text:
If Theravada doesn't posit the selflessness of phenomena, then how to interpret SN 22.95?
This question is closely related to this question and this question and this question.
There is a Sutta in the Pali Canon that seems to explicitly reject that any of the aggregates is real or substantially existent, but instead likening them to a lump of foam, a water bubble, a mirage, a plantain trunk, or an illusion:

“Form is like a lump of foam, Feeling like a water bubble; Perception
  is like a mirage, Volitions like a plantain trunk, And consciousness
  like an illusion, So explained the Kinsman of the Sun.
“However one may ponder it And carefully investigate it, It appears
  but hollow and void When one views it carefully.
“With reference to this body The One of Broad Wisdom has taught That
  with the abandoning of three things One sees this form discarded.
“When vitality, heat, and consciousness Depart from this physical
  body, Then it lies there cast away: Food for others, without volition.
“Such is this continuum, This illusion, beguiler of fools. It is
  taught to be a murderer; Here no substance can be found.
“A bhikkhu with energy aroused Should look upon the aggregates thus,
  Whether by day or at night, Comprehending, ever mindful.
“He should discard all the fetters And make a refuge for himself; Let
  him fare as with head ablaze, Yearning for the imperishable state.”

Depending upon the answers to the previous questions I'd be very interested in how Theravada interprets this Sutta. Generally, I'm confused how Theravada interprets these Suttas into a coherent and non-contradictory whole:

SN 22.85 seems to say that regarding a Realized One as real or genuine is incorrect.
Itivuttaka 44 seems to say that (as per Ruben2020's answer here) the body is real and genuine.
SN 22.95 seems to reject that and say the body is to be considered like foam as "void, hollow, insubstantial."

Finally, Mahayana monastics train believing that the substantial difference between Theravada views of anatta and Mahayana views of shunyata is that Theravada regards the aggregates and all external phenomena as real and possessing intrinsic nature or essence.
How do Theravada proponents reconcile all of this?

You previously listened to the wrong answer. This question here is irrelevant. The Tathagata is real & true but the reality & truth of the Tathagata is wisdom. The suttas say "Seeing the Dhamma, Sees the Buddha".

Sariputra attests that the Realized One is not a real and true and genuine fact in SN 22.85

the Realized One is real and true. But that the Realized One is a SELF-ENTITY is not real and true

Piya Tan in his commentary on the lump of foam sutta, quoted Bhikkhu Bodhi's commentary below:

This sutta is one of the most radical discourses on the empty nature
  of conditioned phenomena; its imagery (especially the similes of the
  mirage and the magical illusion) has been taken up by later Buddhist
  thinkers, most persistently by the Madhyamikas. Some of the images are
  found  elsewhere in the Pali Canon, eg at Dh 46, 170. In the context
  of early Buddhist thought, these similes have to be handled with care.
  They are not intended to suggest an illusionist view of the world but
  to show that our conceptions of the world, and of our own existence,
  are largely distorted by the processes of cognition. Just as the
  mirage and magical illusion are based on real existents — the sand of
  the desert, the magician’s appurtenances — so these false conceptions
  arise from a base that objectively exists, namely, the five
  aggregates; but when seen through a mind subject to conceptual
  distortion, the aggregates appear in a way that deviates from their
  actual nature. Instead of being seen as transient and selfless, they
  appear as substantial and as a self. (Bodhi S:B 1085 n188)

I think the above commentary discusses the Theravada view accurately. The sutta does not talk of an illusionist view of the world. It does not imply that the five aggregates are not real. It simply points towards the five aggregates as being transient and without a self.
Also, please see the Suñña Sutta, which explains this more literally, as the five aggregates being empty of a self.

Ok, I think then this is in keeping with what is taught in the Mahayana monastic textbook about Theravada. That persons are not real and have no objective existence - only conventional -, but external phenomena including the aggregates have objective real existence not just conventional existence.

It's kinda funny how Piya Tan's comment correctly explains Mahayana's understanding of emptiness while at the same time contrasting it with an incorrect understanding which he then (wrongly) attributes to Mahayana.

Hmm, are you sure you are referring to Piya Tan's comment or his quote of Venerable Bodhi? Also, do you think this part, "so these false conceptions arise from a base that objectively exists" is correct understanding according to Mahayana Prasangika?

@YesheTenley thanks for your corrections, yes - I meant Bhikkhu Bodhi's comment that "our conceptions of the world, and of our own existence, are largely distorted by the processes of cognition". As for "a base that objectively exists" - this part is often a point of debate (mostly because it's at the limit of words) but as we all know Mahayana is neither metaphysical nihilism (stating that nothing whatsoever exists) nor ontological idealism (stating that everything is literally an illusion). Even Yogacara was shown as of late to not be an idealistic heresy it was once assumed to be.

The Pali Canon Mulapariyaya Sutta may help in discussing different perspectives on the perception of "real". Note the subtle wording change:
Case 1: Take an uneducated ordinary person...They perceive earth as earth
Case 2:  A mendicant who is perfected...directly knows earth as earth.
In case 1, the earth is perceived as having a potential relationship with self (i.e., "my earth", "his earth", "in earth", etc.). In SN22.85, Reverend Yamaka was initially asserting the total annhiliation of the mendicant (i.e., self) upon death (i.e., dissolution of earth).
In case 2, the earth is directly known as earth. Earth is not self. Yamaka's revised his own answer about death:

What’s suffering has ceased and ended

I see this sutta not as an objective or ontological statement (e.g. form is "real" or "unreal", "true" or untrue) but rather as subjective and prescriptive -- e.g. I see it as saying that "form, and feelings etc., are fragile and unreliable -- so don't crave them, don't attach to them, and don't depend on them."
I guess the interesting or most relevant bit (for the purpose of this question) is found here:

for no substance is found here.
sāro ettha na vijjati.

And see here for a definition of sāra.
I (personally) don't interpret this word as meaning "substance", in what I imagine is a philosophical sense (e.g. ontology) -- instead I interpret it as kind of subjective or pragmatic, e.g. as meaning "the bit that's useful to us, the part that proves to be reliable or everlasting, the valuable/worthwhile bit".
Part of the "true Scotsman" argument wanders into defining what a Scotsman "is", what it even means to "be" a Scotsman -- what's the "essential characteristic" (or "sign") of a Scotsman -- and who knows what a "real", "genuine", or "true" Scotsman is?
Conversely I think that according to Theravada the "characteristic" of everything is simple -- i.e. it's:

Impermanent
Not self (not "me" and not "mine")
Dukkha

Discussing whether the arrow is "real" (and what it's made of) is a bit of a distraction -- this commentary claims that Gautama Buddha's views were "anti-metaphysical".

Cula-Malunkyovada Sutta (MN 63)
And why are they undeclared by me? Because they are not connected with the goal, are not fundamental to the holy life. They do not lead to disenchantment, dispassion, cessation, calming, direct knowledge, self-awakening, Unbinding. That's why they are undeclared by me.
"And what is declared by me? 'This is stress,' is declared by me. 'This is the origination of stress,' is declared by me. 'This is the cessation of stress,' is declared by me. 'This is the path of practice leading to the cessation of stress,' is declared by me. And why are they declared by me? Because they are connected with the goal, are fundamental to the holy life. They lead to disenchantment, dispassion, cessation, calming, direct knowledge, self-awakening, Unbinding. That's why they are declared by me.
"So, Malunkyaputta, remember what is undeclared by me as undeclared, and what is declared by me as declared."

I'm not saying that your question is useless or unanswerable -- this one is not one of the canonical 14 unanswered questions -- just that it seems metaphysical to me, and asking questions that aren't answered n the text.
I guess if you analyse everything using a Mahayana-orthodox "analytic knife" then it will end up looking like a primitive/incomplete simulacrum of Mahayana doctrine -- but I think that the "posits" you're making maybe aren't present in the text -- furthermore the Simsapa Sutta (Handful of Leaves) is meant to assure us that what is in the text is sufficient (or "self-sufficient" if you will).

Thanks @ChrisW, I think you are right there is a distinct strain of Theravada adherents who view delving too deep into these questions as inappropriate or at least not important. They ascribe some of this to the "thicket of views" that Buddha famously redirected confused people from.

@ChrisW I agree with your assessment that the spirit of the teaching as preserved in the Pali Canon is extremely pragmatic. Even its flavor of "emptiness" that can be read between the lines is always pragmatic, no-nonsense, don't-be-a-fool style. This is in stark contrast with both Theravada as well as Mahayana schools with their speculative analysis and obsessive nitpicking. In fact, it was a no-nonsense approach that had drawn me to Kagyu -- the most pragmatic of Tibetan schools whose teaching styles often correlate with their historical origins and political agendas.

FWIW, I view all traditions of Buddhism as focused on the pragmatic as an empirical discipline. IOW, I don't think the question in this OP is divorced from the pragmatic or that Mahayana is less pragmatic because it takes these questions seriously. It is precisely because of our ignorance of how things really are that causes all this mass of suffering and so we have to dispel this ignorance by discovering how things really are.

BTW, I love your reference to the No True Scotsman :) And yes, part of the fallacy is believing there is any such thing as a "True Scotsman" in the first place outside of mere convention.

A marked this answer down because of its unnecessary and wrong discussion of ontology vs subjectivity. That the aggregates are worthless, without value and have no substantive value is their inherent nature. Its "ontological" if that word must be used.

@Dhammadhatu The OP's question seems to me a question of or about ontology, asking how to "reconcile" what suttas say about whether the existence of various things is real and genuine -- my answer is that, IMO, that is not the focus of this sutta -- and that if he's asking for the Theravada viewpoint, it's that Theravada identifies the "three characteristics" etc.

I agree with @AndreiVolkov that the Sutta Pitaka is extremely pragmatic compared to Mahayana and also Theravada. The original Pali suttas do away with unnecessary speculation and intellectual gymnastics. Even in Theravada, the complexity comes from the Abhidhamma and commentaries. While the Abhidhamma is said to be the Buddha's own teachings, I feel that it's derived from his teachings, making it a secondary text. A long time ago, I used to hold the Advaita Vedanta view, but now I have had enough of unnecessary philosophical speculations, intellectual gymnastics and ontological hamster wheels.

