in the future. And similarly, it is only through
  the skillful use of desirous energy and by building up the habit of
  experiencing what we might call true pleasure that we can hope to
  achieve the everlasting bliss and joy of full illumination.

From your example, playing music for my own enjoyment could make me happy and exalted enough so I can utilise this very energy in order to help other beings alleviate suffering in a joyful and courageous manner, and help in cultivating my own Pāramitās such as enthusiasm better. And so on, but that also requires great intelligence what HH Dalai Lama always highlights. Someone else could probably find a better examples though.

"skilful thing and positive" sounds all very well but it did leave me wondering whether or how that's related to "cessation" at all -- i.e. nirodha.

Four Noble truths is common so cessation is omnipresent end goal, but here renunciation means abandonment of sensory object based Self-pleasures. Tantra does not negate utilising these as helpful, whereas Mahayana does.

So, is ... playing music (for example) an example of a "sensory object pleasure"? And is that used skilfully in some way, and what (for example) is the hoped-for outcome of such use? Could you comment on whether it's a "self-pleasure" and/or a pleasure for others -- does that come into it? Or would you prefer to pick a different example, other than music?

Thank you for the reference to the table of comparisons too, as well as the addendum quoting Thubten Yeshe and so on.

Great exposition of secret mantra, Je Tsongkhapa:
How, then, are the two vehicles differentiated? Some say that the difference between Sūtra and Mantra is that Mantra was taught for those who can use desire as an aid in the path whereas the Perfection Vehicle was taught in order to tame beings within the context of separation from desire. This opinion is wrong because both the Perfection Vehicle and the Mantra Vehicle have modes of advancing on the path without having abandoned desire and both have modes of progress by cultivating paths to abandon desire.

@TenzinDorje excerpt you are quoting is Dalai Lama's piece on Tantras from Gelug perspective and Tsongkhapa's perspective. Gelug has slightly different opinion on many matters (also non-conceptuality), as far as I know, on renunciation perspective as well. But I might be wrong. Nonetheless, Within the same chapter it is also noted that "Sutra Bodhisattvas who have not yet thoroughly abandoned afflictions" might also utilise desire for the benefit of others. In this context this is correct, but not implied that Tantric practitioner does have such limitations based on criteria of the path.

The context is that of distinguishing tantra from sutra/perfection. To position is that "using desire into the path" is not unique to tantra. What's unique is deity yoga and divine pride, antidotal practices to ordinary appearances and clinging to ordinary appearances.

And the context is Tsongkhapa’s stance, here I am quite sure most Mahayanists would disagree with such statements as they ground their practice on renunciation. Thubten Yeshe also makes it as a primary distinction from other Buddhist practices if you look at Chapter 2 of the Introduction to Tantra.

Unless you can prove me wrong and provide some Sutric Mahayana textual sources where one is allowed to indulge in Self driven desires in order to achieve progress on the path. As far as my understanding goes renunciation is primary practice of developing bodhicitta.

You misread my statement and the quote. "Using desire into the path" doesn't mean what you think it does, and it is an object of abandonment as you say. As to the "desire" in tantra, it is of another type.


text:
How are the fetters by Anapanasati diminished?
According to the Anapanasati Sutta it is this practise that leads to liberation but how does the destruction of (a) fetter(s) exactly happen? Let's take the stage from once-returner to non-returner. The latter one has removed sensual desire and anger. How did this exactly happen during Anapanasati?

