Is the self an illusion or is it *like* an illusion?

"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".

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 ~~

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

1. When you still believe in god, do you understand 12 paṭiccasamuppāda of god?(no)
2. Then can you think God is impermanent, suffering, non-self? (no).
3. But if you understand how god can analysis as 12 paṭiccasamuppāda, then no god anymore right? (yes)
4. 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

1. 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.
2. The first fetter is sakkāya-diṭṭi, which have to destroyed by the practitioner first of all 10 fetters.
3. After jhāna meditation, whole tipitaka structure focus on diṭṭhi-analysis first for the insight meditation beginner, before comprehensions on "impermanent, suffering, and non-self".
4. Attavādupādāna-cessation, diṭṭhi-analysis/self purging, is taught only inside Buddhism according to MN Cūḷasīhanādasutta.
5. Sāriputta, the right-hand man of Buddha, described insight meditation by that same structure, in Sutta KN Paṭisambhidāmagga (whole structure).
6. 0 BE ancient commentary described insight meditation by that same structure.
7. 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).
8. 10th BE commentary, such as visuddhimagga (path of purification), described insight meditation by that same structure (whole structure).
9. 16th BE commentary, such as abhidhammatthasaṅgaha, described insight meditation by that same structure (whole structure).
10. Vimuttimagga described insight meditation by that same structure (whole structure).
11. Burmese monks, such as pa-auk monastery, described insight meditation by that same structure (whole structure).
12. 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.

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.