This answer is wrong. The characteristics of the aggregates are inherent or ontological.

@ChrisW Pragmatically speaking, is it a distraction OR an example of craving and grasping? Isn't the urge to insist upon the ontological status of the aggregates a form of grasping at them? If so, then from a purely pragmatic perspective doesn't it have to be given up?

The sutta does not explicitly reject that any of the aggregates is real or substantially existent (atthi vs natthi). The sutta does not deny there is a lump of foam, bubbles, mirages, hollow thoughts & the magical quality of consciousness. The sutta merely says the aggregates have no intrinsic value, worth, meaning and lasting quality. The relevant Pali adjectives are ritta, tuccha and asāra. The sutta is unrelated to existent Mahayana obsessions about existence & non-existence.

Thanks @Dhammadhatu, but feel free to ignore my questions/obsessions since they are clearly irrelevant for you. Probably best to leave them alone.

You wanted me to answer this one as well.
[Note: I didn't read all the suttas you've linked to, nor did I read all comments already posted.]

“Form is like a lump of foam, Feeling like a water bubble; Perception is like a mirage, Volitions like a plantain trunk, And consciousness like an illusion, So explained the Kinsman of the Sun.

Are the 5 aggregates substantial or not?
Imho, it's important to know from what point of view someone looks at things. Is it from the normal, everyday-of-life or intellectual, scholar point of view or the experiential point of view. That makes a huge difference.
From an experiential point of view things have only a momentary existence. They arise, leave an impression and cease again. They come and go.
Is there a body? No, experientially speaking there is, so now and then, a feeling of pressure, cold or warm, soft or hard in different locations (wind, fire, earth). At the moment of contact we can know those sensations. At the moment of contact there is something there. And then it's gone. Outside the knowing and the sense impression that can be known, there is nothing.
Are those sense impressions real? Well, yes. For that short moment there was contact, there was something to be known, and that something had an effect.
Are they substantial? No.
Same goes for all other aggregates.
I'm sure that from an intellectual point of view much more could be said. But, as you know, I'm not a scholar. So, it's not my place to get into that.

Do not forget that there is the parallel in chinese translated into english
https://suttacentral.net/sa265/en/analayo
you find the parallels under the little down arrow with the number four, after you click on the down arrow right to the wheel.
it is the usual sequence  Anicca->dukkha->Anatta applied to the usual 5 aggregates, which is  of course the beginning of the sequence Anicca->dukkha->Anatta->dispassion->nibanna
Puthujjanas are obsessed with what they call ''what is real'' and '' what is not real'', but the word real is utterly useless. SOme of them even manage to mix the word true with that, because they claim that there is the ''apparent real'' and the ''true real'' and of course, the true real is really better than the apparent real.
It's like asking if anger is real or cold is real or a number e^\pi in ZFC is real. That's a question which is just as natural for a Puthujjana to ask as it is dumb. The question is not whether it is worth it to qualify something as real, but how do you relate to it, how do you see it as worthy for basing your care, your intention and your actions and spend your energy on it.

If the word 'real' is utterly useless, then why does it exist and why is it so important to people whether things are real or not? ie., why does it bother people or perplex people to say that all those things are unreal? Thanks for the other translation btw!

Why do we teach kids that dreams aren't real and they therefore shouldn't be afraid of nightmares? That TV is not real and so we don't need to be afraid of disturbing stories?

The Agama are terrible and Analayo's translation is terrible because it does not have the meaning of the Pali words ritta, tuccha and asāra found in the Pali version.


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Reference for Thoughts like rain drop bubbles
There is reference in the Thai Forest tradition to a teaching given to sāriputta by Buddha of thoughts like rain drop bubbles rising the mergie into the body of water.
Dose anyone know of this suta and can give a reference to it.
Most appreciated. Robert
Editing... the question is very vague and is poorly referenced the simple fact is I am relying on memory.
I Read an account of the Mahayana concept from the Tibetan Dzogchen teachings of unsubstantial nature of the sense of self and how seeing beyond the conceptual self one realizes that there is no one to preform these actions. Hence the sense the thief finds nothing to steal.
But I have also read a similar description by one of the Ācariya. They use the descriptive citta which is a multifaceted word depending on its use. "'Citta' primarily represents one's mindset, or state of mind. It is the term used to refer to the quality of mental processes as a whole. Citta is neither an entity nor a process; this likely accounts for its not being classified as a skandha, nor mentioned in the paticcasamuppada formula."
Thanks for your effort.
Editing again... For your reference...
"Yangthang Tulku Rinpoche: Nature of Mind Teachings
(excerpts from teachings given in the US in 1990/91)
In the practice of dzogchen, the method of dealing with the conflicting emotions is entirely different from the method of sutra (renunciation) or tantra (transformation).
In dzogchen we are still dealing with the basic problem, the conflicting emotions or the delusions but they are self-liberated.
Simply by recognizing that the conflicting emotions are just the display of intrinsic awareness, in that moment of recognition they vanish, they are no more.
The moment they are recognized as what they are, they are set free, like a snake that uncoils itself. No one else needs to uncoil the snake; it does it by itself.
Conflicting emotions are self-liberated through recognition, through pure awareness.
Some practitioners may achieve the same result, i.e. self-liberation of the conflicting emotions, by experiencing the conflicting emotions or discursive thoughts to be free from benefit or harm. It is like a thief breaking into an empty house. There is nothing for him to steal and there is nothing for the owner to lose, hence nothing happens. And so when the meditator recognizes discursive thoughts or conflicting emotions to be without benefit or harm, they are self-liberated.
Through pure awareness the five poisons and all conceptualization are recognized to be none other than the display of wisdom."
AND
"5. The fifth question -- -"What is the essence of concentration?" --
If we were to classify the mind at this stage, it is appana citta, the fixed mind. As for concentration, it is momentary concentration. Momentary concentration is the basis for the tempered discernment of liberating insight. The mind can't stay long with any preoccupations, for it is constantly wiping them out, like the bubbles formed by rain on the surface of a lake: As soon as they appear, they vanish flat away, like a sea without the striking of waves. When discernment is tempered through the power of a fixed mind, the preoccupations of momentary concentration constantly disband and disappear, not letting the heart get caught up on them. This is termed release (vimutti): The mind is freed from all preoccupations, among them the effluents of sensuality, becoming, views, and unawareness. It becomes a mind beyond all effluents. Thus it is said,
hina jati vusitam brahmacariyam
katam karaniyam
naparam itthattayati pajanatiti
which means, "The Noble Disciple discerns that birth is ended, the holy life is completed, the task done. There is nothing further to be done for the sake of this state."
So ultimately, when the practice of concentration reaches the true essence of the mind, discernment is attained.
This ends the discussion of the fifth topic."
https://www.nku.edu/~kenneyr/Buddhism/lib/thai/lee/craft.html
I will cease editing here as the question is quiet long and the two quotes should be sufficient for anyone to follow the original question.
Again my thanks.

I haven't found it.

Perhaps it's the Phena Sutta (SN 22.95):

Now suppose that in the autumn — when it's raining in fat, heavy drops — a water bubble were to appear & disappear on the water, and a man with good eyesight were to see it, observe it, & appropriately examine it. To him — seeing it, observing it, & appropriately examining it — it would appear empty, void, without substance: for what substance would there be in a water bubble? In the same way, a monk sees, observes, & appropriately examines any feeling that is past, future, or present; internal or external; blatant or subtle; common or sublime; far or near. To him — seeing it, observing it, & appropriately examining it — it would appear empty, void, without substance: for what substance would there be in feeling?

That's not given to Sāriputta, though, and it's about "feelings" rather than "thoughts".

More specifically related to thoughts (still not Sāriputta though, and no "body of water"), is Itivuttaka 87

One who stops such trains of thought
  As a shower settles a cloud of dust,

That's the word vitakka for "thought".

Re. the "body of water" I think that Nibanna is sometimes compared to the ocean (but so is samsara).
In AN 10.15 the ocean is also used as a simile for "heedfulness" being the root of all skilful virtues.

The citta is the mind’s essential knowing nature, the fundamental quality of knowing that underlies all sentient existence.
When associated with a physical body, it is referred to as “mind” or “heart”. Being corrupted by the defiling influence of fundamental ignorance (avijjã), its currents “flow out” to manifest as:
Feelings (vedanã),
Memory (saññã),
Thoughts (sankhãra), and
Consciousness (viññãna),
thus embroiling the citta in a web of self-deception. It is deceived about its own true nature."
The Path to Arahantship by Ajahn Maha Boowa

This is closest I could get:
“So I say to you –
This is how to contemplate our conditioned existence in this fleeting world:”
“Like a tiny drop of dew, or a bubble floating in a stream;
Like a flash of lightning in a summer cloud,
Or a flickering lamp, an illusion, a phantom, or a dream.”
“So is all conditioned existence to be seen.”
It was said to Ven. Subhuti.
Its chapter 32 of the diamond sutra.

Araka’s Instructions  Arakenānusasani Sutta  (AN 7:70)

Not certain the Diamond sutra is used in Theravada... though the concept is used in Mahayana.  In particular the concept of 'nothing to steal', in terms of negative emotions/ thoughts. Which is what the author was suggesting, though using the versatile chitta.

@Tamaso yeah I just tried searching for something closest to what he was looking for as I couldnt get the exacy sutra he was refering to...

This is probably all wrong given I don't speak Pali, but here comes some amateur sleuthing...
The pali for (SN 22.95) that Chris mentioned seems to have "udakapubbuḷaṃ" as the pali for water bubble. This term also appears in this parallel (MND 15) which appears to be a longer form for this sutta (Snp 4.15) in the section which has:

Once I wished a place to stay,
  but all the world is essenceless,
  turmoil in every quarter,
  I saw no place secure.

Empthasis mine. Unfortunately there is no english translation for this longer parallel which might be a synthesis of SN 22.95 and Snp 4.15. I'd note that the translation comes from the Mahāsangiti Tipiṭaka Buddhavasse 2500 which is described as coming from a Princess in Thailand:

"The World Tipiṭaka is a gift of Dhamma for the World from Her Royal
  Highness Princess Galyani Vadhana Krom Luang Naradhiwas Rajanagarindra
  ... Proof-read and published in Roman script by the M.L. Maniratana
  Bunnag Dhamma Society Fund ..."

