user-1: Buddhist writers, such as Joseph Goldstein and Thupten Jinpa, say that although the self is not intrinsically real, that we still accept the "conventional" idea of self. For example:

If we arrive at the knowledge that the self at which we grasp is empty, we may imagine this means that we as individuals with personal identities do not exist.
  But of course this is not the case--our own personal experiences demonstrate that we as subjects and agents of our own lives, we certainly exist.
  So how then do we understand the content of this insight into absence of Self?
  What follows from this insight?
  We must be very clear that only the self that is being grasped as
  intrinsically real needs to be negated. The self as a conventional
  phenomenon is not rejected.
  This is a crucial aspect of the Buddha's teaching on emptiness.
  Without understanding this distinction, one cannot fully understand the meaning of no-self.

If we believe anatta, then how, specifically, can the "conventional" self be accepted? Do they mean we only pretend that the illusion of self is real in order to talk to people in everday language? Or is there some part of the concept of self that even Buddhism cannot reject? 

user6994: Geshe Thubten Jinpa is a Gelug-pa, and a translator of H.H. the Dalaï-Lama. His view is that of Madhyamika Prasangika as presented by lama Je Tsongkhapa. In this tradition, we hold that Buddhapalita, Candrakirti, Aryadeva and Shantideva are Madhyamika-Prasangika. I will answer from this viewpoint.
Whatever is an existant (1) does not exist ultimately but (2) exists conventionally. This includes conventional and ultimate truths: even emptiness exists conventionally. 
The issue here is that 'self' has two meanings:

It refers to persons, and persons exist. Persons are objects of conventional valid cognizers. A valid eye-consciousness sees a person... a valid tactile consciousness touches a person, etc.
It refers to inherent existence, a mode of existence that is utterly non-existent. Persons and phenomena are empty of possessing such a self... they do not exist by way of their own characteristics... they are not established from their own side... they are not truly existent... they are not real...  they do not exist inherently. From a Prasangika viewpoint, all these are synonymous.

Self, in the sense of the person, do exist conventionally. Self, in the sense of inherent existence, is utterly non-existent. To put it another way: the person is an object apprehended by a valid cognizer while inherent existence is perceived by a cognizer that is not valid... a cognizer that is a wrong consciousness. The wrong consciousness apprehending inherent existence is called ignorance. This ignorance is the first of the 12 links of dependent-arising and it is the root of samsara.
The ignorance that is the conception of self of the person apprehends the self (in the sense of the person) as possessing a self (in the sense of being inherently existent). From a Prasangika viewpoint, the eye-consciousness in the continuum of an ordinary being apprehending a person is (1) valid with regard to the entity of the thing (i.e. apprehending a person as a person) but (2) is wrong with regard to the mode of existence of the thing (i.e. apprehending the person to exist inherently).

user254: I'm not confident I can predict what the Dalai Lama was trying to say (and I haven't read the book you referenced), but here are some examples of what "this distinction" means to me.
Vices and virtues
The Zen story "Nothing Exists"

Yamaoka Tesshu, as a young student of Zen, visited one master after another. He called upon Dokuon of Shokoku.
Desiring to show his attainment, he said: "The mind, Buddha, and sentient beings, after all, do not exist. The true nature of phenomena is emptiness. There is no realization, no delusion, no sage, no mediocrity. There is no giving and nothing to be received."
Dokuon, who was smoking quietly, said nothing. Suddenly he whacked Yamaoka with his bamboo pipe. This made the youth quite angry.
"If nothing exists," inquired Dokuon, "where did this anger come from?"

