user471: From the different answers that I have received on various questions that I've asked, I have come to the following ideas:
According to Mahayana Madhyamaka emptiness (shunyata), all phenomena is empty of intrinsic essence (svabhava), and even this emptiness itself is empty of intrinsic essence. However, this intrinsic essence appears to be the essence given to phenomena by reification or objectification-classification (papanca). So this means that my mental idea of how some phenomena is, is not how it actually is.
Now, Nirvana is not a sankhara (conditioned and/or compounded thing) but it is also empty, in the sense that it is empty of the essence given to it by reification. So this means that my mental idea of how Nirvana is, is not how it actually is.
Even "emptiness is empty" means that my mental idea of how Mahayana emptiness is, is not how it actually is.
This is interesting, because it does not mean that a chair, a dog and Nirvana are mind-independently unreal or non-existent according to Madhyamaka. Rather, the mental idea that I have of a chair, a dog and Nirvana is unreal or non-existent.
Now in Theravada, all suffering is related to clinging. Clinging is always related to the self, as seen in this answer. According to Sutta Nipata 4.14 (below), the root of all reification or objectification-classification (papañca) is "I am the thinker".

Seeing in what way is a monk unbound, clinging to nothing in the world?"
  "He should put an entire stop 
  to the root of objectification-classifications (papañca):
  'I am the thinker.'
Commentary (Thanissaro):
  The perception, "I am the thinker" lies at the root of these 
  classifications in that it reads into the immediate present a set of
  distinctions — I/not-I; being/not-being; thinker/thought;
  identity/non-identity — that then can proliferate into mental and
  physical conflict. The conceit inherent in this perception thus forms
  a fetter on the mind. To become unbound, one must learn to examine
  these distinctions — which we all take for granted — to see that they
  are simply assumptions that are not inherent in experience, and that
  we would be better off to be able to drop them.

Also from MN 1 (below), an arahant who is fully liberated from suffering would see phenomena as they truly are, without reification where his mental idea of phenomena associates it with his self (of persons). This is apparently also known as tathata.

“Bhikkhus, a bhikkhu who is an arahant with taints destroyed, who has
  lived the holy life, done what had to be done, laid down the burden,
  reached his own goal, destroyed the fetters of being, and is
  completely liberated through final knowledge, he too directly knows
  earth as earth. Having directly known earth as earth, he does not
  conceive himself as earth, he does not conceive himself in earth, he
  does not conceive himself apart from earth, he does not conceive earth
  to be ‘mine,’ he does not delight in earth. Why is that? Because he
  has fully understood it, I say.

According to the Suñña Sutta, the five aggregates are empty of a self (of persons), including that they have no association with self (of persons). All reified mental ideas are mental fabrications (sankhara), so they too are empty of a self (of persons).
So, linking the Mahayana Madhyamaka emptiness to the Theravada emptiness, I can say that all phenomena is empty of a mentally reified intrinsic essence, where this reification or objectification-classification is rooted in "I am the thinker". Thanissaro Bhikkhu explains this as "the perception, 'I am the thinker' lies at the root of these classifications in that it reads into the immediate present a set of distinctions — I/not-I; being/not-being; thinker/thought; identity/non-identity — that then can proliferate into mental and physical conflict." I take it here that "I am the thinker" creates a duality between self (of persons) and non-self (of persons) that creates mental and physical conflict.
So, since Mahayana emptiness says that all phenomena is empty of mentally reified essence, and since all reification is rooted in a self (of persons), and Theravada emptiness states that all phenomena is empty of a self (of persons), then these two definitions of emptiness could be logically linked in this way.
Furthermore, the enlightened one who sees the Theravada emptiness of all phenomena through wisdom, will also simultaneously see the Mahayana emptiness of all phenomena, due to having his reification (papanca) ended, due to having his fetters concerning a self (of persons) uprooted. So, the enlightened one sees things as they truly are, which apparently is called tathata.
Both these emptiness seem to be connected together in Bahiya Sutta (Udana 1.10):

