user13375: Counterfactual definiteness is, "is the ability to speak "meaningfully" of the definiteness of the results of measurements that have not been performed."
The classic question to illustrate is, "When a tree falls in a lonely forest, and no animal is near by to hear it, does it make a sound? Why?"
Another classic example is Einstein asking Bohr whether he really believed that, "the moon does not exist if nobody is looking at it?"
What does Buddhism have to say about these questions if anything at all? 
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. However, doesn't this procedure implicitly rely upon the supposition that existing things can be found if one investigates and looks for them? That which can't be observed must not truly exist?
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?

user471: 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 ...


user13972: 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.

13375: <p><a href="https://en.wikipedia.org/wiki/Counterfactual_definiteness" rel="nofollow noreferrer">Counterfactual definiteness</a> is, "is the ability to speak "meaningfully" of the definiteness of the results of measurements that have not been performed."</p>

<p>The classic question to illustrate is, <a href="https://en.wikipedia.org/wiki/If_a_tree_falls_in_a_forest" rel="nofollow noreferrer">"When a tree falls in a lonely forest, and no animal is near by to hear it, does it make a sound? Why?"</a></p>

<p>Another classic example is Einstein asking Bohr whether he really believed that, "the moon does not exist if nobody is looking at it?"</p>

<p>What does Buddhism have to say about these questions if anything at all? </p>

<p>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. However, doesn't this procedure implicitly rely upon the supposition that existing things can be found if one investigates and looks for them? That which can't be observed must not truly exist?</p>

<p>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?</p>
 471: <p><em>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.</em> </p>

<p>Anatta is not-self. It is not no self. From <a href="https://www.accesstoinsight.org/tipitaka/mn/mn.148.than.html" rel="nofollow noreferrer">MN 148</a>:</p>

<blockquote>
  <p>"If anyone were to say, 'The eye is the self,' that wouldn't be
  tenable. The arising &amp; falling away of the eye are discerned. And when
  its arising &amp; falling away are discerned, it would follow that 'My
  self arises &amp; 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 &amp; falling away of craving are
  discerned. And when its arising &amp; falling away are discerned, it would
  follow that 'My self arises &amp; 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.</p>
</blockquote>

<p><em>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?</em></p>

<p>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 <a href="https://www.accesstoinsight.org/tipitaka/mn/mn.038.than.html" rel="nofollow noreferrer">MN 38</a>.</p>

<p>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.</p>

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

<p>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.</p>

<p>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.</p>

<p>This is based on <a href="https://www.accesstoinsight.org/tipitaka/mn/mn.148.than.html" rel="nofollow noreferrer">MN 148</a>:</p>

<blockquote>
  <p>"Dependent on the eye &amp; 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, &amp; 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 &amp; stress in the
  here &amp; now: such a thing is possible.</p>
  
  <p>"Dependent on the ear &amp; sounds...</p>
  
  <p>"Dependent on the nose &amp; aromas...</p>
  
  <p>"Dependent on the tongue &amp; flavors...</p>
  
  <p>"Dependent on the body &amp; tactile sensations...</p>
  
  <p>"Dependent on the intellect &amp; ideas ...</p>
</blockquote>

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

<blockquote>
  <p>"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.'</p>
  
  <p>"One assumes about the ear...</p>
  
  <p>"One assumes about the nose...</p>
  
  <p>"One assumes about the tongue...</p>
  
  <p>"One assumes about the body...</p>
  
  <p>"One assumes about the intellect ...</p>
</blockquote>
 13972: <p><strong>What does Buddhism have to say about these questions if anything at all?</strong></p>

<p>That's easy to answer: the only good use of <em>mano</em> ("mind") for anybody who want to stop dukkha is the <em>yoniso manasikara</em> ("appropriate attention"), which is, in one word, phrasing <em>sati</em> (awareness, mindfulness) and what you do with <em>sati</em>, in terms of <em>mano</em>. This is the first step of the path (after, of course, <strong>hearing</strong> 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.</p>

<p>Also, The standard procedure for understanding <em>anatta</em> 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 <em>puthujjanas</em> (wordlings): the logicians, the daydreamers, the creators of views, the people who love to argue about views.</p>

<p>Use <em>mano</em> only for ascertainment, for attestation, for witnessing, of the source and fall of phenomena, of <em>vedana</em> (feelings), of <em>sanna</em> (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).</p>

<p>Here is what happens when a <em>puthujjana</em> uses <em>mano</em> for something else than <em>yoniso manasikara</em>:</p>

<blockquote>
  <p><a href="https://www.accesstoinsight.org/tipitaka/sn/sn09/sn09.011.than.html" rel="nofollow noreferrer">Ayoniso-manasikara Sutta: Inappropriate Attention (SN 9.11</a>)</p>
  
  <p>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.</p>
  
  <p>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:</p>
  
  <p>From inappropriate attention<br>
  you're being chewed by your thoughts.<br>
  Relinquishing what's inappropriate,<br>
      contemplate<br>
      appropriately.</p>
  
  <p>Keeping your mind on the Teacher,<br>
  the Dhamma, the Sangha, your virtues<br>
  you will arrive at<br>
      joy,<br>
      rapture,<br>
      pleasure<br>
      without doubt.</p>
  
  <p>Then, saturated<br>
      with joy,<br>
  you will put an end<br>
  to suffering &amp; stress.</p>
  
  <p>The monk, chastened by the devata, came to his senses.</p>
</blockquote>

<p>Here is the proper use of <em>mano</em>:</p>

<ul>
<li><a href="https://legacy.suttacentral.net/en/sn12.37" rel="nofollow noreferrer">Natumha Sutta -- Not Yours (SN 12.37)</a></li>
<li><a href="https://legacy.suttacentral.net/en/sn35.87" rel="nofollow noreferrer">Channa Sutta -- With Channa (SN 35.87)</a></li>
</ul>

<p>Use <em>mano</em> 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 <em>puthujjana</em> craving to cram the word "real").</p>

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

<p>Since the bikkhus  do not know what is <em>anicca</em>, but are already more or less good at getting the <em>citta</em> in <em>samadhi</em> by being good ascetics, they once more rely on a discourse, this time directly from the Buddha, like the second one (<a href="https://www.accesstoinsight.org/lib/authors/nanamoli/wheel017.html#s2" rel="nofollow noreferrer">Anatta-lakkhana-sutta -- The Not-self Characteristic</a>) where as usual the five aggregates that any human knows and experiences are <em>anatta</em> -- so no need to go deep looking for <em>anatta</em>.</p>

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

<blockquote>
  <p>This is mine, this is I, this is my self</p>
</blockquote>

<p>... and what does this apply to? The 5 aggregates -- which is the <em>sakya-ditthi</em> (i.e. the view that the aggregates are self) and the only <em>ditthi</em> (view) that you must care about and reject, once you want to stop <em>dukkha</em> --- which of course has nothing do with eternalism or annihilism, and the fantasy of some <em>puthujjanas</em> 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.</p>

<p>The (non-ascetic) lay people who stop being <em>puthujjanas</em> 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 <em>puthujjana</em> is done with views as as soon as the <em>puthujjana</em> become a <em>sotapana</em>.</p>