I'd also note that the pali for that parallel also has 'citta' mentioned many times unlike SN 22.95.
Anyway, thank you for asking this question since it led to reading of Snp 4.15 and Mnd 15!

Attadaṇḍa sutta (Snp 4.15) is one of my favorite pieces of poetry in the Pali Canon, its authorship sometimes attributed to Gotama himself. Reportedly in the Early Sangha it was recited by an elder bhikkhu before shaving hair of a novice. That particular translation sucks though. The original has a rather dramatic rhythm that reads something like: "Saw this world's without essence / Anywhere you go, are problems / Tried to find my own place in it / Saw that places all've been taken." etc.

There are 3 more translations of Snp 4.15 here.

These are not exactly what you've asked for, but they are somewhat related.
From SN 12.23:

"Just as when the gods pour rain in heavy drops & crash thunder on the
  upper mountains: The water, flowing down along the slopes, fills the
  mountain clefts & rifts & gullies. When the mountain clefts & rifts &
  gullies are full, they fill the little ponds. When the little ponds
  are full, they fill the big lakes. When the big lakes are full, they
  fill the little rivers. When the little rivers are full, they fill the
  big rivers. When the big rivers are full, they fill the great ocean.
  In the same way:
"Fabrications have ignorance as their prerequisite, consciousness has
  fabrications as its prerequisite, name-&-form has consciousness as
  their prerequisite, the six sense media have name-&-form as their
  prerequisite, contact has the six sense media as its prerequisite,
  feeling has contact as its prerequisite, craving has feeling as its
  prerequisite, clinging has craving as its prerequisite, becoming has
  clinging as its prerequisite, birth has becoming as its prerequisite,
  stress & suffering have birth as their prerequisite, conviction has
  stress & suffering as its prerequisite, joy has conviction as its
  prerequisite, rapture has joy as its prerequisite, serenity has
  rapture as its prerequisite, pleasure has serenity as its
  prerequisite, concentration has pleasure as its prerequisite,
  knowledge & vision of things as they actually are present has
  concentration as its prerequisite, disenchantment has knowledge &
  vision of things as they actually are present as its prerequisite,
  dispassion has disenchantment as its prerequisite, release has
  dispassion as its prerequisite, knowledge of ending has release as its
  prerequisite."

This is from the Dhammapada:

Dhp 121. Think not lightly of evil, saying, "It will not come to me." Drop by drop is the water pot filled. Likewise, the fool, gathering it
  little by little, fills himself with evil.
Dhp 122. Think not lightly of good, saying, "It will not come to me." Drop by drop is the water pot filled. Likewise, the wise man, gathering it
  little by little, fills himself with good.

From SN 35.203:

"When, monks, a monk lives and practices like this, it occasionally
  happens that, through a lapse of mindfulness, evil and unskilled
  states arise, memories and thoughts pertaining to the fetters. His
  mindfulness is aroused only slowly, but then he soon abandons that
  state, drives it out, abolishes it, puts an end to it. Just as if,
  monks, a man were to let fall two or three drops of water into an iron
  pot that had been heated all day, those few drops would soon be wiped
  out and vanish — in the same way it occasionally happens to a monk
  living and practicing like this... but he soon puts an end to it.

This is not from the Pali Canon, but rather, it's from Mahasi Sayadaw's discourse on the Bhara Sutta (from a selection of Mahasi's discourses entitled "Thoughts on the Dhamma"):

Becoming and Dissolution
A bubble bursts soon after it has been formed. A mirage conjures up an
  image of reality which disappears on close examination. There is
  absolutely no substance in either of them. This is common knowledge.
  As we know their true nature, so also must we know the true nature of
  the phenomena. When a meditator acquires knowledge of concentration
  through the observance of the dissolution of the Aggregates (khandha),
  he will discover that the known object and the knowing mind are all in
  a state of flux, now appearing, now vanishing. They are transitory.
  There is no essence or substance worthy to be named "mine" in them.
  They signify only the processes of becoming and dissolution.
— Discourse on the Bhara Sutta

Like effervescent bubbles
In one of my ten-day meditation courses I experienced the following:  I could feel a hot, burning shape, not unlike a piece of shrapnel in the middle of my forehead.  It was seemingly solid and three-dimensional.   As I paid it attention it became white hot.  Then it began to wriggle.  As it disintegrated I had a terrible vision along with an emotion of terror.  I dropped through a trapdoor! I was being hanged.
The next moment I felt not only utter peace but something else.   My entire being - certainly my physical body - seemed to be nothing but a mass of bubbles rising within me.  It could be likened to effervescent bubbles rising in a bottle of lemonade.   They came into existence and went out of existence at great speed.  They arose and passed away, moving upwards as they did so.   It was very pleasant.
Time must have seemed to have stood still, because I was eventually brought back to 'worldly reality' when an assistant teacher tapped me on the shoulder.   The meditation hall was empty.  They'd all gone.  I had simply been enjoying this wondrous phenomenon of 'arising and passing way.'
I had never experienced this before, nor since, though I've undertaken fourteen ten-day Vipassana retreats and been practising now of over thirty-two years.

Sāriputta enlightened as sotāpanna in Vinaya. Mahā (1) Mahākhandhaka, then he enlightened as arahanta in Sutta. Ma. Ma. Dīghanakhasuttaṃ, which it's atthakathā gave the similitude of vedanā arising and vanishing as bubbles.
Another, In sāriputta's cannons, KN Cūḷaniddeso Mogharājamāṇavakapañhāniddeso, used the similitude of viññāṇakhandha as bubble as well.
So, sāriputta maybe one of monks who listening  Phena Sutta (SN 22.95), then he described his arahanta-enlightening-moments to his students. Then at 1st saṅgāyanā, his students put his description into that ancient atthakathā and into that KN Cūḷaniddeso which authored by sāriputta.

Also, in KN Dhammapada's atthakatha Dha.A.6 atta-kodhavagga Buddhavaggavaṇṇanā 2. Yamakappāṭihāriyavatthu. (149), there are the sāriputta's conversation with the buddha about  he is a genius who can count every rain's drops into the ocean, mountain, and the ground.

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What is the best of Jhanas and breathing meditation?
I have heard two ways off approaching mindfulness of breathing:

Breath in a inhale-pause-exhale-pause pattern, focusing on the
sensations of the breath at the nostrils and the silences at the
pauses between breaths.You would control your breath in this method.
Quiet your mind and just follow the sensations of your breath as it naturally arises.

Questions are

Should you control your breathing if you want to reach the Jhanas?
Which one is best if you want to attain the jhanas?

At the start of practice, it helps to cultivate concentration, so focusing on one object single-pointedly, whether it's the breath, a sound, or something in the visual field. The manners in which this concentration is developed can give different results for different people, so I'd say to experiment and see which works for you.
I will say though, that focusing on the natural arising and passing of the breath can lead to a subtle realisation that the breath is arising and falling all by itself, utterly disconnected from the noticing of it. It's very interesting to 'catch' your body breathing, independent of your control.

Method #2, as the Buddha taught:

There is the case where a monk, a disciple of the noble ones, making it his object to let go, attains concentration, attains singleness of
  mind. Quite withdrawn from sensuality, withdrawn from unskillful
  mental qualities, he enters & remains in the first jhana....
SN 48.10

What about the second jhana, third jhana, etc.?

Same method. Just let go & be silent. Also, completely forget about "jhana". Just keep the mind in the silent present moment.

So pranayama and breath control has no use for actual meditation?

pranayama and breath control  are Hindu yoga and useless for Buddhist jhana. You should try to realise that when the mind is quiet & silent; it will automatically become aware of the breathing because in silence the breathing is the grossest sense object. This is similar to when the mind is silent it can hear sounds automatically. When the mind is silent; completely abandoning any type of ambition for any type of meditation; the mind, in its silence & surrender; will automatically know the breathing; just like the quiet mind automatically hears sounds like birds, cars or the wind.

But siddhis are part Buddhist jhana or Hindu jhanas? Your method seems at odds with this answer from Absolutus: https://www.reddit.com/r/Meditation/comments/93m5by/change_brain_structure_greater_behavior/e3f9o9q/?context=3  Note the last comment of regulating your breath in a inhale-pause-exhale-pause format.

I am just saying aren't there multiple methods to the same outcome? Buddhas's technique is not the only way right?

Siddhi happens automatically also. My method is the right method. If you practise both methods, you might discover which one works.

Should you control your breathing if you want to reach the Jhanas?

In the Anapanasati Sutta, there's no mentioning of controlling one's breath. Instead the emphasis is on the "awareness" of one's natural breathing. If it's long, simply aware that it's long; if it's short, simply aware that it's short:

Breathing in long, he discerns, 'I am breathing in long'; or breathing out long, he discerns, 'I am breathing out long.' [2] Or breathing in short, he discerns, 'I am breathing in short'; or breathing out short, he discerns, 'I am breathing out short.' [3] He trains himself, 'I will breathe in sensitive to the entire body.'[2] He trains himself, 'I will breathe out sensitive to the entire body.' [4] He trains himself, 'I will breathe in calming bodily fabrication.'[3] He trains himself, 'I will breathe out calming bodily fabrication."

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Abhidhamma on Chittas and Chetasikas of Bi-polar disorders, Autism, and many mental disorders
Here's what I'm given to understand:
The Abhidhamma manual classifies all possible mental states of a human being into - various different kinds of Chittas and Chetasikas.
Here's what I want to know:

Are the mental states of (what is generally considered to be a) disorder, like say - Bipolar disorder, Autism etc. also considered and classified in this text?
Is there a way out of it? Is there anyway for someone who wants to help those in deeper suffering because of this. Meditation, medication, perspective, world view etc.

