user471: What exactly is svabhāva in Nagarjuna's Madhyamaka?
It is translated as inherent nature or inherent existence or inherent substance. But what does that really mean?
Does it carry the same meaning as being unconditioned? If yes, then Nirvana and the Buddha's Dharma, being unconditioned, must have svabhāva. But they don't, according to Madhyamaka.
Why does a chair or a photon or empty space or concepts or the Dharma (teachings) or Nirvana have no svabhāva?
From the Wikipedia article on Madhyamaka, it sounds like something that is unconditioned has svabhāva. But that's not right according to Madhyamaka.

Nagarjuna's critique of the notion of own-nature
  argues that anything which arises according to conditions, as all
  phenomena do, can have no inherent nature, for what is depends on what
  conditions it. Moreover, if there is nothing with own-nature, there
  can be nothing with 'other-nature' (para-bhava), i.e. something which
  is dependent for its existence and nature on something else which has
  own-nature. Furthermore, if there is neither own-nature nor
  other-nature, there cannot be anything with a true, substantial
  existent nature (bhava). If there is no true existent, then there can
  be no non-existent (abhava).


user10100: In abhidhamma:
Sabhāva =  saka-bhava = own saṇkhāra = saṅkhata = sappaccaya = sahetuka = an effect of causes.
So, the answer is "an effect of causes".
Note: This is the same reason that why saṅkhāra equal to kamma-bhava.

user43: An analogy I always give is that of a bush that looks like a dog. You see the dog from afar, but once you come closer the illusion falls apart and you see the individual branches and leaves. There is no dog. 
Everything is like that: not only difficult things like "self" or "USA" or "love" but literally every single thing, as simple as a "chair". They seem solid and well-defined until you examine them carefully, and then they turn out to be simplifications that depend on observer defining context, scale of observation, and criteria for their delineation. 
Coming back to the bush, the dog was observer's projection. There was no dog. Or was there? The experience of the dog existed in observer's subjective space. The dog was observer's interpretation. 
When we look at things conventionally, from far away, without examining them carefully, it seems like they exist apart from our interpretation. That existence is called svabhava. Sva means own and bhava means individual being or individual existence. It seems that individual things have their own individual existence, apart from observers. But that is an extremely naive simplification that only holds because we look at things from inside a very limited subset of all possible observation modes.
The question ancient thinkers asked, is there any dharma that has svabhava. In other words, is there any phenomenon that under careful scrutiny will not fall apart like the dog and turn out to be a bunch of unrelated phenomena assembled and delineated by the observing mind.
It's not just the parts and the name as Tenzin explained. That's a simplification. It's not that things are made from parts (like the dog was made from branches) and rely on observer for a name (the dog). It is that we picked a certain area of observation (part of the mountain covered in bushes) we chose certain scale, we picked criteria for delineation (in this case color), and most importantly we ignored lots of details that were there, that did not fit with our idea of dog! 
A very good non-Buddhist explanation of this process can be found in book called 'Hierarchy Theory' by Valerie Ahl. And of course the best Buddhist explanation is Nagarjuna's Mulamadhyamikakarika, translated as 'The Fundamental Wisdom Of The Middle Way' by Jay Garfield. 
You are also right about equating sankhara with (absence of) svabhava. Sankhara means "assembly", not just an assembly of parts though, but rather a bundle of causal chains. Causal chains on both the object side and the observer side. When you see every thing in its temporal aspect, as opposed to statically, when you see causal chains bundling together for a while and then breaking apart, you will see that our notion of "identity" only made sense in a static view of the world.
There is no "identity" carried through from one moment of time to another. Instead, things constantly morph, rather like clouds. We see individual things in the clouds, but those things don't have fixed identities, they don't have svabhava. Instead, there's humidity and temperature and areas of low and high pressure, and the observer at a certain point on the ground with something on their mind, projecting things on the clouds. This observer itself and the observer's mind does not have separate individual existence either, does not have svabhava. Observer and observer's mind is also a bundle of causal chains, not something solid, static, and separate from the rest of the world. 