"Then, Bāhiya, you should train yourself thus: In reference to the
  seen, there will be only the seen. In reference to the heard, only the
  heard. In reference to the sensed, only the sensed. In reference to
  the cognized, only the cognized. That is how you should train
  yourself. When for you there will be only the seen in reference to the
  seen, only the heard in reference to the heard, only the sensed in
  reference to the sensed, only the cognized in reference to the
  cognized, then, Bāhiya, there is no you in connection with that. When
  there is no you in connection with that, there is no you there. When
  there is no you there, you are neither here nor yonder nor between the
  two. This, just this, is the end of stress."

I believe my description of the Theravada doctrine above is correct, but I am not sure if my description of the Mahayana Madhyamaka doctrine above is correct or not.
So, my questions are:

Is the Mahayana Madhyamaka doctrine described above correct?
Would this linking of Mahayana Madhyamaka emptiness to Theravada emptiness according to the description above make sense to you, as a Mahayana or Theravada Buddhist? Or am I missing something?


user13375: Short answer is you seem very close to what I think, however I might quibble with the way you use words. It is very hard to communicate precisely about the doctrine of emptiness so agreeing upon a definite jargon becomes ever more critical to picking out any actual differences vs just apparent differences. This is why the monks and nuns in Gelug monasteries spend years nailing down the jargon and conventions and mutually agreeing to it. Then they spend many more years debating each other in order to more firmly establish the conceptual understanding of emptiness.
"This is interesting, because it does not mean that a chair, a dog and Nirvana are mind-independently unreal or non-existent according to Madhyamaka. Rather, the mental idea that I have of a chair, a dog and Nirvana is unreal or non-existent."
Purported prasangika perspective... all errors or misunderstandings are my own.
This seems the most problematic part of your question to me. A chair, a dog and Nirvana are indeed existent according to Madhyamaka. However, from the ultimate perspective they are indeed unreal just like a dream or illusion is unreal. They have no true existence whatsoever. They only exist conventionally. It is not like, if you take away all the reification and elaboration that there is some real or truly existing thing that 'dog' or 'chair' or 'Nirvana' points to. Thinking otherwise is itself an example of reification or objectification.
This is very hard for us to understand as we hear the above and think, "My god, if it only exists conventionally without being based on any real thing, then it must not really exist at all!" and then fall into nihilism or annihilationism. Yet, this is how things exist. It is the only possible way for things to exist.
To back all this up have a look at Lama Tsongkhapa in his Great Treatise describing the object of negation:

Question: How does ignorance superimpose intrinsic nature?
Reply: In general, there appear in Candrakırti’s texts many usages of
  verbal conventions such as “nature” or “essence” with regard to
  objects that exist only conventionally. However, here in the case of
  reification by ignorance, there is, with regard to objects, be they
  persons or other phenomena, a conception that those phenomena have
  ontological status—a way of existing—in and of themselves, without
  being posited through the force of an awareness. The referent object
  that is thus apprehended by that ignorant conception, the independent
  ontological status of those phenomena, is identified as a hypothetical
  “self” or “intrinsic nature.” For, Aryadeva’s Four Hundred Stanzas
  says:
All of this is without its own power; Therefore there is no self.

Commenting on this, Candrakırti’s Commentary on the “Four Hundred
  Stanzas” says:
It is that which exists essentially, intrinsically, autonomously, and without depending on another....

Thus, he says that those are synonyms. “Without depending on another”
  does not mean not depending on causes and conditions. Instead, “other”
  refers to a subject, i.e., a conventional consciousness, and something
  is said not to depend on another due to not being posited through the
  force of that conventional consciousness.
Therefore, “autonomously” refers to the nature of an object that has
  its own unique ontological status or manner of being. It is just this
  that is called “essence” or “intrinsic nature.”