I highly doubt you can find a one-to-one correspondence between modern psychiatric disorders and the classification of mental factors in Buddhist Abhidhamma. The two have completely unfamiliar zeitgeists or views of the world.
That said, I think you will find that many of the symptoms or more granular descriptions of the western psychiatric disorders are present or reflective of similar mental factors in the Abhidhamma. One thing you will not find in the latter is a classification of brain states or the physical mechanisms underlying many of the former. That is to say that western psychiatric disorders are - not entirely unwarranted - preoccupied with the workings of the brain as opposed to the workings of the mind. The two are not the same although with neural plasticity the two can lead to change in the other.
So, I think you will find that the efficacy of treating mental factors in Abhidhamma will be non-linear with treating western psychiatric disorders although they will have some effect on one another.
BTW, this is the canonical place where western psychiatric disorders are catalogued and described: Diagnostic and Statistical Manual of Mental Disorders. It is important to note that although this is the de facto canonical catalogue of western psychiatry that many western psychiatrists themselves view this catalog as subjective and arbitrary and providing only superficial and unreliable classification of disorders.
Hope this helps!

I think western psychiatrists are interested in the brain because they'd like to understand (more than they do now about) why psychiatric medicines have whatever effects they have. Also so far as I know the DSM suggests diagnoses based on observed behaviours and subjective (self-reported) perceptions only: even if it were useful to know, I suppose that brain chemistry isn't easy to measure.

To answer this question one should have a deep understanding in Abhidhamma and also clinical, medicinal expertise. I must say first that I'm not an expert in none of these areas. I'll try to answer this question as much as possible according to my understanding. Please correct me if I'm wrong.

Are the mental states of (what is generally considered to be a) disorder, like say - Bipolar disorder, Autism etc. also considered and classified in this text?

The short answer for this question is NO. But in Abhidhamma it has mentioned about ultimate truth. Each and every dhamma inside the world and outside the world are made of 82 numbers of very subtle substances called paramatta sacca. In the Great Book of Causal Relationships (Patthana Pakarana) it has mentioned how these elements interrelated and build phenomena. So if you have thorough understanding in Abhidhamma, you should be able to explain each and every phenomena. It's like if you have building blocks and you know how they can be connected and their output. Then you can explain how to build a house, train, bridge, etc... out of them.
In sentient beings in realms where all 5 aggregates (skandha) are available (pancavokara bhumi) name (nāma) and form (rūpa) are interrelated (each one dependent on the other). Most of the diseases are caused by diseased bundles of form (rūpa kalāpa). Since name and form are interrelated these diseased bundles of form may disturb the normal function of name. That's why someone gets unconsciousness when s/he met with an accident or when suffering from high fever. That's why someone lose their sight by exposing their eyes to UV radiation.
One can argue the other way around that name will affect form and leads to diseases. This is also true. That's why you get high levels of bad cholesterol (cholesterol is made of bundles of form) when you're suffering from stress (mental condition).

Is there a way out of it? Is there anyway for someone who wants to help those in deeper suffering because of this. Meditation, medication, perspective, world view etc.

There are four causes which produce form.

Kamma (Actions)
Citta (Consciousness)
Utu (Heat)
Ahara (nutriment/sustenance)

There are bundles of form in a body which are arisen with one (ekaja rūpa), two (dvija rūpa), three (tija rūpa), or four (catuja rūpa) causes above mentioned.
If the diseased bundles of form are caused by kamma, I suppose there is no cure for such diseases. Although it's not guaranteed, the only option is to try to mitigate the effect by doing as much as good deeds (kusala kamma) in this very life.
If the diseased bundles of form are caused by citta, I suppose meditation will help to cure such diseases. Counseling and maintaining a good mind always is beneficial.
If the diseased bundles of form are caused by utu, I suppose use of protectors to avoid expose to heat and use of ointments to recover diseased/damaged bundles of form will help to cure such diseases.
If the diseased bundles of form are caused by ahara, I suppose these diseases can be cured by medicines, physical exercises and changing diet.
To cure diseased dvija rūpa, tija rūpa, or catuja rūpa, a combination of above methods can be used.
Note: This is what I understood. I may be wrong but not Dhamma.

Where do the four causes come from? Do you have references?

@ruben2020 Sir, Chapter 6 - Analysis of Matter --> The Arising of Material Phenomena of the book, A Manual of Abhidhamma by Narada Thero pp. 341-342

@ruben2020 Sir, "A Discourse on Paticcasamuppada" written by Venerable Mahasi Sayadaw has rich content about the causes.


text:
Is the self an illusion or is it *like* an illusion?
Recently, in explaining the relative unimportance of the question whether phenomena lack true existence it was claimed that, "the self is definitely an illusion" and lacked true existence. This seemed to be held up as an important fact that has significance in the pragmatic soteriological aims of Theravada in contrast to the above mentioned question.
A few questions that arise:

First, is the self an illusion or not? Here it was said by the same person above that the self was not an illusion?
If either the self is like an illusion or is literally an illusion, is this synonymous with saying that it lacks true or real existence from the Theravada viewpoint?
Why does Theravada regard this question about the ontological status of the self of persons to be an important question? Why can't we just say that the self of persons is real and true like other phenomena, but transient or lacking sara as Chris said was the correct interpretation of SN 22.95
Why does Theravada regard the question of whether the aggregates have intrinsic value, worth, meaning and lasting quality an important question? If the self does not truly exist like an illusion, then what does it matter if the aggregates have intrinsic value, worth, meaning and lasting quality since the self cannot be found in them?

Some Theravada adherents say that, "the original Pali sutta's" do away with unnecessary speculation or "ontological hamster wheels." :) However, paradoxically it seems some Theravada regard the question of the ontological status of the self to be very important. It's also clear that Sariputra thought it very important to correct Yamaka about this. And the Buddha himself thought it important to instruct how the aggregates and other phenomena were to be regarded as lacking intrinsic value, worth, meaning and lasting quality irregardless questions of the self.

I've updated the old answer. Now it does not say that the self is not an illusion. Sorry for the inconsistency.

No apologies necessary :) So your current view is that the self is an illusion and not truly existent and this is relevant? Whereas consciousness is like an illusion and whether it is truly existent or not is irrelevant?

You can find my response in my answer.

@ruben2020 thanks, but I still don't see an answer, but maybe I'll just have to settle for that :)

You continue to assert wrong answers are "right" and then ask more questions based on those wrong answers.

@Dhammadhatu obviously we disagree, so just ignore my questions

I will answer your questions until your understanding conforms with Right View. The Buddha said: "And how do students engage with the teacher in friendliness and not in opposition? There is the case where a teacher teaches the Dhamma to his students sympathetically, seeking their well-being, out of sympathy: 'This is for your well-being; this is for your happiness.' His disciples listen, lend ear, & apply their minds to gnosis. Not turning aside, they don't stray from the Teacher's message. This is how students engage with the teacher as friends and not as opponents.".

@Dhammadatu, I do not regard you as my teacher. I do not find your answers helpful. Your advice is unsolicited.

@YesheTenley What is an illusion?

@TenzinDorje, Paraphrasing Je Tsongkhapa, an illusion can be known using two kinds of awareness. For example, first one relies upon a visual consciousness that sees an illusory horse or elephant and second a mental consciousness that knows that the horse or elephant doesn't exist as it appears. The same is required to establish the illusory nature of a person. First, you need an undeniable appearance of a conventional person. Second, you need reasoned knowledge that the person does not exist as it appears.

@YesheTenley You defined an illusory-like appearance, not an illusion :)

@TenzinDorje, Perhaps, but that paraphrase comes from the Great Treatise in a section that begins with, "“Illusion” is said to have two meanings." :)

Let's take it the way you say, then. Thus, an object is not an illusion in general, but is an illusion only in the perspective of one who knows it to be an illusion.

Is the self an illusion or is it like an illusion? Well, let's just say that it's not truly existent. The lute analogy in the Vina Sutta explains that very well. Using a musical instrument you can play nice music. But if you break it down to its constituent parts, you cannot find music. Music cannot be isolated from the musical instrument. Similarly, the self arises from the inter-working of the five aggregates. You cannot isolate the self from the five aggregates. This is in stark contrast with the Hindu view found in Bhagavad Gita 2.20.
Next, why is it so important in the Pali Suttas that the self of persons is not truly existent, but it is not important in the Pali Suttas that the self of phenomena is truly existent or not truly existent?
This is an easy question to answer in my opinion.
The self of persons is strongly related to the cause of a person's suffering. That's why it is so important in the Pali Suttas. The Cula-Saccaka Sutta (MN 35) explains why the self of persons is strongly related to the cause of a person's suffering.
On the other hand, the self of chairs is unrelated to the cause of a person's suffering. The self of chairs is also unrelated to the cause of a chair's suffering (or rather, I cannot imagine how a chair would experience suffering). This is why whether a chair has a self of chairs or not, is not important in the Pali Suttas.
In fact, the self of phenomena may even fall into the category of unconjecturables in the Acintita Sutta as follows:

"Conjecture about [the origin, etc., of] the world is an
  unconjecturable that is not to be conjectured about, that would bring
  madness & vexation to anyone who conjectured about it.

The point here is that the world may or may not be truly existent. The world may or may not have a self of phenomena. The world may or may not be an illusion.  The world may or may not be like an illusion. But in all these cases, it is not related to the cause of a person's suffering, and hence it is not important to the path to the end of suffering. At least, this, in my opinion, is how Theravada views it according to the Pali Suttas.
And this also shows how the Pali Suttas are extremely pragmatic.

Hi Ruben, maybe I'm not going to get an answer, but I'm going to try once again. You say the self of phenomena is not an important question that suffering can be eliminated by understanding that self is not truly existent and is either an illusion or like an illusion. However, SN 22.95 does not talk about the self it is strictly a sutta about how we should regard the aggregates. Here Buddha is clearly saying it is important how we regard the aggregates and that if we regard them wrong we can cause suffering. And he explicitly likens consciousness to an illusion.

And in this Sutta: https://suttacentral.net/snp4.15/en/mills you can see Buddha declares that the world (not persons or the self) is essenceless. So he clearly believes this important otherwise he would not have said it. How do you reconcile SN 22.95 and Snp 4.15 with the idea that these questions of the status of the aggregates or the world are not of practical consequence?