I think the progression described in the Anapanasati Sutta can only lead to stream-entry and once-returner but not to non-returner or Arahant because the Anapanasati Sutta includes knowing of in & out breathing at every stage therefore does not yet include the jhana (that has no knowing of breathing) required for non-returner or Arahant.
This said, both the stream-enterer and particularly the once-returner have significantly reduced sensual desire and anger.
How this exactly happens during Anapanasati is insight (vipassana) into not-self (anatta) reduces the self-centredness that is the root of sensual desire and anger and particularly the calming (samatha) stages (4, 8, 10, 11, 12, 14 & 15) provide the non-sensual happiness that allows the mind to naturally lose interest in sensual pleasures. Once sensual desire reduces, the impulse to worldly anger reduces (although some tendency to anger due to moral righteousness may remain).
Stages 5, 6 & 7 are also important (vipassana) because they allow the mind to transcend or decouple from enslavement to pleasant feelings; when it is discerned the peace of non-attachment & samatha is more pleasant than the strong vibrations of pleasant feelings; particularly the agitating quality of rapture (piti). Naturally losing interest in rapture by intimitately experiencing rapture's true nature is a very significant step to losing interest in sensuality.
Stage 9 is also important, where the ugly polluting nature of defilements are discerned directly; like coming face to face with the devil.
In summary, an important result of Anapansati is calm (samatha). When calm is experienced, it feels better than sensual desire or anger; thus breaking/reducing these fetters. Feeling this calm starts at stage 3, which is actually called: "experiencing all bodies (kaya)". The word 'kaya' refers to the physical body, breath-body and mental-body (nama-kaya). Stage 3 is experiencing how a mind of non-desire, non-anger & non-attachment results in the breathing calming and the physical body calming. Stage 3 is about experiencing the 'inter-relatedness' between the mind, breath & body. At stage 3 alone (when properly practised), it is experienced how a mind without sensual desire & without anger causes the breathing, body & mind to calm & feel satisfying peace.

If I can ask, in the first paragraph, when you say "the jhana (that has no knowing of breathing)" do you mean a formless jhana (i.e. beyond the first four)? And why say this is "required for a non-returner"? And are you sure it's a prerequisite (i.e. required before attainment), or is it perhaps subsequent (easier to enter without the fetter) or consequent?

Breathing is not a factor mentioned in suttas in rupa jhana. Ajahn Brahm says there is no awareness of breathing in rupa jhana. Generally it is said non-returner has developed 4 rupa jhana (example commentary to MN 140). Sutta definitely says (somewhere) non-returners can enter the 9th jhana but don't reach arahantship. You could start a new question about this.

Dhammadhatu, monks like Ajahn Jayasaro and many others say that one should curiously observe the breath with interest and not try to strive for concentration. Would you share this? How long would it take to get to the level of vedana and citta and then dhammic phenomena?

My view is even more passive than Ajahn Jayasaro; that is; don't even try to observe the breath at all; only observe the mind to ensure the mind is silent & without any ambition. The mind is naturally conscious and the silent mind naturally knows the breathing. Intent to observe is not required. If there are no hindrances; it takes around 75 minutes of constant observing & calming of breathing to reach rapture. Spine must be natural and erect in posture.

In this case, the means by which we bring the mind to silence is not that important, is it? Is your approach not way too hard? Since by observing the mind (thought processes), one might get caught up in them.

No. No thought processes. No thinking. The mind must be silent in a way that is without craving.

I heard that before doing meditation of breathing it is good to use a more contemplative meditation like metta or asubha to let the mind think systematically and then slowly introduce it to the breath, since going straight to the breath can be a challenge for the mind (because the breath is a rather neutral object)

I did ask another question, including about once- and non-returners and jhanas and/or mindfulness -- here -- not as you would have asked it, most likely, but please feel welcome to answer any part of it.

Anapanasati MN118 is a progression of meditating with breath. This progression is very methodical and it is a guide to relinquishing what we hold on to, a guide to letting go. The progression starts with the breath itself and invites an awareness of the quality of the breath, not a controlling awareness to make the breath anything, but an abiding awareness to observe what the breath is doing. Retaining and extending that awareness as the sutta progresses, one finds this:

Whenever a mendicant practices breathing while experiencing the mind...at that time they meditate observing an aspect of the mind—keen, aware, and mindful, rid of desire and aversion for the world.

As noted by @Dhammadhattu, the phrase rid of desire and aversion for the world occurs in each of the four tetrads, so the release to these happens progressively via each tetrad. Skipping tetrads to achieve a particular result is ineffective. Instead, simply follow the progression. The progression works. Sometimes even the first few steps are enough to deal with daily issues. Relinquishing the fetters is a gradual process. One thread at a time. One day at a time. Fetters are intricate and constant practice attending to breath is most effective. Be thorough. Be diligent.
You may also find MN10 similar and helpful--it provides rousing encouragement, but do perhaps expect much more than a fortnight to succeed.

"Rid of desire and aversion for the world" is found in each tetrad.

Thank you. I had not realized that. Edited answer.