... implies that the self, the sense of self, conceit, identification (with form but also self-importance), is manifested as or associated with defilements and obstacles, fetters (for example, anger).
I guess this is what people mean when they talk about "the ego", being "egocentric", "selfish", etc.
The story may be, also, a reminder of social conventions: be polite (not boastful), don't attack people (be gentle), be skillful (appropriate interaction with the right person at the right time), etc.
I think that uprooting "defilements" is one the main aims of Buddhism, isn't that so?
Still, if there are bad deeds and afflictive emotions, there's also skillful virtue -- including generosity, for example, being a good friend, even avoiding bad friends -- which may lead to the next topic.
Social roles
If you look at the five skandhas, you can't (or shouldn't) look at them and say "that's me, that's mine, that's permanent" -- a body for example, or any single/specific thought, is more-or-less transient, impermanent. You might say, "That's me", but maybe you won't want to: because clinging to impermanent things like that is (or would be) a cause of suffering.
Socially though, in society, people exist -- with names and so on. As well as the five skandhas, there are also (or one might say, "people also have") names and relationships, duties, jobs, families, skills, assets (like a house or money), etc. These too are temporary, severable -- and may be dissatisfactory, a cause of suffering if you cling to them or identify with them.
Even so, society, human life, couldn't exist with them -- without parents, for example, or without children, and so on. One of the definitions of "wrong view", in the suttas, goes,

"And how is right view the forerunner? One discerns wrong view as wrong view, and right view as right view. This is one's right view. And what is wrong view?

'There is nothing given, nothing offered, nothing sacrificed. There is no fruit or result of good or bad actions. There is no this world, no next world, no mother, no father, no spontaneously reborn beings; no brahmans or contemplatives who, faring rightly & practicing rightly, proclaim this world & the next after having directly known & realized it for themselves.'


I think that this is an important part of the conventional self -- it's relative -- there's a "this world" because there is (or was) "another world", there's a "next world" because there's a "this world", there's a "mother" and "father" because there's a "child", etc.
"Relative" also implies "conditioned" -- A exists because B exists, A and B are related, A is conditioned by B -- and anything conditioned is impermanent (A ceases or changes when B ceases).
Although these relations exist, they're impermanent (so shouldn't be taken to be a permanent self), yet they exist (to deny they exist would be wrong view).
Salvation
We're told to consider that,

‘I must be parted and separated from all I hold dear and beloved.’ …
I am the owner of my deeds and heir to my deeds. Deeds are my womb, my relative, and my refuge.
I shall be the heir of whatever deeds I do, whether good or bad.’

... where "deeds" is kamma in the above.
So perhaps "I am" (the owner) and "I have" (the fruit or result of good and bad actions), until I am able to "end kamma".
The Dhammapada says,

You yourselves should make the effort; the Tathagatas (Buddhas) only can show the way.

I guess this might be the kind of message which the Dalai Lama had in mind, when he was quoted as saying, "our own personal experiences demonstrate that we as subjects and agents of our own lives, we certainly exist".
Speaking of "refuge", I think the "island" passage from the Maha-parinibbana Sutta implies some agency or responsibility:

Therefore, Ananda, be islands unto yourselves, refuges unto yourselves, seeking no external refuge; with the Dhamma as your island, the Dhamma as your refuge, seeking no other refuge.

I think of that as a defining characteristic of Buddhism, perhaps unlike some other religions where worshippers might expect another agent (God) to be an instrument or agent of their salvation.
I think that other schools of Buddhism (e.g. Tibetan) might have slightly different doctrines, though, so, again, this is just how I understand the "distinction", based on the suttas (not the Heart Sutra nor the Dalai Lama's teachings, especially "a crucial aspect of the Buddha's teaching on emptiness").

By the way, even though this appears to emphasise "you" (or "self") as agent, it's also possible to describe the process (of following and/or not following the way, the dhamma) using a non-self kind of metaphor: as important as the conventional self is, it doesn't or needn't override a non-self view.
If you'll forgive my introducing it, here is one of the parables of Jesus (note Christian, not Buddhist):

"Listen! A farmer went out to plant some seeds. As he scattered them across his field, some seeds fell on a footpath, and the birds came and ate them. Other seeds fell on shallow soil with underlying rock. The seeds sprouted quickly because the soil was shallow. But the plants soon wilted under the hot sun, and since they didn’t have deep roots, they died. Other seeds fell among thorns that grew up and choked out the tender plants. Still other seeds fell on fertile soil, and they produced a crop that was thirty, sixty, and even a hundred times as much as had been planted! Anyone with ears to hear should listen and understand."

