What is Buddhist doctrine on the question of counterfactual definiteness?

When a tree falls in a lonely forest, and no animal is near by to hear it, does it make a sound?

I think Buddhism says something about "contact" between sense-object, sense-organ, sense-consciousness.

the moon does not exist if nobody is looking at it

Maybe this calls for a joke, about enlightenment (of which the moon is a symbol) being non-self.

The standard procedure for understanding anatta is to investigate and look for the self and upon not finding it concluding that the self does not exist as we imagined.

That's not how I interpret the Anattalakkhaṇasutta -- I interpret it as saying that the aggregates don't obey our will, are impermanent, are dukkha, and are therefore not fit to describe as self -- not that "self doesn't exist" but that "it's not clever, healthy, proper" to describe the aggregates as self.

Couldn't someone relying upon counterfactual definiteness just say ...

Yes it sounds to me like back-and-forth argument.

Quoting again from 7 Things the Buddha Never Said:

3. “There is no self.”

   This is the other Big Lie. The one time the Buddha was asked point-blank if there is or isn’t a self, he refused to answer (Samyutta Nikaya 44.10). In Majjhima Nikaya (the “Middle-Length Discourses” of the Buddha) 2 he stated that the views “I have a self” and “I have no self” are both a thicket of views that leave you stuck in suffering. When the Buddha taught not-self (anatta) — as opposed to no self — he was recommending a strategy for overcoming attachment, a way of cutting through the mind’s tendency to cling to things by claiming them as “me” or “mine.”

   The Buddha never said that “There is no separate self” either. He declined to get involved in the issue of whether any kind of self exists or doesn’t exist.

See also How is it wrong to believe that a self exists, or that it doesn't?

I think that "the self exists" and "the self doesn't exist" and so on are all categorised as "views of self" and a "thicket of views".

I don't have sutra reference but I am going to answer this as a personal understanding of the universe.

"the moon does not exist if nobody is looking at it?"

The black-holes cannot be seen, even if someone is looking at it, you cannot see them. The existence of a black hole was first predicted mathematically on paper. So did it exist then? Later its existence was confirmed only as an inference from the trajectory of nearby stars. So it does exist. Everything exists irrespective of a human or sentient entity of observation.

And also the tree does make a sound even when no animal is around to hear it.

But that is just one aspect of reality.

Actually, in a way, the moon does not exist when no one is looking at it. When you are not looking at it, the whole lump of matter called moon is just probability waves of subatomic particles moving in empty space. At that level of reality its just a distortion in space, a changing entropy. There really, in reality, is no moon.

Similarly, when the tree falls, there is no sound, just longitudinal waves which are a disturbance in the air. There is no sound. The sound is a mental construct of a sentient entity which can hear.

But there is also another twist in this.

According to recent work of scientist and philosopher Bernardo Kastrup, something like the color is inherently there. It's not because of the photon of particular frequency strikes on your retina and your brain interpreting in a particular way, but the information of the experience of green is inherent. So with or without the sentient entity, there are green trees.

So, maybe even if no animal is there to hear, there is sound which is heard by trees around, and even if we are not looking at the moon, the earth is looking at the moon.

So the short answer is it depends upon the vantage point of reality you are in, it depends on the frame of reference from which you are cognizing the reality.

Adding the Buddhist twist to this,

• eye produces eye consciousness, ear produces ear consciousness and so on... so consciousness is human experience product of senses.

                        OR
  

• There is a plane of infinite consciousness and it being the aggregate it has an independent existence. So consciousness is just there.

So based on what you choose to believe you have your version of reality. it's not absolute.

The Pali suttas say not-self (anatta) is the true nature of all things; even when there are no Buddhas in the world to reveal this truth. In other words, just because there is no mind to experience something (such as a sound or anatta) does not mean that something does not exist. The idea that a sound only exists when it is heard is Theism; the belief a God creates the world. It is Brahmanism.

Below is quoted the difference between Buddhism and Brahmanism:

Whether or not there is the arising of Tathagatas, this property stands—this steadfastness of the Dhamma, this orderliness of the Dhamma: All phenomena are not-self.

The Tathagata directly awakens to that, breaks through to that. Directly awakening & breaking through to that, he declares it, teaches it, describes it, sets it forth. He reveals it, explains it & makes it plain: All phenomena are not-self.

AN 3.136

---

Whether or not there is the arising of Tathagatas, this property stands — this regularity of the Dhamma, this orderliness of the Dhamma, this this/that conditionality. The Tathagata directly awakens to that, breaks through to that. Directly awakening & breaking through to that, he declares it, teaches it, describes it, sets it forth. He reveals it, explains it, makes it plain, & says, 'Look.' From birth as a requisite condition comes aging & death....From becoming as a requisite condition comes birth...

