user151: Did the Buddha teach that a self or soul (whether permanent and fixed or impermanent and changing) cannot be found, did he teach that it cannot exist, or what? 

user10084: In Sravakayana Sutras he stated that any dependently originated phenomenon are not self and in Mahayana Sutras he makes it clear that the Tathagatagharba and Nirvana hold the qualities of Permanence, Bliss, Self and Purity.

user8157: SN 35.85 states the world is completely void/empty (sunnata) of self or anything belonging to self. 
SN 5.10 and SN 12.15 state there is no temporary conditioned 'self' because, in reality, what is regarded as a temporary delusion or view of 'self' is really only 'suffering'. 

Why now do you assume 'a being'? Mara, have you grasped a view? This is a heap of sheer constructions: Here no being is found.
Just as, with an assemblage of parts, The word 'chariot' is used, So, when the aggregates are present, There's the convention 'a being.'
It's only suffering that comes to be, Suffering that stands and falls away. Nothing but suffering comes to be, Nothing but suffering
  ceases.
SN 5.10

~~

By & large, Kaccayana, this world is in bondage to attachments, clingings & biases. But one such as this does not get involved with or
  cling to these attachments, clingings, fixations of awareness, biases
  or obsessions; nor is he resolved on 'my self.' He has no uncertainty
  or doubt that only stress, when arising, is arising; only stress, when
  passing away, is passing away. SN 12.15


user-1: In the Pali canon, it seems there is no categorical denial of a permanent self by the Buddha.
The most common texts about the not-self (anatta) doctrine are taught in the form " [something] is not self", where [something] is a phenomenon that is cognized: forms, feelings, thoughts, perceptions, etc. For example:

“Feeling is impermanent…. Perception is impermanent…. Volitional formations are impermanent…. Consciousness is impermanent. What is impermanent is suffering. What is suffering is nonself. What is nonself should be seen as it really is with correct wisdom thus: ‘This is not mine, this I am not, this is not my self.’
-- SN 22.45

A generalization of this teaching is found in AN 3.136:

sabbe dhammā anattā'ti
  all phenomena are non-self (Bodhi translation)

Where "phenomena" (dhammā) stands as a constituent of experience,  something or anything that can be experienced.
Now, the Buddha has been asked point blank if there's a self, but he refused to answer:

Then the wanderer Vacchagotta went to the Blessed One and, on arrival, exchanged courteous greetings with him. After an exchange of friendly greetings & courtesies, he sat to one side. As he was sitting there he asked the Blessed One: "Now then, Venerable Gotama, is there a self?"
When this was said, the Blessed One was silent.
"Then is there no self?"
A second time, the Blessed One was silent.
Then Vacchagotta the wanderer got up from his seat and left.
-- SN 44.10

He then proceeds to explain why he did not answer (another explanation is given in SN 44.7):

"Ananda, if I — being asked by Vacchagotta the wanderer if there is a self — were to answer that there is a self, that would be conforming with those brahmans & contemplatives who are exponents of eternalism [the view that there is an eternal, unchanging soul]. If I — being asked by Vacchagotta the wanderer if there is no self — were to answer that there is no self, that would be conforming with those brahmans & contemplatives who are exponents of annihilationism [the view that death is the annihilation of consciousness]. If I — being asked by Vacchagotta the wanderer if there is a self — were to answer that there is a self, would that be in keeping with the arising of knowledge that all phenomena are not-self?"  
— "No, lord."  
"And if I — being asked by Vacchagotta the wanderer if there is no self — were to answer that there is no self, the bewildered Vacchagotta would become even more bewildered: 'Does the self I used to have now not exist?'"