Ponder SN 22.93. The aggregates not having a self of phenomena is not useful to me, because this fact is not related to me. The aggregates are related to me, only because I am clinging onto or grasping the aggregates. But if I understand that the aggregates are impermanent and inconstant, and if I understand that the aggregates are empty of a self, then I could develop dispassion towards the aggregates and not cling to them. In this way, the lump of foam sutta is talking about the aggregates being empty of a self of persons.

This will suffice @ruben2020, thank you for your patience and explanations.

I will give a logical answer.
First we need to understand what illusion is ? Illusion is a false belief about something which gets generated due to six senses. For example we see water from a distant distance but when we reach near the source of water we find that there is no water then we say 'sight' of water was an illusion in other words mirage. Every illusion ends when observed carefully using the six senses. Once illusion ends we recognize the truth as it is.
Next we need to understand what is self ? Self also arises due to false belief. When self is examined carefully we are set on the path to Nirvana. But the Self did not arise due to six senses. It arose due to clinging or craving to the six senses. And it doesn't end end when examined through mind(one of the six senses). It ends when clinging or craving ends.
Therefore Self is like an illusion but not exactly an illusion.

The notion that any self is permanent is a delusion simply linked by the invariant word, "I". To say the self is real pulls us immediately into the morass of entanglement that links all these ever-changing phenomena to that one little word "self". The only reality of self is that it is a four-letter word.

Why does Theravada regard this question about the ontological status of the self of persons to be an important question?

Actually it's not a valid question to begin with as far as all schools of Buddhism, not only Theravada is concerned. The Buddha made it clear that there's no self to be found in the Five Aggregates:

“Bhikkhus, form is nonself. For if, bhikkhus, form were self, this form would not lead to affliction, and it would be possible to have it of form: ‘Let my form be thus; let my form not be thus.’ But because form is nonself, form leads to affliction, and it is not possible to have it of form: ‘Let my form be thus; let my form not be thus.’
“Feeling is nonself…. … Perception is nonself…. Volitional formations are nonself…. Consciousness is nonself. For if, bhikkhus, consciousness were self, this consciousness would not lead to affliction, and it would be possible to have it of consciousness: ‘Let my consciousness be thus; let my consciousness not be thus.’ But because consciousness is nonself, consciousness leads to affliction, and it is not possible to have it of consciousness: ‘Let my consciousness be thus; let my consciousness not be thus." ~~ SN 22.59 ~~

The Buddha also defined the scope of which question can be pursued and which are considered irrelevant, maybe even harmful to the cultivation of the Path:

There are these four unconjecturables that are not to be conjectured about, that would bring madness & vexation to anyone who conjectured about them. Which four?
“The Buddha-range of the Buddhas is an unconjecturable that is not to be conjectured about, that would bring madness & vexation to anyone who conjectured about it.
“The jhana-range of a person in jhana…
“The [precise working out of the] results of kamma…
“Conjecture about [the origin, etc., of] the world is an unconjecturable that is not to be conjectured about, that would bring madness & vexation to anyone who conjectured about it. ~~ AN 4.77 ~~

And:

Nevertheless they came to be of views like this: that the world is eternal, also that the world is not eternal; and that the world is an ending thing, also that the world is not an ending thing; and that the life principle and the body are the same, also that the life principle and the body are different; and that the Tathāgata becomes after dying, also that the Tathāgata does not become after dying, also that the Tathāgata both becomes and does not become after dying, also that the Tathāgata neither becomes nor does not become after dying.
Thus, monks, neither did this third kind of recluse and brahman escape from Māra's mastery. ~~ MN 25  ~~

That fact that no self can be found anywhere is important though and you would not classify that as an ontological question? ie., the existence of the self? Also, do you accept that the Buddha divided his teachings up according to the skilllevel of the listeners? If so, might it be possible that his "thicket of views" or "unconjecturables" was to ward off those who were not ready to understand or who had preexisting misconceptions that precluded them from understanding?

But how can you define an ontological question if there's nothing there to be defined to start with? Nowhere in the suttas can you find any ontological definition of "the self", and this applies to all practitioners, novices and experts alike.

Clearly we all suffer because we assume the self does exist and clearly the Buddha taught us that we should question this and settle that the self does not truly exist. That is the ontological question.

Then obviously it's not an ontological question for us to keep pondering any more for the Buddha had clearly spelled it out loud for all of us that there's no self to be found in the five aggregates. The only real question is what and how to practice to penetrate this truth, not the illusory nature of the self, or whatever it is.

I get the impression -- see MN 22 -- that statements about self are described as a "view" (diṭṭhi), more particularly a wrong view (diṭṭhigata) ... or a "doctrine" (attavādupādāna -- Ven. Sujato translates that as doctrine but this definition says it means more literally "clinging to the belief in self") ... or "seeing" (samanupassati).
I think there are several kinds of view (self-views, or views about the self) described:

One in MN 22:

They regard form like this: ‘This is mine, I am this, this is my self.’ They also regard feeling … perception … choices … etc.

These are views about the aggregates, taking the aggregates as self, which I think is called sakkāya-diṭṭhi and/or what sakkāya-diṭṭhi is, where sakkāya-diṭṭhi is one of the fetters, and kaya means something like "body".
Others in MN 22, e.g.:

The self and the cosmos are one and the same. After death I will be permanent, everlasting, eternal, imperishable, and will last forever and ever

Others (perhaps more generally) of the style described as examples of wrong view in MN 2:

"There is the case where an uninstructed, run-of-the-mill person... does not discern what ideas are fit for attention, or what ideas are unfit for attention. This being so, he does not attend to ideas fit for attention, and attends instead to ideas unfit for attention... This is how he attends inappropriately:

'Was I in the past? Was I not in the past? What was I in the past? How was I in the past? Having been what, what was I in the past? Shall I be in the future? Shall I not be in the future? What shall I be in the future? How shall I be in the future? Having been what, what shall I be in the future?'

Or else he is inwardly perplexed about the immediate present:

'Am I? Am I not? What am I? How am I? Where has this being come from? Where is it bound?'

"As he attends inappropriately in this way, one of six kinds of view arises in him: The view I have a self arises in him as true & established, or the view I have no self... or the view It is precisely by means of self that I perceive self... or the view It is precisely by means of self that I perceive not-self... or the view It is precisely by means of not-self that I perceive self arises in him as true & established, or else he has a view like this: This very self of mine — the knower that is sensitive here & there to the ripening of good & bad actions — is the self of mine that is constant, everlasting, eternal, not subject to change, and will endure as long as eternity. This is called a thicket of views, a wilderness of views, a contortion of views, a writhing of views, a fetter of views. Bound by a fetter of views, the uninstructed run-of-the-mill person is not freed from birth, aging, & death, from sorrow, lamentation, pain, distress, & despair. He is not freed, I tell you, from suffering & stress.
"The well-instructed disciple of the noble ones... discerns what ideas are fit for attention, and what ideas are unfit for attention. This being so, he does not attend to ideas unfit for attention, and attends [instead] to ideas fit for attention... He attends appropriately, This is stress... This is the origination of stress... This is the cessation of stress... This is the way leading to the cessation of stress. As he attends appropriately in this way, three fetters are abandoned in him: identity-view, doubt, and grasping at precepts & practices.
  (e.g. "I exist", or, "I don't exist")

I think they're described as wrong, not because they're true or untrue, not because the self is or isn't an illusion, but because it's a result of attending inappropriately, and not attending appropriately.
And (importantly) it's "wrong" in the sense that it leads to suffering (which I think is like saying that it's unskillful or unwise) -- MN 22 again:

Mendicants, it would make sense to be possessive about something that’s permanent, everlasting, eternal, imperishable, and will last forever and ever. But do you see any such possession?” “No, sir.” “Good, mendicants! I also can’t see any such possession.
It would make sense to grasp at a doctrine of self that didn’t give rise to sorrow, lamentation, pain, sadness, and distress. But do you see any such doctrine of self?” “No, sir.” “Good, mendicants! I also can’t see any such doctrine of self.
It would make sense to rely on a view that didn’t give rise to sorrow, lamentation, pain, sadness, and distress. But do you see any such view to rely on?” “No, sir.” “Good, mendicants! I also can’t see any such view to rely on.
Mendicants, were a self to exist, would there be the thought, ‘Belonging to my self’?”
“Yes, sir.”
“Were what belongs to a self to exist, would there be the thought, ‘My self’?” “Yes, sir.”
“But self and what belongs to a self are not acknowledged as a genuine fact. This being so, is not the following a totally foolish teaching: ‘The self and the cosmos are one and the same. After death I will be permanent, everlasting, eternal, imperishable, and will last forever and ever’?”
“What else could it be, sir? It’s a totally foolish teaching.”
“What do you think, mendicants? Is form permanent or impermanent?”

In summary I think the dhamma advises people to not "acknowledge 'self' as a genuine fact".
See also How are 'conceit' and 'identity-view' not the same? which explains that "I am" may arise as a (transient) conceit instead of being a (established) view.

I think that modern "philosophy of science" describes a "theory" as being something which:

Fits with and explains observed facts (i.e. previous observations)
Makes useful (usable, beneficial, testable) predictions about future observations

According to that system I'd gather that the Dhamma says that "self" is a type of failed theory, which more or less fails both of these criteria (doesn't fit observed facts, and isn't beneficial).
Is the self an illusion or is it like an illusion?
I think it's like an inappropriate (unskilful or even harmful) theory, for example like "the world is flat" or "wouldn't it be fun to put my hand in the fire".
Incidentally when I was young and before I had access to any reliable literature on Buddhism (but instead only paraphrases by modern authors) I heard it said that "the world is an illusion" and similar statements -- but I didn't find that useful, constructive, prescriptive.
The whole question of whether 'self' is an illusion is still a type of self-view IMO -- "do I exist? do I not exist? is self an illusion? is it like an illusion? etc." -- e.g. as listed in MN 2 above, i.e. part of the "thicket of views."