SN 12.20

Theistic Brahmanism:

'I, monk, am Brahma, the Great Brahma, the Conqueror, the Unconquered, the All-Seeing, All-Powerful, the Sovereign Lord, the Maker, Creator, Chief, Appointer and Ruler, Father of All That Have Been and Shall Be.'

DN 11

About the arising of sense contact, the Pali sutta say:

sense-object, sense-organ, sense-consciousness.

However, the Pali suttas do not say if there is no consciousness there is no sound.

Unlike the dodgy Buddhists who assert consciousness comes first, the Pali suttas say sense objects, such as sounds, come first:

Dependent on eye & forms, eye-consciousness arises....

Now, when there is no eye, when there are no forms, when there is no eye-consciousness, it is impossible that one will delineate a delineation of contact.

I try to warn people about the danger of "Phenomenology" but the Phenomenologists trapped by the Phenomenological Spell of Mara believe Dhammadhatu (rather than Phenomenology) is Mara.

The standard procedure for understanding anatta is to investigate and look for the self and upon not finding it concluding that the self does not exist as we imagined.

Anatta is not-self. It is not no self. From MN 148:

"If anyone were to say, 'The eye is the self,' that wouldn't be tenable. The arising & falling away of the eye are discerned. And when its arising & falling away are discerned, it would follow that 'My self arises & falls away.' That's why it wouldn't be tenable if anyone were to say, 'The eye is the self.' So the eye is not-self. If anyone were to say, 'Forms are the self,' that wouldn't be tenable... Thus the eye is not-self and forms are not-self. If anyone were to say, 'Consciousness at the eye is the self,' that wouldn't be tenable... Thus the eye is not-self, forms are not-self, consciousness at the eye is not-self. If anyone were to say, 'Contact at the eye is the self,' that wouldn't be tenable... Thus the eye is not-self, forms are not-self, consciousness at the eye is not-self, contact at the eye is not-self. If anyone were to say, 'Feeling is the self,' that wouldn't be tenable... Thus the eye is not-self, forms are not-self, consciousness at the eye is not-self, contact at the eye is not-self, feeling is not self. If anyone were to say, 'Craving is the self,' that wouldn't be tenable. The arising & falling away of craving are discerned. And when its arising & falling away are discerned, it would follow that 'My self arises & falls away.' That's why it wouldn't be tenable if anyone were to say, 'Craving is the self.' Thus the eye is not-self, forms are not-self, consciousness at the eye is not-self, contact at the eye is not-self, feeling is not self, craving is not-self.

Couldn't someone relying upon counterfactual definiteness just say that even though we can't observe the self that it still truly exists just like an unobserved tree in the forest that falls still makes a real sound?

I've heard Advaita adherents saying that the one cannot see his own eye, because the eye cannot see itself, but it doesn't mean that the eye is not there. Here, the self is equated with some kind of universal consciousness (the same "I" in every being, the silent witness). But the Buddha debunked this by his analysis on consciousness in MN 38.

Now back to the context of what's useful in Buddhism. The question as you ask it does not contribute to the cessation of suffering. It will simply result in a lot of philosophical speculation and intellectual gymnastics. Why? Once suffering has ceased for an enlightened one, it doesn't matter whether there is still a self sneakily hiding somewhere or not, because he has already understood through wisdom how dependent origination works.

But the analogy of the unobserved tree can be re-purposed and reframed to make it useful for the ending of suffering.

If a tree falls in the forest, and there are no observers, would there still be the sound of it? The answer is NO. Why? When a tree falls, it simply causes air molecules to move as waves. It only becomes a sound when there is an observer i.e. the movement of air molecules have to have contact with the ear drum to cause the stimulation of the auditory nerves, which in turn causes the brain to perceive sound. The same applies to sight and photons.

Similarly I can ask, if there is no clinging to what is felt through the six senses, would there still be the experience of suffering? The answer is NO. There is only the experience of suffering, when there is clinging to what is felt through the six senses. When there is no clinging to what is felt through the six senses, there would be no experience of suffering.

This is based on MN 148:

"Dependent on the eye & forms there arises consciousness at the eye. The meeting of the three is contact. With contact as a requisite condition, there arises what is felt either as pleasure, pain, or neither pleasure nor pain. If, when touched by a feeling of pleasure, one does not relish it, welcome it, or remain fastened to it, then one's passion-obsession doesn't get obsessed. If, when touched by a feeling of pain, one does not sorrow, grieve, or lament, beat one's breast or become distraught, then one's resistance obsession doesn't get obsessed. If, when touched by a feeling of neither pleasure nor pain, one discerns, as it actually is present, the origination, passing away, allure, drawback, & escape from that feeling, then one's ignorance-obsession doesn't get obsessed. That a person — through abandoning passion-obsession with regard to a feeling of pleasure, through abolishing resistance-obsession with regard to a feeling of pain, through uprooting ignorance-obsession with regard to a feeling of neither pleasure nor pain, through abandoning ignorance and giving rise to clear knowing — would put an end to suffering & stress in the here & now: such a thing is possible.