Some people take that Vacchagotta episode, plus the lack of any categorical denial and a few other texts and try to create evidence that the Buddha actually taught a permanent self doctrine. But all of them are considered  attempts of fitting a square into a circle hole -- usually they are not very convincing.
It's quite reasonable that If there was a permanent self that could be grasped, all the Buddha had to do was declare it and teach it. It would be much easier to understand then his doctrine of dependent origination and he wouldn't have to answer puzzling questions like "if there's no self, what reborns?".
To the best of my knowledge, the closest refutation for a doctrine of permanent self in the pali canon is the following sutta:

"Bhikkhus, you may well cling to that doctrine of self that would not arouse sorrow, lamentation, pain, grief, and despair in one who clings to it. But do you see any such doctrine of self, bhikkhus?"
  —"No, venerable sir."
  —"Good, bhikkhus. I too do not see any doctrine of self that would not arouse sorrow, lamentation, pain, grief, and despair in one who clings to it."
-- MN 22

If this teaching holds true, then the only possibility for a permanent soul to exist is if it exists outside the reach of experience, outside the possibility of contact.
But if we can't reach it to assess if it exist or not, if we cannot come into contact with it, then either it doesn't exist, or it exists but doesn't seem to have any effect in our existence -- since it's completely isolated from our experience. Thus, even if no phenomenon is our permanent self, but such a self still exists somewhere else, certainly it is irrelevant for our life, and believing or not seems to do little to help in the path towards nirvana -- after all, that permanent soul does not affect us in anyway.

user43: Buddha did not teach that things exist (that's one extreme) or that things do not exist (that's another extreme). Buddha teaches that things exist to some extent, in some context, relative to some frame of reference – and do not exist in other contexts. It's the same with the "self".

151: <p>Did the Buddha teach that a self or soul (whether permanent and fixed or impermanent and changing) cannot be found, did he teach that it cannot exist, or what? </p>
 10084: <p>In Sravakayana Sutras he stated that any dependently originated phenomenon are not self and in Mahayana Sutras he makes it clear that the Tathagatagharba and Nirvana hold the qualities of Permanence, Bliss, Self and Purity.</p>
 8157: <p>SN 35.85 states the world is completely void/empty (<em>sunnata</em>) of self or anything belonging to self. </p>

<p>SN 5.10 and SN 12.15 state there is no temporary conditioned 'self' because, in reality, what is regarded as a temporary delusion or view of 'self' is really <em>only</em> 'suffering'. </p>

<blockquote>
  <p><em>Why now do you assume 'a being'? Mara, have you grasped a view? This is a heap of sheer constructions: Here no being is found.</em></p>
  
  <p><em>Just as, with an assemblage of parts, The word 'chariot' is used, So, when the aggregates are present, There's the convention 'a being.'</em></p>
  
  <p><em>It's <strong>only</strong> suffering that comes to be, Suffering that stands and falls away. <strong>Nothing but</strong> suffering comes to be, Nothing but suffering
  ceases.</em></p>
  
  <p><em>SN 5.10</em></p>
</blockquote>

<p>~~</p>

<blockquote>
  <p><em>By &amp; large, Kaccayana, this world is in bondage to attachments, clingings &amp; biases. But one such as this does not get involved with or
  cling to these attachments, clingings, fixations of awareness, biases
  or obsessions; nor is he resolved on 'my self.' He has no uncertainty
  or doubt that <strong>only</strong> stress, when arising, is arising; <strong>only</strong> stress, when
  passing away, is passing away. SN 12.15</em></p>
</blockquote>
 -1: <p>In the Pali canon, it seems there is no categorical denial of a permanent self by the Buddha.</p>

<p>The most common texts about the not-self (<em>anatta</em>) doctrine are taught in the form " <code>[something]</code> is not self", where <code>[something]</code> is a phenomenon that is cognized: forms, feelings, thoughts, perceptions, etc. For example:</p>

<blockquote>
  <p>“Feeling is impermanent…. Perception is impermanent…. Volitional formations are impermanent…. Consciousness is impermanent. What is impermanent is suffering. What is suffering is nonself. What is nonself should be seen as it really is with correct wisdom thus: ‘This is not mine, this I am not, this is not my self.’</p>
  
  <p>-- <a href="https://suttacentral.net/en/sn22.45" rel="nofollow noreferrer">SN 22.45</a></p>
</blockquote>

<p>A generalization of this teaching is found in AN 3.136:</p>

<blockquote>
  <p><em>sabbe dhammā anattā'ti</em><br>
  all phenomena are non-self (Bodhi translation)</p>
</blockquote>