The parable/metaphor there is:

Farmer "scattering seeds" = "giving dhamma talks"
"Unfertile ground" = "some people hear the talk but the dhamma doesn't take root"
"Fertile ground" = "some people hear the talk, and practice appropriately as well as spread the word"

Further to that metaphor you could argue that (notwithstanding what I said above about being the owner of or heir to the fruit of kamma) there is still no self and maybe even no "free-will" -- there's just ground, fertile or unfertile.
Curiously the last sentence of that quote ("Anyone with ears to hear should listen and understand") is rather similar to the Buddha's "beings with little dust in their eyes":

Open are the doors to the Deathless
to those with ears.


user13375: This question is answered in Insight into Emptiness where an analogy is given that was helpful to my mind. The following is my paraphrase from the example given by this book.
The President of the United States is a self that exists conventionally, but is not the slightest bit intrinsically real.
This is a label that we designate on the basis of an individual person using human rules and customs. In order to use this label correctly it is necessary to have a valid basis of designation that everyone agrees upon. There is a specific context in which this labeling is valid. Outside of this context - the community of humans and our associated traditions - this label is meaningless. It is only within the context of human speech and human political/cultural traditions that this label has any meaning. 
It is an agreed upon label by convention according to definite rules and customs. For instance, if I went around declaring myself to be "President of the United States" and then tried to assume some power of the President it would not work. So it is clear that just because something exists by convention does not mean that it does not exist at all. Nor does it mean that we can just magically label anything whatever we want.
In what way can the President of the United States be said to exist? When we say that the President of the United States is not intrinsically real, what do we mean? There is no permanent independent thing that is universally understood by all inhabitants of the universe that is "President of the United States" by means of its own inherent power. It exists only by convention and depending upon human rules and conditions.  
Like this, all phenomena are said to exist conventionally without even the slightest bit of intrinsic reality. This goes for persons as well as generalized phenomena.

user111: The usage of the word 'self' in a conventional sense is the same as the usage of the word 'chair'. There's nothing intrinsic in the material it is made of that makes a chair a chair. But the usage of concepts are useful in day to day life for the purpose of identifying functions.

-1: <p>Buddhist writers, such as Joseph Goldstein and Thupten Jinpa, say that although the self is not intrinsically real, that we still accept the "conventional" idea of self. <a href="https://rads.stackoverflow.com/amzn/click/B003VYBP2O" rel="nofollow noreferrer">For example</a>:</p>

<blockquote>
  <p>If we arrive at the knowledge that the self at which we grasp is empty, we may imagine this means that we as individuals with personal identities do not exist.
  But of course this is not the case--our own personal experiences demonstrate that we as subjects and agents of our own lives, we certainly exist.
  So how then do we understand the content of this insight into absence of Self?
  What follows from this insight?
  We must be very clear that <em>only the self that is being grasped as
  intrinsically real</em> needs to be negated. The self as a conventional
  phenomenon is not rejected.
  This is a crucial aspect of the Buddha's teaching on emptiness.
  Without understanding this distinction, one cannot fully understand the meaning of no-self.</p>
</blockquote>

<p>If we believe anatta, then how, specifically, can the "conventional" self be accepted? Do they mean we only pretend that the illusion of self is real in order to talk to people in everday language? Or is there some part of the concept of self that even Buddhism cannot reject? </p>
 6994: <p>Geshe Thubten Jinpa is a Gelug-pa, and a translator of H.H. the Dalaï-Lama. His view is that of Madhyamika Prasangika as presented by lama Je Tsongkhapa. In this tradition, we hold that Buddhapalita, Candrakirti, Aryadeva and Shantideva are Madhyamika-Prasangika. I will answer from this viewpoint.</p>

<p>Whatever is an existant (1) does not exist ultimately but (2) exists conventionally. This includes conventional and ultimate truths: even emptiness exists conventionally. </p>