He goes on to describe the famous snake and rope allegory and says that all things exist just like the snake in that allegory. That there is nothing on the side of the object (a rope) at all that makes it a snake. In other words, take a snake and a rope... both of them equally lack any intrinsic 'snake' nature. To whatever extent you can find a 'snake' nature in a rope, to that exact same extent you can find a 'snake' nature in a snake -> that is not. at. all. To really put an exclamation point on it: there is nothing on the side of the object that makes a snake a snake as opposed to a rope.
So, linking the Mahayana Madhyamaka emptiness to the Theravada emptiness, I can say that all phenomena is empty of a mentally reified intrinsic essence, where this reification or objectification-classification is rooted in "I am the thinker".
I think it is important to talk more about how this rooting in "I am the thinker" takes place. Here is a theory, but mind you I can't support any of this with authoritative sources.
The thing we reify most is ourselves. For all of our lives in cyclic existence we've identified first and foremost with this "I am the thinker." And on that basis we've carved out a piece and objectified it and thought, "this "I" is separate from everything else in a real and intrinsic way." On the basis of this little island of "I" we then carve up the rest and objectify this and that. Put another way, the "I" is at the center of our conventions. We conceive of everything else in relation to this "I" and on that basis it is the root of our objectification.

user43: Yes, your understanding is correct as far as I see. Specifically the point that splitting the phenomena into "I" (the perceiving subject and pursuing agent) and "the other" (the object of pursuit or aversion) is the ultimate root of papanca and the way the two emptinesses are connected.
This is explicitly explained in an early Mahayana work called Madhyāntavibhāga (aka "Maitreya’s Distinguishing the Middle from the Extremes") that cross-links Mahayana and Early Buddhism concepts. It's a rather difficult read, but Mario D'Amato's translation of Vasubandhu's commentary and his own commentary on that, makes it pretty readable, if one goes slow enough to appreciate the implications. It's also available on the Internet in other translations, e.g. this commentary by Thrangu Rinpoche.  Another work that covers similar topics is Mipham Rinpoche's Beacon of Certainty.
And no, your definition of Emptiness does not disagree with Yogacara, because Madhyāntavibhāga is specifically a Yogacara work. In Madhyāntavibhāga their definition of Emptiness is exactly: "phenomena are empty of a (mentally reified) intrinsic essence". They also have this notion of "false imagination" - which is what they call the idea that "I" and "objects" are two different things.
Overall, I believe your theoretical understanding is pretty complete. The only point you're missing (I think?) is connection between tathata and cessation of suffering. Why exactly suffering does not arise?

471: <p>From the different answers that I have received on various questions that I've asked, I have come to the following ideas:</p>

<p>According to Mahayana Madhyamaka emptiness (shunyata), all phenomena is empty of intrinsic essence (<a href="https://buddhism.stackexchange.com/a/25198/471">svabhava</a>), and even this emptiness itself is empty of intrinsic essence. However, this intrinsic essence appears to be the essence given to phenomena by reification or objectification-classification (<a href="https://buddhism.stackexchange.com/a/26823/471">papanca</a>). So this means that my mental idea of how some phenomena is, is not how it actually is.</p>

<p>Now, Nirvana is not a sankhara (conditioned and/or compounded thing) but it is also empty, in the sense that it is empty of the essence given to it by reification. So this means that my mental idea of how Nirvana is, is not how it actually is.</p>

<p>Even "emptiness is empty" means that my mental idea of how Mahayana emptiness is, is not how it actually is.</p>

<p>This is interesting, because it does not mean that a chair, a dog and Nirvana are mind-independently unreal or non-existent according to Madhyamaka. Rather, the mental idea that I have of a chair, a dog and Nirvana is unreal or non-existent.</p>

<p>Now in Theravada, all suffering is related to clinging. Clinging is always related to the self, as seen in <a href="https://buddhism.stackexchange.com/a/28803/471">this answer</a>. According to <a href="https://www.accesstoinsight.org/tipitaka/kn/snp/snp.4.14.than.html" rel="nofollow noreferrer">Sutta Nipata 4.14</a> (below), the root of all reification or objectification-classification (<a href="https://buddhism.stackexchange.com/a/26823/471">papañca</a>) is "I am the thinker".</p>