In tipitaka, only 121 minds, 52 mind-factors, 28 matters, and 1 nibbāna are not illusion. The other else are illusion. This is very important, because it is a start point to understand 3 characterizes.
12 paṭiccasamuppāda, both arising and cessation, are only the relativity of minds, mind-factors, matters, and nibbāna. They cause each other arise by themselves. If the practitioner still believe in an illusion, such as person, as the cause of 12 paṭiccasamuppāda, then he will not see the relativity of 12 paṭiccasamuppāda. Therefore, he can not meditate insight meditation in 3 characterizes in every second of life.
For the example, god is an illusion

When you still believe in god, do you understand 12 paṭiccasamuppāda
of god?(no)
Then can you think God is impermanent, suffering, non-self? (no).
But if you understand how god can analysis as 12 paṭiccasamuppāda, then no god anymore right? (yes)
When no god anymore, 12 paṭiccasamuppāda, which you have been called it as
god, can appear as impermanent, suffering, and non-self, right?
(yes)

So whole pali canon focus on illusion analysis for purge illusion first

The first of all sutta, Sutta Pitaka Vol 1 : 1. Sutta. Tī. Sī
Brahmajālasuttaṃ, is the biggest sutta which teaching about 62
self-illusion analysis. After buddha showed all 62 self-illusion,
then buddha conclude them, 62 self-illusion analysis, as 12
paṭiccasamuppāda at the end.
The first fetter is sakkāya-diṭṭi, which have to destroyed by the
practitioner first of all 10 fetters.
After jhāna meditation, whole tipitaka structure  focus on diṭṭhi-analysis first for the insight meditation beginner, before comprehensions on "impermanent, suffering, and non-self".
Attavādupādāna-cessation, diṭṭhi-analysis/self purging, is taught only inside Buddhism according to MN Cūḷasīhanādasutta.
Sāriputta, the right-hand man of Buddha, described insight meditation by that same structure, in Sutta KN Paṭisambhidāmagga (whole structure).
0 BE ancient commentary described insight meditation by that same structure.
3th BE 3rd buddhist council members, arahanta, judge titthiya-monks by illusion analysis ability testing as well. See Abhidhamma Pitaka Vol 4 : Abhi. Kathāvatthu  (whole structure).
10th BE commentary, such as visuddhimagga (path of purification), described insight meditation by that same structure  (whole structure).
16th BE commentary, such as abhidhammatthasaṅgaha, described insight meditation by that same structure  (whole structure).
Vimuttimagga described insight meditation by that same structure  (whole structure).
Burmese monks, such as pa-auk monastery, described insight meditation by that same structure  (whole structure).
Thai monks, such as Bh. Mun Bhuridatta who is the leader teacher of all thai forest monk, described insight meditation follow to abhidhammatthasangaha as well.

"the self is definitely an illusion" and lacked true existence. This seemed to be held up as an important fact that has significance in the
  pragmatic soteriological aims of Theravada

Indeed. Ideas about rocks & clouds existing or not-existing or neither existing or non-existing is unrelated to  the soteriological aim of the Buddha. The illusion of self is the root of suffering and it is the illusion of self that must be understood for the soteriological purpose.

First, is the self an illusion or not? Here it was said by the same person above that the self was not an illusion?

Self is an illusion or superstition (fabricated assumption), as said in SN 22.81.

If either the self is like an illusion or is literally an illusion, is this synonymous with saying that it lacks true or real existence
  from the Theravada viewpoint?

It lacks lacks true or real existence. The Buddha said "self" is a "disease" & the "arising of suffering".

Why does Theravada regard this question about the ontological status of the self of persons to be an important question?

Theravada does not ever mention the word "ontological". Why do you keep using this Western word? Regardless, the question is important for the soteriological aim of the Buddha. The illusion of self is the root of suffering and it is the illusion of self that must be understood for the soteriological purpose.

Why can't we just say that the self of persons is real and true like
  other phenomena, but transient or lacking sara as Chris said was the
  correct interpretation of SN 22.95

Chris's comment was wrong. Why are you here asking questions from ignorance but then, despite your ignorance, making judgments of what is right & wrong?
Regardless, the "self" is a fabrication that can be observed to not exist for prolonged periods; for a Buddha for their whole life. However, the five aggregates will always exist.
To repeat: When the mental fabrication of "self" ceases to exist in the mind; the mind will continue to exist.

Why does Theravada regard the question of whether the aggregates have intrinsic value, worth, meaning and lasting quality an important
  question?

So craving does not arises towards worthless phenomena.

If the self does not truly exist like an illusion, then what does it
  matter if the aggregates have intrinsic value, worth, meaning and
  lasting quality since the self cannot be found in them?

This question is wrong. The self does not truly exist like an illusion for enlightened minds rather than for idiots (puthujjana). Therefore, many aspects of insight are useful for overcoming craving, which is a cause for the illusion of suffering generating suffering.
This is why in his 2nd sermon, the Buddha gave a gradual teaching about: (i) impermanence; (ii) unsatisfactoriness; and (iii) not-self. The Buddha did not start with "not-self".

Some Theravada adherents say that, "the original Pali sutta's" do away with unnecessary speculation or "ontological hamster wheels."

Please try to no ask questions about "ontological". This word is foreign or alien to Buddhism.

However, paradoxically it seems some Theravada regard the question
  of the ontological status of the self to be very important.

The illusion of self is the root of suffering and it is the illusion of self that must be understood for the soteriological (liberation) purpose.

It's also clear that Sariputta thought it very important to correct
  Yamaka about this. And the Buddha himself thought it important to
  instruct how the aggregates and other phenomena were to be regarded as
  lacking intrinsic value, worth, meaning and lasting quality
  irregardless questions of the self.

In his 2nd sermon the Buddha explained the Three Characteristics (which per AN 3.136 are inherent or "ontological"). The teaching in the Phena Sutta is related to the 2nd characteristic of "dukkha", namely, the inherent characteristic that conditioned things cannot bring lasting happiness because they are meeaningless & worthless. The Phena Sutta (SN 22.95) does not mention the words "anatta" or "sunnata" because the Phena Sutta is not about the "selflessness of the aggregates".

Ontological the word has been used many times in translation of Buddhist texts your own aversion to the word notwithstanding.

Please follow the precept of Truthful Speech. Please quote where Ontological the word has been used many times in translation of Buddhist texts?

In light of your just posted question https://buddhism.stackexchange.com/questions/28751/dhamma%e1%b9%ad%e1%b9%adhitat%c4%81-and-dhammaniy%c4%81mat%c4%81-versus-ontology-phenomenology I assume you found via an easy google search will you retract your implication that I was untruthful?

The quotes I made are not found in any translations of Pali. They are comments made by Western scholars that are independent from the Pali teachings.

You said the word was foreign or alien to Buddhism and yet just as I said it is found in numerous Buddhist texts proving your contention wrong. The Pali texts are just one part of Buddhist texts. The writers you quote are Theravada practitioners and yet you imply I am untruthful. If you are interested in truth you will acknowledge and retract your erroneous implication. If you are just interested in not admitting error lest it damage your ego or self-conception... well, that is on you.

Bhikkhu Bodhi is not the suttas. Bhikkhu Bodhi made a commentary unrelated to the suttas.

Let us continue this discussion in chat.


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Is an 'Existential Crisis' a necessary condition to start on the path of Dhamma?
The path of Dhamma is a journey towards the end of all suffering through the attainment of Nibbana. The Buddha set out to find the cure for human suffering, but there are so many people around us today, suffering in so many ways. Most of the people end up still finding a cure in the material world. There are very few people who are suffering might end up starting to think about life itself as suffering for e.g. philosophers like Schopenhauer. But even these intellectuals don't seem to have come to the conclusion of the need to transcend the mind. As against there are those might not be in a lot of suffering but in an, existential crisis seem to arrive at the path of Dhamma.
I am asking, is existential-crisis a pre-requisite and more fundamental human need than wanting to end suffering to start the journey towards Nibbana?

Is this a dupe of Why have I awoken Now?

No the answer below looks like a answer to that question. The question is inherently different. Here I am asking about the role crisis for meaning plays in arriving and not about tge probablity of arriving.

Understood. Still, please check my answer to that question, specifically the part about "enough suffering in your life and enough confusion to push you to seek some sort of resolution", and "combination of positive and negative factors".

Schopenhauer refers to the consciousness beyond subject and object as his 'better consciousness', so maybe he had some idea of transcending mind.

AN 3.38 describes Gotama having an existential crisis.

Even though I was endowed with such fortune, such total refinement, the thought occurred to me: 'When an untaught, run-of-the-mill person,
  himself subject to death, not beyond death, sees another who is dead,
  he is horrified, humiliated, & disgusted, oblivious to himself that he
  too is subject to death, not beyond death. And if I — who am subject
  to death, not beyond death — were to be horrified, humiliated, &
  disgusted on seeing another person who is dead, that would not be
  fitting for me.' As I noticed this, the living person's intoxication
  with life entirely dropped away.

Also, the traditional biography of Sariputta & Mogallana shows them having an existential crisis:

Now at Rajagaha there was an annual event called the Hilltop Festival. Seats were arranged for both youths and they sat together to
  witness the celebrations. When there was occasion for laughter, they
  laughed; when the spectacles were exciting, they became excited; and
  they paid their fees for the extra shows. In this manner they enjoyed
  the festival for a second day; but on the third day their
  understanding was awakened and they could no longer laugh or get
  excited, nor did they feel inclined to pay for extra shows as they had
  done on the first days. Each of them had the same thought: "What is
  there to look at here? Before these people have reached a hundred
  years they will all have come to death. What we ought to do is to seek
  for a teaching of deliverance."
It was with such thoughts in mind that they took their seats at the festival. Then Kolita said to Upatissa: "How is this, my dear
  Upatissa? You are not as happy and joyous as you were on the other
  days. You seem now to be in a discontented mood, What is on your
  mind?"
"My dear Kolita, to look at these things here is of no benefit at all. it is utterly worthless! I ought to seek a teaching of
  deliverance for myself. That, my Kolita, is what I was thinking,
  seated here. But you, Kolita, seem to be discontented, too."
And Kolita replied: "Just as you have said, I also feel." When he knew that his friend had the same inclinations, Upatissa said: "That
  was a good thought of ours. But for those who seek a teaching of
  deliverance there is only one thing to do: to leave home and become
  ascetics. But under whom shall we live the ascetic life?