<p>The issue here is that 'self' has two meanings:</p>

<ol>
<li>It refers to <strong>persons</strong>, and persons exist. Persons are objects of conventional valid cognizers. A valid eye-consciousness sees a person... a valid tactile consciousness touches a person, etc.</li>
<li>It refers to <strong>inherent existence</strong>, a mode of existence that is utterly non-existent. Persons and phenomena are empty of possessing such a self... they do not exist by way of their own characteristics... they are not established from their own side... they are not truly existent... they are not real...  they do not exist inherently. From a Prasangika viewpoint, all these are synonymous.</li>
</ol>

<p>Self, in the sense of the person, do exist conventionally. Self, in the sense of inherent existence, is utterly non-existent. To put it another way: the person is an object apprehended by a <strong>valid</strong> cognizer while inherent existence is perceived by a cognizer that is not valid... a cognizer that is a wrong consciousness. The wrong consciousness apprehending inherent existence is called ignorance. This ignorance is the first of the 12 links of dependent-arising and it is the root of samsara.</p>

<p>The ignorance that is the conception of self of the person apprehends the self (in the sense of the person) as possessing a self (in the sense of being inherently existent). From a Prasangika viewpoint, the eye-consciousness in the continuum of an ordinary being apprehending a person is (1) valid with regard to the entity of the thing (i.e. apprehending a person as a person) but (2) is wrong with regard to the mode of existence of the thing (i.e. apprehending the person to exist inherently).</p>
 254: <p>I'm not confident I can predict what the Dalai Lama was trying to say (and I haven't read the book you referenced), but here are some examples of what &quot;this distinction&quot; means to me.</p>
<p><strong>Vices and virtues</strong></p>
<p>The Zen story &quot;<a href="https://www.google.fr/search?q=zen+nothing+exists" rel="nofollow noreferrer">Nothing Exists</a>&quot;</p>
<blockquote>
<p>Yamaoka Tesshu, as a young student of Zen, visited one master after another. He called upon Dokuon of Shokoku.</p>
<p>Desiring to show his attainment, he said: &quot;The mind, Buddha, and sentient beings, after all, do not exist. The true nature of phenomena is emptiness. There is no realization, no delusion, no sage, no mediocrity. There is no giving and nothing to be received.&quot;</p>
<p>Dokuon, who was smoking quietly, said nothing. Suddenly he whacked Yamaoka with his bamboo pipe. This made the youth quite angry.</p>
<p>&quot;If nothing exists,&quot; inquired Dokuon, &quot;where did this anger come from?&quot;</p>
</blockquote>
<p>... implies that the self, the sense of self, <a href="https://buddhism.stackexchange.com/q/9415/254">conceit</a>, identification (with form but also self-importance), is manifested as or associated with <a href="https://en.wikipedia.org/wiki/Kleshas_(Buddhism)" rel="nofollow noreferrer">defilements</a> and <a href="https://suttacentral.net/an6.86/en/sujato" rel="nofollow noreferrer">obstacles</a>, <a href="https://en.wikipedia.org/wiki/Fetter_(Buddhism)" rel="nofollow noreferrer">fetters</a> (for example, anger).</p>
<p>I guess this is what people mean when they talk about &quot;the ego&quot;, being &quot;egocentric&quot;, &quot;selfish&quot;, etc.</p>
<p>The story may be, also, a reminder of social conventions: be polite (not boastful), don't attack people (be gentle), be skillful (appropriate interaction with the right person at the right time), etc.</p>
<p>I think that uprooting &quot;defilements&quot; is one the main aims of Buddhism, isn't that so?</p>
<p>Still, if there are bad deeds and afflictive emotions, there's also skillful virtue -- including generosity, for example, being a good friend, even avoiding bad friends -- which may lead to the next topic.</p>
<p><strong>Social roles</strong></p>
<p>If you look at the five skandhas, you can't (or shouldn't) look at them and say &quot;that's me, that's mine, that's permanent&quot; -- a body for example, or any single/specific thought, is more-or-less transient, impermanent. You <em>might</em> say, &quot;That's me&quot;, but maybe you won't <em>want</em> to: because <em>clinging</em> to impermanent things like that is (or would be) a cause of suffering.</p>
<p>Socially though, in society, people exist -- with names and so on. As well as the five skandhas, there are also (or one might say, &quot;people also <em>have</em>&quot;) names and relationships, duties, jobs, families, skills, assets (like a house or money), etc. These too are temporary, severable -- and may be dissatisfactory, a cause of suffering if you cling to them or identify with them.</p>
<p>Even so, society, human life, couldn't exist with them -- without parents, for example, or without children, and so on. One of the definitions of &quot;wrong view&quot;, in the suttas, goes,</p>
<blockquote>
<p>&quot;And how is right view the forerunner? One discerns wrong view as wrong view, and right view as right view. This is one's right view. And what is wrong view?</p>
<blockquote>
<p>'There is nothing given, nothing offered, nothing sacrificed. There is no fruit or result of good or bad actions. There is no this world, no next world, no mother, no father, no spontaneously reborn beings; no brahmans or contemplatives who, faring rightly &amp; practicing rightly, proclaim this world &amp; the next after having directly known &amp; realized it for themselves.'</p>
</blockquote>
</blockquote>