<blockquote>
  <p>Seeing in what way is a monk unbound, clinging to nothing in the world?"<br>
  "He should put an entire stop 
  to the root of objectification-classifications (<a href="https://buddhism.stackexchange.com/a/26823/471">papañca</a>):<br>
  'I am the thinker.'</p>
  
  <p><strong>Commentary (Thanissaro):</strong><br>
  The perception, "I am the thinker" lies at the root of these 
  classifications in that it reads into the immediate present a set of
  distinctions — I/not-I; being/not-being; thinker/thought;
  identity/non-identity — that then can proliferate into mental and
  physical conflict. The conceit inherent in this perception thus forms
  a fetter on the mind. To become unbound, one must learn to examine
  these distinctions — which we all take for granted — to see that they
  are simply assumptions that are not inherent in experience, and that
  we would be better off to be able to drop them.</p>
</blockquote>

<p>Also from <a href="https://suttacentral.net/mn1/en/bodhi" rel="nofollow noreferrer">MN 1</a> (below), an arahant who is fully liberated from suffering would see phenomena as they truly are, without reification where his mental idea of phenomena associates it with his self (of persons). This is apparently also known as <a href="https://buddhism.stackexchange.com/a/12735/471">tathata</a>.</p>

<blockquote>
  <p>“Bhikkhus, a bhikkhu who is an arahant with taints destroyed, who has
  lived the holy life, done what had to be done, laid down the burden,
  reached his own goal, destroyed the fetters of being, and is
  completely liberated through final knowledge, he too directly knows
  earth as earth. Having directly known earth as earth, he does not
  conceive himself as earth, he does not conceive himself in earth, he
  does not conceive himself apart from earth, he does not conceive earth
  to be ‘mine,’ he does not delight in earth. Why is that? Because he
  has fully understood it, I say.</p>
</blockquote>

<p>According to the <a href="https://www.accesstoinsight.org/tipitaka/sn/sn35/sn35.085.than.html" rel="nofollow noreferrer">Suñña Sutta</a>, the five aggregates are empty of a self (of persons), including that they have no association with self (of persons). All reified mental ideas are mental fabrications (sankhara), so they too are empty of a self (of persons).</p>

<p>So, linking the Mahayana Madhyamaka emptiness to the Theravada emptiness, I can say that <strong>all phenomena is empty of a mentally reified intrinsic essence, where this reification or objectification-classification is rooted in "I am the thinker"</strong>. Thanissaro Bhikkhu explains this as "<em>the perception, 'I am the thinker' lies at the root of these classifications in that it reads into the immediate present a set of distinctions — I/not-I; being/not-being; thinker/thought; identity/non-identity — that then can proliferate into mental and physical conflict.</em>" I take it here that "I am the thinker" creates a duality between self (of persons) and non-self (of persons) that creates mental and physical conflict.</p>

<p><strong>So, since Mahayana emptiness says that all phenomena is empty of mentally reified essence, and since all reification is rooted in a self (of persons), and Theravada emptiness states that all phenomena is empty of a self (of persons), then these two definitions of emptiness could be logically linked in this way.</strong></p>

<p>Furthermore, the enlightened one who sees the Theravada emptiness of all phenomena through wisdom, will also simultaneously see the Mahayana emptiness of all phenomena, due to having his reification (papanca) ended, due to having his fetters concerning a self (of persons) uprooted. So, the enlightened one sees things as they truly are, which apparently is called <a href="https://buddhism.stackexchange.com/a/12735/471">tathata</a>.</p>

<p>Both these emptiness seem to be connected together in <a href="https://www.accesstoinsight.org/tipitaka/kn/ud/ud.1.10.than.html" rel="nofollow noreferrer">Bahiya Sutta (Udana 1.10)</a>:</p>