Can you elaborate on how you concluded that the Buddha had an existential crisis? He had all the material comforts that a person could desire. Does the fact that he got horrified necessarily mean that he was in existential crisis?

Siddhartha led a privileged life and was an intelligent and curious person. The story of he and his attendent seeing the three marks of living- illness, old age and death created an existential crisis for him. The crisis raised the haunting question of what is the meaning of life? Is it only to become ill, old and die? This created anxiety, a malaise, dysphoria or Suffering that he could not shake or eventually ignore. This is the Suffering the Buddha later talks about as having transcended and ended. This was the strong reason why he left his family to find the answer to the existential question of the meaning to life. Also, he wanted to find the answer so his loved ones would not suffer from the doubt and insecurity of a meaningless life of only living for sense pleasure gratification. He sought out leading gurus but eventually they did not have the answer. It was only until his Awakening to the non-duality of existence that he understood that this suffering or insecurity about the meaning of life was a cognitive event and once he transcended this he no longer was worried since the question is born out of the ignorance of dualism. He became the Buddha.

There are two types of existential crisis. One makes a person extremely corrupted, harmful to themselves and others. The second type of existential crisis leads a person to a spiritual opening. The second type of existential crisis is a very rare event in the human world, that's why there are very few people in the world who are interested to walk in the path of the dhamma.
In the modern world I think that the most people experiences existantial crisis, that's why when you look to the news you'll see many horrible things are happening daily all around the world. The wrong beliefs, ideas and modern age's advanced technology's effect on the human mind leads people to be "living deads". But the existantial crisis of the most of the humans don't lead them to the dhamma because most people are clinging to collective culture, wrong ideas and beliefs. So they continue the normal way of living with clinging to collective culture, wrong beliefs and ideas even more. People try to suppress their sufferings with using different kinds of tools, but this suppressing only makes them worse.
The important thing is to be disloyal to the collective culture, wrong beliefs and ideas in order to the start on the path of dhamma. You experience existantial crisis or not doesn't matter, but understanding the suffering aspect of the collective culture, society, beliefs, ideas and becoming at least a little bit detached from them is absolutely necessary in order to start the path.
For the ordinary people existantial crisis makes their heart more stiff, makes them more worldling. In the spiritual path the person also have these "existantial crisis" time to time but these experiences makes the person's heart open more to the nature of reality. As a result, the person gradually disidentifes from the collective humanity's insanity and eventually enters to the stream of enlightenment and after the purification and disidentification reaches to a point these existantial crisis periods ends and what remains is only very deep peace, happiness, contentment. So existantial crisis actually helps the spiritual people to walk in the direction of non-self and freedom from suffering. Because mindfulness of suffering eventually leads to complete freedom from suffering. As Thich Nhat Hanh said "Suffering and happiness is one". But for the beginners being "disloyal" to the collective culture, society, beliefs and ideas is the main necessity for starting to the path of the dhamma.

Yes, dukkha is the pre-requisite for Saddha, samvega, for pasada. No fear, no dhukka perceived, the path for escape the truths in the world is neither desired nor seen.

In Therigatha 6.1 (quoted below), the nun Bhikkhuni Patacara had an existential crisis over her son's untimely death. Recalling the Buddha's words, she had a deep realization, perhaps even enlightenment, that led her to take refuge in the Buddha, the Dhamma and the Sangha.

[Patacara recalls the Buddha's words:]
  "You don't know the path
  of his coming or going,
  that being who has come from where?
  — the one you lament as 'my son.'
  But when you know the path
  of his coming or going,
  you don't grieve after him,
  for that is the nature of beings.
Unasked,
  he came from there.
  Without permission,
  he went from here
  — coming from where?
  having stayed a few days.
  And coming one way from here,
  he goes yet another from there.
  Dying in the human form,
  he will go wandering on.
  As he came, so he has gone
  — so what is there to lament?"
Pulling out
  — completely out
  — the arrow so hard to see,
  embedded in my heart,
  he expelled from me
  — overcome with grief
  — the grief over my son.
Today — with arrow removed,
  without hunger, entirely Unbound
  — to the Buddha, Dhamma, & Sangha I go,
  for refuge to the Sage.

Yes I was thinking of that ("the one you lament as 'my son.'") too. Or actually I was thinking of Gautami, rather than Patacara. But conversely "the weaver's daughter" (who attained stream entry just before she died), it's not clear she was having some existential crisis (unless her having been thinking about the impermanence of life for a while counts as that), nor why she alone (among the people of Alavi) took up that meditation at the Buddha's suggestion in the first place.

Those beings fortunate enough to be born a person is as rare as a blind sea-turtle coming to the surface every hundred years in a world covered in oceans managing to put its neck through the hole of a yoke tossed about by the wind.
Those persons fortunate to encounter the dharma, recognize it as a refuge as such, in a time when the dharma hasn't completely disappeared, and have the leisure and opportunity to practice are at least as rare as that.
We should all be rejoicing that we've been able to find such a precious jewel given such meager chances!
See the Chiggala Sutta.
I can't speak for others, but I think I've been a seeker my whole life starting at a very early age. I read Siddhartha in high school which was my first introduction to Buddhism, but did not pursue it or inquire too much more. However, I do recall thinking that Buddhism seemed familiar or something about it warranted more investigation, but that didn't occur until into middle age. I can't speak for past lives, but I don't think there was existential crisis although again I've always been a seeker in this life.

Yes, but do we arrive here due to a crisis to find a meaning of life or sheer discretion on our part about the cure for suffering? How much do this search for meaning play its part? That seems more fundamental to me.

A teacher of mine once said that there are two kinds of people who follow the dharma

People who have seen through things already and had a level of insight
People who just weren't very good at living in the modern world and were looking for something different

I guess you could view both groups as having some kind of crisis.
Supporting this, I read a forum post by Daniel Ingram who said that anyone interested enough in the dharma to be reading that kind of post probably already had had significant levels of insight. Or to read it another way - a crisis.
I have to say both figures (my old teacher and Daniel Ingram) are quite controversial.


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How to navigate the impracticality of Sigalovada sutra?
Consider the advice of Buddha about friends and Wife in the Siglovada Sutta.

friends and colleagues so respected reciprocate with compassion in five ways: by protecting you when you are vulnerable, and likewise your wealth, being a refuge when you are afraid, not abandoning you in misfortunes, and honoring all your descendants.
Some are drinking buddies,
  Some say, 'Dear friend! Dear friend!'.
  But whoever in hardship stands close by,
  That one truly is a friend.

Sleeping late, adultery,
Hostility, meaninglessness,
Harmful friends, utter stinginess:
These six things destroy a person....
In today's world where Smoking and drinking has become such a common thing and where socializing has become equivalent to having a few drinks at least a glass of wine, it's hard to find a guy to make a friend who would fit into Buddha's description of a friend here. I mean I have given up the vices but if I will try to find a mate like me its impossible, I will be left alone.
A similar thing goes with the wife,

And, the wife so respected reciprocates with compassion in five ways: by being well-organized, being kindly disposed to the in-laws and household workers, being faithful, looking after the household goods, and being skillful and diligent in all duties.

In today's time of the hit and run relationships and all that we know of modern day relationships, this seems impractical.
Following this Sutta will leave you lonely. How do you navigate this problem?

This question might, I don't know, be on-topic on Interpersonal Skills SE -- check What topics can I ask about here? before you post there though, and their Meta.

No, the question has meaning only in the context of buddhism and the answer is also, as I wanted in context of Buddhist practice which I got...otherwise I do know what to do to solve the problem.

The answer comes in the Rhinoceros Sutta (mentioned by @santa100):

If you gain a mature companion,
  a fellow traveler, right-living & wise,
  overcoming all dangers
  go with him, gratified, mindful.
If you don't gain a mature companion,
  a fellow traveler, right-living & wise,
  wander alone
  like a king renouncing his kingdom,
  like the elephant in the Matanga wilds, his herd.
We praise companionship — yes!
  Those on a par, or better,
  should be chosen as friends.
  If they're not to be found,
  living faultlessly,
  wander alone
  like a rhinoceros
Avoid the evil companion
  disregarding the goal,
  intent on the out-of-tune way.
  Don't take as a friend
  someone heedless & hankering.
  wander alone
  like a rhinoceros.
Consort with one who is learned,
  who maintains the Dhamma,
  a great & quick-witted friend.
  Knowing the meanings,
  subdue your perplexity,
  [then] wander alone
  like a rhinoceros.

The truth of the Buddha's teaching is timeless and doesn't get affected by modern norms or customs. Imagine if it's influenced by social norms, then there'll be a possible scenario in a distant future where human virtures and values becoming severely degenerated. It'll be common practice and acceptable social norm for humans to do all kinds of evil and little to none of virtuous conducts. If going by the standard of that future time, the Buddha's teaching will be perceived as completely irrelevant, or at least only deemed valuable to a very very small number of people. The Dhamma drum will have so many pegs that it won't be able to make audible sound. So for the OP question, you'd have a better chance of finding a friend or a soulmate with similar mentality or conducts if s/he also cultivates similar virtues. Finding fellow Buddhist practitioners would be best, but any other sincere followers of other world religions would also be fine since they pretty much share similar codes of conduct. If all else fail, then it's perfectly ok to walk the path alone like a proud Rhinoceros

Following this Sutta will leave you lonely. How do you navigate this problem?

It's actually quite a relief to be free of those who are scoundrels, drunkards, addicts, frauds, swindlers, and thugs. And I am always surprised and grateful at how many others are left in the world to meet and greet in passing or again as friends.
Ultimately, when one becomes a good friend, loneliness ends.

The Buddha said he teaches about suffering & freedom from suffering. Drugs, alcohol, cigarettes, women with broken capacity for fidelity, etc, are suffering and to be avoided; for financial reasons and for reasons of mental & physical health.


text:
Sutta reference or teachings about Sleep timings?
In a Vipassana retreat you are made to wake up at 4 am, also similar is the case in the Zen retreat.
I have read numerous articles on advantage on waking up early.
Are there any Sutta references or teachings of Monks or Lama or Zen master which give advise on waking up early and going to bed early?