<p>I think that this is an important part of the conventional self -- it's relative -- there's a &quot;this world&quot; because there is (or was) &quot;another world&quot;, there's a &quot;next world&quot; because there's a &quot;this world&quot;, there's a &quot;mother&quot; and &quot;father&quot; because there's a &quot;child&quot;, etc.</p>
<p>&quot;Relative&quot; also implies &quot;conditioned&quot; -- A exists because B exists, A and B are related, A is conditioned by B -- and anything conditioned is impermanent (A ceases or changes when B ceases).</p>
<p>Although these relations exist, they're impermanent (so shouldn't be taken to be a permanent self), yet they exist (to deny they exist would be wrong view).</p>
<p><strong>Salvation</strong></p>
<p><a href="https://www.accesstoinsight.org/tipitaka/an/an05/an05.057.than.html" rel="nofollow noreferrer">We're told</a> to consider that,</p>
<blockquote>
<p>‘I must be parted and separated from all I hold dear and beloved.’ …</p>
<p>I am the owner of my deeds and heir to my deeds. Deeds are my womb, my relative, and my refuge.</p>
<p>I shall be the heir of whatever deeds I do, whether good or bad.’</p>
</blockquote>
<p>... where &quot;deeds&quot; is <em>kamma</em> in the above.</p>
<p>So perhaps &quot;I am&quot; (the owner) and &quot;I have&quot; (the fruit or result of good and bad actions), until I am able to &quot;<a href="https://www.accesstoinsight.org/lib/authors/thanissaro/wings/part1.html#part1-b" rel="nofollow noreferrer">end kamma</a>&quot;.</p>
<p>The <a href="http://www.tipitaka.net/tipitaka/dhp/verseload.php?verse=273" rel="nofollow noreferrer">Dhammapada says</a>,</p>
<blockquote>
<p>You yourselves should make the effort; the Tathagatas (Buddhas) only can show the way.</p>
</blockquote>
<p>I guess this might be the kind of message which the Dalai Lama had in mind, when he was quoted as saying, &quot;our own personal experiences demonstrate that we as subjects and agents of our own lives, we certainly exist&quot;.</p>
<p>Speaking of &quot;refuge&quot;, I think the &quot;island&quot; passage from the <a href="https://www.accesstoinsight.org/tipitaka/dn/dn.16.1-6.vaji.html" rel="nofollow noreferrer">Maha-parinibbana Sutta</a> implies some agency or responsibility:</p>
<blockquote>
<p>Therefore, Ananda, be islands unto yourselves, refuges unto yourselves, seeking no external refuge; with the Dhamma as your island, the Dhamma as your refuge, seeking no other refuge.</p>
</blockquote>
<p>I think of that as a defining characteristic of Buddhism, perhaps unlike some other religions where worshippers might expect another agent (God) to be an instrument or agent of their salvation.</p>
<p>I think that other schools of Buddhism (e.g. Tibetan) might have slightly different doctrines, though, so, again, this is just how I understand the &quot;distinction&quot;, based on the suttas (not the Heart Sutra nor the Dalai Lama's teachings, especially &quot;a crucial aspect of the Buddha's teaching on emptiness&quot;).</p>
<hr />
<p>By the way, even though this appears to emphasise &quot;you&quot; (or &quot;self&quot;) as agent, it's also possible to describe the process (of following and/or not following the way, the dhamma) using a non-self kind of metaphor: as important as the conventional self is, it doesn't or needn't override a non-self view.</p>
<p>If you'll forgive my introducing it, here is <a href="https://www.biblegateway.com/passage/?search=Matthew+13&amp;version=NLT" rel="nofollow noreferrer">one of the parables of Jesus</a> (note Christian, not Buddhist):</p>
<blockquote>
<p>&quot;Listen! A farmer went out to plant some seeds. As he scattered them across his field, some seeds fell on a footpath, and the birds came and ate them. Other seeds fell on shallow soil with underlying rock. The seeds sprouted quickly because the soil was shallow. But the plants soon wilted under the hot sun, and since they didn’t have deep roots, they died. Other seeds fell among thorns that grew up and choked out the tender plants. Still other seeds fell on fertile soil, and they produced a crop that was thirty, sixty, and even a hundred times as much as had been planted! Anyone with ears to hear should listen and understand.&quot;</p>
</blockquote>
<p>The parable/metaphor there is:</p>
<ul>
<li>Farmer &quot;scattering seeds&quot; = &quot;giving dhamma talks&quot;</li>
<li>&quot;Unfertile ground&quot; = &quot;some people hear the talk but the dhamma doesn't take root&quot;</li>
<li>&quot;Fertile ground&quot; = &quot;some people hear the talk, and practice appropriately as well as spread the word&quot;</li>
</ul>
<p>Further to that metaphor you could argue that (notwithstanding what I said above about being the owner of or heir to the fruit of kamma) there is still no self and maybe even no &quot;<a href="/questions/tagged/free-will" class="post-tag" title="show questions tagged &#39;free-will&#39;" rel="tag">free-will</a>&quot; -- there's just ground, fertile or unfertile.</p>
<p>Curiously the last sentence of that quote (&quot;Anyone with ears to hear should listen and understand&quot;) is rather similar to the Buddha's &quot;<a href="https://www.accesstoinsight.org/tipitaka/sn/sn06/sn06.001.than.html" rel="nofollow noreferrer">beings with little dust in their eyes</a>&quot;:</p>
<blockquote>
<p>Open are the doors to the Deathless<br />
to those with ears.</p>
</blockquote>
 13375: <p>This question is answered in <a href="https://rads.stackoverflow.com/amzn/click/B008YFZBCK" rel="nofollow noreferrer">Insight into Emptiness</a> where an analogy is given that was helpful to my mind. The following is my paraphrase from the example given by this book.</p>