<blockquote>
  <p>"Then, Bāhiya, you should train yourself thus: In reference to the
  seen, there will be only the seen. In reference to the heard, only the
  heard. In reference to the sensed, only the sensed. In reference to
  the cognized, only the cognized. That is how you should train
  yourself. When for you there will be only the seen in reference to the
  seen, only the heard in reference to the heard, only the sensed in
  reference to the sensed, only the cognized in reference to the
  cognized, then, Bāhiya, there is no you in connection with that. When
  there is no you in connection with that, there is no you there. When
  there is no you there, you are neither here nor yonder nor between the
  two. This, just this, is the end of stress."</p>
</blockquote>

<p>I believe my description of the Theravada doctrine above is correct, but I am not sure if my description of the Mahayana Madhyamaka doctrine above is correct or not.</p>

<p>So, my questions are:</p>

<ol>
<li><p>Is the Mahayana Madhyamaka doctrine described above correct?</p></li>
<li><p>Would this linking of Mahayana Madhyamaka emptiness to Theravada emptiness according to the description above make sense to you, as a Mahayana or Theravada Buddhist? Or am I missing something?</p></li>
</ol>
 13375: <p>Short answer is you <em>seem</em> very close to what I think, however I might quibble with the way you use words. It is very hard to communicate precisely about the doctrine of emptiness so agreeing upon a definite jargon becomes ever more critical to picking out any <em>actual</em> differences vs just <em>apparent</em> differences. This is why the monks and nuns in Gelug monasteries spend <em>years</em> nailing down the jargon and conventions and mutually agreeing to it. Then they spend many more years debating each other in order to more firmly establish the conceptual understanding of emptiness.</p>

<p><strong>"This is interesting, because it does not mean that a chair, a dog and Nirvana are mind-independently unreal or non-existent according to Madhyamaka. Rather, the mental idea that I have of a chair, a dog and Nirvana is unreal or non-existent."</strong></p>

<p>Purported prasangika perspective... all errors or misunderstandings are my own.</p>

<p>This seems the most problematic part of your question to me. A chair, a dog and Nirvana are indeed existent according to Madhyamaka. However, from the ultimate perspective they are indeed unreal just like a dream or illusion is unreal. They have no <em>true</em> existence whatsoever. They <em>only</em> exist conventionally. It is not like, if you take away all the reification and elaboration that there is some <em>real</em> or <em>truly existing</em> thing that 'dog' or 'chair' or 'Nirvana' points to. Thinking otherwise is itself an example of reification or objectification.</p>

<p>This is very hard for us to understand as we hear the above and think, "My god, if it <em>only</em> exists conventionally without being based on any <em>real</em> thing, then it must not <em>really</em> exist at all!" and then fall into nihilism or annihilationism. Yet, this is how things exist. It is the only possible way for things to exist.</p>

<p>To back all this up have a look at Lama Tsongkhapa in his <em>Great Treatise</em> describing the object of negation:</p>

<blockquote>
  <p>Question: How does ignorance superimpose intrinsic nature?</p>
  
  <p>Reply: In general, there appear in Candrakırti’s texts many usages of
  verbal conventions such as “nature” or “essence” with regard to
  objects that exist only conventionally. However, here in the case of
  reification by ignorance, there is, with regard to objects, be they
  persons or other phenomena, a conception that those phenomena have
  ontological status—a way of existing—in and of themselves, without
  being posited through the force of an awareness. The referent object
  that is thus apprehended by that ignorant conception, the independent
  ontological status of those phenomena, is identified as a hypothetical
  “self” or “intrinsic nature.” For, Aryadeva’s <em>Four Hundred Stanzas</em>
  says:</p>

<pre><code>All of this is without its own power; Therefore there is no self.
</code></pre>
  
  <p>Commenting on this, Candrakırti’s <em>Commentary on the “Four Hundred
  Stanzas”</em> says:</p>