"Dependent on the ear & sounds...

"Dependent on the nose & aromas...

"Dependent on the tongue & flavors...

"Dependent on the body & tactile sensations...

"Dependent on the intellect & ideas ...

And clinging to what is felt through the six sense bases, is based on association of the five aggregates with the self:

"This, monks, is the path of practice leading to self-identification. One assumes about the eye that 'This is me, this is my self, this is what I am.' One assumes about forms... One assumes about consciousness at the eye... One assumes about contact at the eye... One assumes about feeling... One assumes about craving that 'This is me, this is my self, this is what I am.'

"One assumes about the ear...

"One assumes about the nose...

"One assumes about the tongue...

"One assumes about the body...

"One assumes about the intellect ...

What does Buddhism have to say about these questions if anything at all?

That's easy to answer: the only good use of mano ("mind") for anybody who want to stop dukkha is the yoniso manasikara ("appropriate attention"), which is, in one word, phrasing sati (awareness, mindfulness) and what you do with sati, in terms of mano. This is the first step of the path (after, of course, hearing the doctrine to remember) -- the famous "proper attention" on the source and ending of whatever is dukkha, from the reply "you need a good friend and proper attention" of the buddha, when he was asked what is required to reach nibanna.

Also, The standard procedure for understanding anatta has nothing to do with "investigate and look for the self and upon not finding it concluding that the self does not exist as we imagined." Leave drawing conclusion to the toxic puthujjanas (wordlings): the logicians, the daydreamers, the creators of views, the people who love to argue about views.

Use mano only for ascertainment, for attestation, for witnessing, of the source and fall of phenomena, of vedana (feelings), of sanna (perceptions) and so on -- and of course, for the ascertainment of the failure or the success, from the activities you have done so far, of your practice (then you pursue successful activities and you abandon failing activities).

Here is what happens when a puthujjana uses mano for something else than yoniso manasikara:

Ayoniso-manasikara Sutta: Inappropriate Attention (SN 9.11)

I have heard that on one occasion a certain monk was dwelling among the Kosalans in a forest thicket. Now at that time, he spent the day's abiding thinking evil, unskillful thoughts: i.e., thoughts of sensuality, thoughts of ill will, thoughts of doing harm.

Then the devata inhabiting the forest thicket, feeling sympathy for the monk, desiring his benefit, desiring to bring him to his senses, approached him and addressed him with this verse:

From inappropriate attention
you're being chewed by your thoughts.
Relinquishing what's inappropriate,
contemplate
appropriately.

Keeping your mind on the Teacher,
the Dhamma, the Sangha, your virtues
you will arrive at
joy,
rapture,
pleasure
without doubt.

Then, saturated
with joy,
you will put an end
to suffering & stress.

The monk, chastened by the devata, came to his senses.

Here is the proper use of mano:

• Natumha Sutta -- Not Yours (SN 12.37)
• Channa Sutta -- With Channa (SN 35.87)

Use mano for striving to find the sources of what comes to be, and the ending of what came to be -- of how things arise and how they pass away (and not "see things as they really are", contrary to the worst translation ever, created by a puthujjana craving to cram the word "real").

Now, tHe standard procedure to "understand anatta" is the one to become an arahant -- and the standard procedure to become an arahant is for the citta to have samadhi, and once the citta has stable samadhi, to use sati to focus on anatta through the sequence anicca, dukkha, anatta -- or to just hear the discourse by a Buddha which will be about this sequence anyway.

Since the bikkhus do not know what is anicca, but are already more or less good at getting the citta in samadhi by being good ascetics, they once more rely on a discourse, this time directly from the Buddha, like the second one (Anatta-lakkhana-sutta -- The Not-self Characteristic) where as usual the five aggregates that any human knows and experiences are anatta -- so no need to go deep looking for anatta.

Now atta is only a word, so what experience is there behind this word? Well as usual the answer is given, and it is:

This is mine, this is I, this is my self

... and what does this apply to? The 5 aggregates -- which is the sakya-ditthi (i.e. the view that the aggregates are self) and the only ditthi (view) that you must care about and reject, once you want to stop dukkha --- which of course has nothing do with eternalism or annihilism, and the fantasy of some puthujjanas that the dhamma is some middle way between the two, because those people love to (very dubiously) tack their favorite words like "existence", "real", "self" on their experience and these words are even more meaningless when they are used to talk about the Buddha.

The (non-ascetic) lay people who stop being puthujjanas do so by listening to the Buddha, and they become stream-enterers. After that the remaining work no longer concerns views. Instead the remaining task is to destroy various lusts, and the energy spent fueling those lusts. A puthujjana is done with views as as soon as the puthujjana become a sotapana.