<p><em>The President of the United States</em> is a self that exists conventionally, but is not the slightest bit intrinsically real.</p>

<p>This is a label that we designate on the basis of an individual person using human rules and customs. In order to use this label correctly it is necessary to have a valid basis of designation that everyone agrees upon. There is a specific context in which this labeling is valid. Outside of this context - the community of humans and our associated traditions - this label is meaningless. It is only within the context of human speech and human political/cultural traditions that this label has any meaning. </p>

<p>It is an <em>agreed upon</em> label by <em>convention</em> according to definite rules and customs. For instance, if I went around declaring myself to be "President of the United States" and then tried to assume some power of the President it would not work. So it is clear that just because something exists by convention does not mean that it does not exist at all. Nor does it mean that we can just magically label anything whatever we want.</p>

<p>In what way can the President of the United States be said to exist? When we say that the President of the United States is not intrinsically real, what do we mean? There is no permanent independent thing that is universally understood by all inhabitants of the universe that is "President of the United States" by means of its own inherent power. It exists only by convention and depending upon human rules and conditions.  </p>

<p>Like this, all phenomena are said to exist conventionally without even the slightest bit of intrinsic reality. This goes for persons as well as generalized phenomena.</p>
 111: <p>The usage of the word 'self' in a conventional sense is the same as the usage of the word 'chair'. There's nothing intrinsic in the material it is made of that makes a chair a chair. But the usage of concepts are useful in day to day life for the purpose of identifying functions.</p>