<p>Where "phenomena" (<em>dhammā</em>) stands as a constituent of experience,  something or anything that can be experienced.</p>

<p>Now, the Buddha has been asked point blank if there's a self, but he refused to answer:</p>

<blockquote>
  <p>Then the wanderer Vacchagotta went to the Blessed One and, on arrival, exchanged courteous greetings with him. After an exchange of friendly greetings &amp; courtesies, he sat to one side. As he was sitting there he asked the Blessed One: "Now then, Venerable Gotama, is there a self?"</p>
  
  <p>When this was said, the Blessed One was silent.</p>
  
  <p>"Then is there no self?"</p>
  
  <p>A second time, the Blessed One was silent.</p>
  
  <p>Then Vacchagotta the wanderer got up from his seat and left.</p>
  
  <p>-- <a href="http://www.accesstoinsight.org/tipitaka/sn/sn44/sn44.010.than.html" rel="nofollow noreferrer">SN 44.10</a></p>
</blockquote>

<p>He then proceeds to explain why he did not answer (another explanation is given in SN 44.7):</p>

<blockquote>
  <p>"Ananda, if I — being asked by Vacchagotta the wanderer if there is a self — were to answer that there is a self, that would be conforming with those brahmans &amp; contemplatives who are exponents of eternalism [the view that there is an eternal, unchanging soul]. If I — being asked by Vacchagotta the wanderer if there is no self — were to answer that there is no self, that would be conforming with those brahmans &amp; contemplatives who are exponents of annihilationism [the view that death is the annihilation of consciousness]. If I — being asked by Vacchagotta the wanderer if there is a self — were to answer that there is a self, would that be in keeping with the arising of knowledge that all phenomena are not-self?"  </p>
  
  <p>— "No, lord."  </p>
  
  <p>"And if I — being asked by Vacchagotta the wanderer if there is no self — were to answer that there is no self, the bewildered Vacchagotta would become even more bewildered: 'Does the self I used to have now not exist?'"</p>
</blockquote>

<p>Some people take that Vacchagotta episode, plus the lack of any categorical denial and a few other texts and try to create evidence that the Buddha actually taught a permanent self doctrine. But all of them are considered  attempts of fitting a square into a circle hole -- usually they are not very convincing.</p>

<p>It's quite reasonable that If there was a permanent self that could be grasped, all the Buddha had to do was declare it and teach it. It would be much easier to understand then his doctrine of dependent origination and he wouldn't have to answer puzzling questions like "if there's no self, what reborns?".</p>

<p>To the best of my knowledge, the closest refutation for a doctrine of permanent self in the pali canon is the following sutta:</p>

<blockquote>
  <p>"Bhikkhus, you may well cling to that doctrine of self that would not arouse sorrow, lamentation, pain, grief, and despair in one who clings to it. But do you see any such doctrine of self, bhikkhus?"<br>
  —"No, venerable sir."<br>
  —"Good, bhikkhus. I too do not see any doctrine of self that would not arouse sorrow, lamentation, pain, grief, and despair in one who clings to it."</p>
  
  <p>-- <a href="https://suttacentral.net/en/mn22" rel="nofollow noreferrer">MN 22</a></p>
</blockquote>

<p>If this teaching holds true, then the only possibility for a permanent soul to exist is if it exists outside the reach of experience, outside the possibility of contact.</p>

<p>But if we can't reach it to assess if it exist or not, if we cannot come into contact with it, then either it doesn't exist, or it exists but doesn't seem to have any effect in our existence -- since it's completely isolated from our experience. Thus, even if no phenomenon is our permanent self, but such a self still exists somewhere else, certainly it is irrelevant for our life, and believing or not seems to do little to help in the path towards nirvana -- after all, that permanent soul does not affect us in anyway.</p>
 43: <p>Buddha did not teach that things exist (that's one extreme) or that things do not exist (that's another extreme). Buddha teaches that things exist <em>to some extent</em>, <em>in some context</em>, <em>relative to some frame of reference</em> &ndash; and do not exist in other contexts. It's the same with the "self".</p>