Sutta Pitaka Vol 4 : Sutta. Ma. Mū. Mahāassapurasuttaṃ:

What more is there to do?
You should train yourselves like this: ‘We will be committed to
  wakefulness.

When practicing walking and sitting meditation by day, we will
  purifying our mind from obstacles.
In the evening, we will continue to practice walking and sitting
  meditation.
In the middle of the night, we will lie down in the lion’s
  posture—on the right side, placing one foot on top of the
  other—mindful and aware, and focused on the time of getting up.
In the last part of the night, we will get up and continue to
  practice walking and sitting meditation, purifying our mind from
  obstacles.’

Now, mendicants, you might think: ‘We have conscience and prudence,
  our bodily, verbal, and mental behavior is pure, our livelihood is
  pure, our sense doors are restrained, we don’t eat too much, and we
  are committed to wakefulness. Just this much is enough …’


text:
Do the words, Dharmakaya, Nirmanakaya or Samboghakaya appear in any Teravada Buddhist Scriptures?
I read some articles and saw some references to the words , Dharmakaya, Samboghakaya and Nirmanakaya used by Buddha , as mentioned in the Theravada scriptures , at least a few times during His Lifetime. Has anyone come across this , too?

The Trikaya concept is a Mahayana concept although the origin to the term Dharmakaya could be found in the Pali Canon at SN 22.87:

Enough, Vakkali! What is there to see in this vile body? He who sees Dhamma, Vakkali, sees me; he who sees me sees Dhamma. Truly seeing Dhamma, one sees me; seeing me one sees Dhamma."

Please note that in the original Pali sutta, it actually says "Dhammakayo".

Very good answer.

@AndreiVolkov I don't understand this answer and your comment. The word "Dhammakayo" does exist in a few suttas, but not in SN 22.87. Maybe SN 22.87 includes something like the idea of "Dhammakayo", but not the word in question.

Oh no, looks like I confused sutta with its commentary @ChrisW - my apologies, apparently it was Buddhaghosa who explained Dhamma in that passage to refer to Dhammakaya.

My search finds dhammakayo is only found in the dodgy DN 27 https://suttacentral.net/dn27/en/sujato

Thank you for your kind answers and the time you took . I wasn't referring to the Tri-kaya. I just asked if these words had ever been used in Pali Suttas, i.e. "words of the Buddha". . I read a commentary , with some examples , that this was the case. But, alas, I did not keep this source. Apologies.

Not that I'm aware of

@Pasquale As Dhammadhatu commented, the word "dhammakāyo" exists in DN 27 -- with brahmakāyo (translated "embodiment of holiness") and dhammabhūto (translated "one who has become the truth")

In my understanding, in the Pali Canon the Buddha had used the word "Dhammakaya" to refer metaphorically to the body of his teachings. Another term that was used in the same sense was "Dhammasarira" (Dharma-sharira) - playing on the notion of Buddha's cremation relics to refer specifically to the dispersed collection of teachings left after the Buddha's parinirvana.
Since Buddha himself said that "whoever sees Dhamma sees me" and that "the Dhamma exists as a natural law whether Tathagatas arise or not", it was easy enough for the eager students to add two and two together and assume that Dhammakaya implies the eternal cosmic body of the primordial Buddha.
The other two terms presumably evolved at the later times, at least they were not found in any of the early texts.


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Dhammaṭṭhitatā and Dhammaniyāmatā versus "Ontology" & "Phenomenology"
In AN 3.136 and SN 12.20, it is said the Three Characteristics and that suffering arises via Dependent Origination are "sā dhātu, dhammaṭṭhitatā dhammaniyāmatā", namely:

law of nature, regularity of natural principles, invariance of natural principles
this property stands—this steadfastness of the Dhamma, this orderliness of the Dhamma

Yet Westerners appear of often debate about whether Buddhism is "Ontology" or "Phenomenology". It appears some Westerners, such as Bhikkhu Bodhi, cannot even make up their mind, as shown with a quote (below) from 1993 arguing in favour of Ontology and then a quote (below) from the year 2000 (pages 515 & 527 of SN) in favour of Phenomenology.
My questions are:

What are the reasons why students, such as Bhikkhu Bodhi, should compare Buddhism to "Ontology" & "Phenomenology"?
Why are the reasons why students should not attempt to clearly understand the Buddha's teaching about "sā dhātu, dhammaṭṭhitatā and dhammaniyāmatā"?

It's described as "ontology" because "ontology" means the science/study/philosophy/description of "being" -- i.e. whether things "are" (and how they "become" and so on).
"Ontology" is derived from a Greek root, ὤν --

Etymology
  From Proto-Indo-European *h₁s-ónt-, present participle of *h₁es- (“to be”).
  Cognate with ... Sanskrit सत् (sát, “being, essence, reality”).
Participle
  ὤν • (ṓn)

present participle of εἰμί (eimí)
actual, real

Conversely, phenomenology --

Etymology
  From the Ancient Greek φαινόμενον (phainómenon, “thing appearing to view”), from the verb φαίνω (phaínō, “to show itself, to be manifest”).
And from the Ancient Greek λόγος (lógos, “the study of, an account, speech, oration, discourse, word, ratio, calculation, reason”).
Thus, by extension "the study of what shows itself (to consciousness").
According to Heidegger's Introduction to Phenomenological Research, "the expression “phenomenology” first appears in the eighteenth century in Christian Wolff’s School, in Lambert’s Neues Organon, in connection with analogous developments popular at the time, like dianoiology and alethiology, and means a theory of illusion, a doctrine for avoiding illusion." (p.3)
Noun

(philosophy) The study of structures of consciousness as experienced from the first-person point of view.
(philosophy) A movement based on this, originated about 1905 by Edmund Husserl.

It seems to me that Buddhist doctrine makes (various different) statements that are relevant to both -ologies ... even though it's sometimes claimed that the two -ologies describe mutually-exclusive domains:

https://www.google.fr/search?q=define%3APhenomenology
  the science of phenomena as distinct from that of the nature of being

For example, "every thing is dependently originated" seems to me an ontological statement; and "every perception is dependently originated" seems to me a phenomenological statement.
In my personal opinion Western philosophy is a bit poisoned by a persistent subjective/objective split (and maybe a self-vs.-other duality) ... a split which Buddhism seems to me to be immune to.
"Everything has independent existence" is one extreme (refuted) -- and "Everything is merely a perceived illusion" would be an opposite extreme (which is also, I think, not Buddhist doctrine).
What are the reasons why students, such as Bhikkhu Bodhi, should compare Buddhism to "Ontology" & "Phenomenology"?
I don't know why anyone (Bhikkhu Bodhi) does that. Perhaps it's the effort to explain a new topic (Buddhism) using existing (Western) language and in comparison to existing (Western) philosophy -- the same kind of reason for which we (reluctantly) allow comparative-religion questions on this site.
If I use "ontological" I mean it as a bit of a criticism, meaning "IMO it seems to me that this topic is excessively interested in the logic of whether something 'exists'" -- not that I should criticise, exactly, because I infer that some schools find a soteriological benefit in that kind of analysis.
I used it in this answer, though, because I thought the OP was asking ontological question and making ontological assertions (e.g. "There is a Sutta in the Pali Canon that seems to explicitly reject that any of the aggregates is real or substantially existent") -- whereas I think that the sutta isn't trying to make an ontological statement (about whether and to what extent things exist) ... that if the OP is trying to read between the lines to find an ontological statement, then the OP is trying to read into the text a statement about ontology that isn't there ... and that instead the sutta can (IMO should) be understood as making a statement that follows from the Three Characteristics.

I marked this answer down because the Three Characteristics are not "how things become" nor are they really "things" but rather are the characteristics of things. Also, they are not :what shows itself (to consciousness)" because they exist, per the sutta, regardless of consciousness of them.

I also marked this answer down because of the entire irrelevance of the discussion about ontology & phenomenology; which I would regard falls into the category of frivolous unbeneficial speech or "animal talk". Thanks anyway for your effort Chris.

I didn't say that the Three Characteristics are "how things become", nor that they're "things", etc.; but vote however you want. It does leave me wondering whether you read the answer, how/why is it there seems to be a failure to communicate. I suppose you already had an answer in your mind, and what you had in mind wasn't this answer.

I found it difficult to read the answer intellectually with the Dhamma-Eye. It was painful to read or waste time on such matters. The Buddha said: "the days & nights are relentlessly passing; how beneficially are you spending your time?".

What are the reasons why students, such as Bhikkhu Bodhi, should compare Buddhism to "Ontology" & "Phenomenology"?

There are no reasons to do the above. It is wrong to make Buddhism appeal to those that it is unsuitable for because it can only harm the Dhamma. "Ontology" & "Phenomenology" are "tiracchānakathaṃ" or "monkey chatter". Buddhism should be about knowledge that directly extinguishes suffering.

Why are the reasons why students should not attempt to clearly understand the Buddha's teaching about "sā dhātu, dhammaṭṭhitatā and
  dhammaniyāmatā"?

There are no reasons to do the above. The Dhamma student should clearly know with truth-discerning-suffering-destroying wisdom that the Three Characteristics are:

The state of the Absolute Lawfulness of Nature (dhammaniyāmatā)
The Normal Natural Ordinary Inherent way things are  (dhammaṭṭhitatā)

Therefore, when change occurs, such as loss of possession, death of loved one, natural disaster, nuclear war, etc, the mind with mindfulness-&-clear-comprehension (sati-sampajanna) clearing knows: "this is just the way things are, according to the law of nature; it cannot be any other way".
In short, I doubt very few, if any members, of this & other Buddhist chat sites even know of or have ever heard of "dhammaniyāmatā" and "dhammaṭṭhitatā", which are similar to a "God" of Buddhism. They don't even know the most important things yet preoccupy themselves with alien foreign non-suffering-destroying philosophies.
Students can listen to a live translation of Buddhasadasa, here: Nine Vipassana Eyes, which includes discussion of "dhammaniyāmatā" and "dhammaṭṭhitatā".
When I was a beginner student, I heard about these crucial suffering destroying realities, I never heard before.