<pre><code>It is that which exists essentially, intrinsically, autonomously, and without depending on another....
</code></pre>
  
  <p>Thus, he says that those are synonyms. “Without depending on another”
  does not mean not depending on causes and conditions. Instead, “other”
  refers to a subject, i.e., a conventional consciousness, and something
  is said not to depend on another due to not being posited through the
  force of that conventional consciousness.</p>
  
  <p>Therefore, “autonomously” refers to the nature of an object that has
  its own unique ontological status or manner of being. It is just this
  that is called “essence” or “intrinsic nature.”</p>
</blockquote>

<p>He goes on to describe the famous snake and rope allegory and says that <em>all things</em> exist just like the snake in that allegory. That there is <em>nothing</em> on the side of the object (a rope) at all that makes it a snake. In other words, take a snake and a rope... both of them <em>equally</em> lack any intrinsic 'snake' nature. To whatever extent you can find a 'snake' nature in a rope, to that exact same extent you can find a 'snake' nature in a snake -> that is not. at. all. To really put an exclamation point on it: there is <em>nothing</em> on the side of the object that makes a snake a snake as opposed to a rope.</p>

<p><strong>So, linking the Mahayana Madhyamaka emptiness to the Theravada emptiness, I can say that all phenomena is empty of a mentally reified intrinsic essence, where this reification or objectification-classification is rooted in "I am the thinker".</strong></p>

<p>I think it is important to talk more about <em>how</em> this rooting in "I am the thinker" takes place. Here is a theory, but mind you I can't support any of this with authoritative sources.</p>

<p>The thing we reify most is ourselves. For all of our lives in cyclic existence we've identified first and foremost with this "I am the thinker." And <em>on that basis</em> we've carved out a piece and objectified it and thought, <em>"this "I" is separate from everything else in a real and intrinsic way."</em> On the basis of this little island of "I" we then carve up the rest and objectify this and that. Put another way, the "I" is at the center of our conventions. We conceive of everything else in relation to this "I" and on that basis it is the root of our objectification.</p>
 43: <p>Yes, your understanding is correct as far as I see. Specifically the point that splitting the phenomena into "I" (the perceiving subject and pursuing agent) and "the other" (the object of pursuit or aversion) is the ultimate root of <em>papanca</em> and the way the two emptinesses are connected.</p>

<p>This is explicitly explained in an early Mahayana work called Madhyāntavibhāga (aka "Maitreya’s Distinguishing the Middle from the Extremes") that cross-links Mahayana and Early Buddhism concepts. It's a rather difficult read, but Mario D'Amato's translation of Vasubandhu's commentary and his own commentary on that, makes it pretty readable, if one goes slow enough to appreciate the implications. It's also available on the Internet in other translations, e.g. <a href="http://lirs.ru/lib/Madhyantavibhanga,Maitreya,Thrangu,Levinson,2000.pdf" rel="nofollow noreferrer">this commentary by Thrangu Rinpoche</a>.  Another work that covers similar topics is <a href="https://static1.squarespace.com/static/53e0268de4b0f2394fee5f54/t/5730b47886db435d014b25d4/1462809722094/Excerpts+from+Mipham%27s+Beacon+of+Certainty+-+Illuminating+the+View+of+Dzogchen%2C+the+Great+Perfection.pdf" rel="nofollow noreferrer">Mipham Rinpoche's Beacon of Certainty</a>.</p>

<p>And no, your definition of Emptiness does not disagree with Yogacara, because Madhyāntavibhāga is specifically a Yogacara work. In Madhyāntavibhāga their definition of Emptiness is exactly: "phenomena are empty of a (mentally reified) intrinsic essence". They also have this notion of "false imagination" - which is what they call the idea that "I" and "objects" are two different things.</p>

<p>Overall, I believe your theoretical understanding is pretty complete. The only point you're missing (I think?) is connection between <em>tathata</em> and cessation of suffering. Why exactly suffering does not arise?</p>