user10304: Svabhāva, traditional Chinese Buddhist text translated as "自性", i.e., Self-nature. A Svabhava is a Thing-of-itself, it exists on it's own, cannot be deconstructed by the Eight Conditions quested by Nagarjuna; it is not caused by Causal-correlations (因緣), nor Compounded (和合). However, the world is made by (1)Causal-correlations and (2)Compounding, of every phenomena that the intellectual mind able to conceive. Therefore, it is empty. Because anything that's coming from Causal-correlations or Compounding, when investigating by the intellectual examination incisively with a superior mind, the result is - unobtainable. For nothing is obtainable therefore, the term to address it: "Emptiness". 
My elaboration is, Causal-correlations and Compounding shorted as Correlative-arising (緣起). In my investigation, "dependent-arising", or most of the English translated terms I came across are, questionable; creating unnecessary hindrances to understand what precisely it meant. 
(1) Causal-correlations
There are four types of Causal-correlations, Sanskrit: Catvārah-pratyayāh (四緣). Nagarjuna listed and deconstructed each as:
(the translated terms are my designations)
a) Correlative-cause (因緣): Cause and effect. Deconstructed as: an effect not appeared the cause can't be defined; if the effect not in the cause, the cause cannot cause the effect, but if the effect already in the cause the effect doesn't need the cause for it existed already... etc.  
b) Consecutive-cause (次第緣): A temporal cause, i.e., with the factor of time. Deconstructed as: if the effect not appeared, the cause can't disappear; however if the cause not disappeared how could the effect appear... etc.? 
c) Causative-cause (緣緣): A spatial cause, i.e., with the factor of another object. Deconstructed as: for due to a) the cause and effect cannot be established therefore not a "thing" there, there's no object to give as a cause.  
d) Superlative-cause(增上緣): All the above causes multiplied. Deconstructed as: since the above three can't be established this also null. 
I'm afraid Jay Garfield's understanding of the Catvārah-pratyayāh which a very basic Abhidharma concept so questionable in his The Fundamental Wisdom of The Middle Way; I read his chapter 10, then 1 and 2, put aside.   
(2) Compounding Compounding is unobtainable. For if things are different, they can't be compounded to be one thing; yet if they are the same, can't be compounded either, for same thing doesn't compound :). (I was laughing all the way when reading Madhyamaka (Classical Chinese translated by Kumarajiva) the 1st time, now I can't help laughing again when writing at here :))... difference due to differing therefore differences, different object unobtainable... etc.  
Since all phenomena of the world are made by Causal-correlations and compounding, none is having Svabhava. Since all phenomena none is with Self-nature therefore it is empty, i.e., unobtainable (不可得). It is impermanent, conditioned. However, Nagarjuna didn't stop at here, not stopping at deconstructing, what he pointed to is, what beyond this Emptiness that given rise to all phenomena, the world and sentient... etc. Here is most of the scholastic Buddhist Masters/teachers fell. Such as, Tibetan Tsongkhapa by holding onto Madhyamika-Prasangika (wrong) viewpoint constructed his two Chenmo(s) misleading many Buddhists, bolting on the Intellect-mind (意識心), the 6th Vijñāna as permanent [which needed maintenance of each day 16 hours of xxx Tantric OgsM, all months, all years... well maybe good news for some, who knows!? ;] .   
Nirvana and the Buddhahood are of the 5th Statement. The Intellect-mind is able to come as far as the Four-statements (Catuskoti) limitation. To go beyond the Intellect-mind, what should be looked for by all practitioners but the Self-nature as in Ch'an (6th Patriarch Huineng: How so the Self-nature, originally is self-sufficient (何期自性, 本自具足)), or the Tathagatagarbha, or the Alaya... the teachings only available in the Mahayana Canon (excluding the later Tantric texts). One of the most important Sutras is Prajna-paramita Sutra, which the related is Heart Sutra. I'm afraid Thich Nhat Hanh though a respectable teacher I respected, his interpretation of Heart Sutra as quoted in this post is questionable. It's only max. to the level of a Śrāvaka, not for the Bodhisattva or Buddha, i.e., not of the Prajna-paramita Heart Sutra the ultimate Emptiness. 
The OP asked another question on usefulness of Madhyamaka, the key answer is, due to the decline of man's capacity, very rare few able to see directly the Ultimate Reality (still an ignorant claims able to see in meditation and, libeling Nagarjuna :), as stated in the beginning of the Madhyamaka Chinese Text. One of the purposes of Nagarjuna, I think, was enabling a glimpse of Ultimate Reality by pushing the Intellect-mind to the ultimate, by exhausting the Four-statements. If one able to read the original Classical Chinese one will at least sharpen his mind, have a shot of intelligence. Those who incessantly libeling the Mahayana Sutras, pity are they misled by their teachers or traditions. However, this very act is so detrimental to wisdom cultivation even to the worst severed the root of Prajna-paramita rendered these people the Icchantikas warned the Buddha. The Buddha explaint what is Icchantika and why they became the Icchantikas, one of the karmic deeds was they libeled Mahayana teaching due to their ignorance they lack the wisdom to understand the profound deep deep Mahayana doctrines, recorded in Prajna Paramita Sutra. There some so-called "Sutras" inserted, the later Tantric text, unfortunately, in the Tripitaka; but those great Sutras of Prajna-paramita - The 2nd Turning, also Tathagatagarbha - The 3rd Turning, are spoken by Buddha Shakyamuni.                      

user6994: Svabhāva stands for inherent existence.
From an early Madhyamika viewpoint, there are two types of dependent-arising:

Causal dependence
Dependence on parts

While impermanent phenomena depend on both causes and parts, permanent phenomena do not depend on causes and conditions but they do depend on parts. For instance, a chair is impermanent and depends on causes (if it is made of wood, wood is a substantial cause, etc) and depends on its parts (the legs, etc). Permanent phenomena such as space, emptiness, cessations, etc. depend on parts. For instance, emptiness is emptiness of something on which it depends (not causally, but in terms of part). Therefore, even emptiness, a permanent phenomena, is empty of inherent existence because it is a dependent-arising.
From a Madhyamika-Prasangika viewpoint, there are two types of dependent-arising. The third level is the most subtle:

Dependence on name.

We say that the meaning of something being empty of svabhāva is that, if you look for it with a mind analyzing the ultimate, you will not find it. Now, if you ask yourself "is the chair its legs... is it the material it's made of... etc" you will find that the chair is merely labeled upon these without being any of these. We say that it is "merely labeled".

This presentation is incomplete and cartoonish because there are various Madhyamika [sub]schools, some for which inherent existence and true existence are synonymous, some not.

471: <p>What exactly is svabhāva in Nagarjuna's Madhyamaka?</p>

<p>It is translated as inherent nature or inherent existence or inherent substance. But what does that <strong>really</strong> mean?</p>

<p>Does it carry the same meaning as being unconditioned? If yes, then Nirvana and the Buddha's Dharma, being unconditioned, must have svabhāva. But they don't, according to Madhyamaka.</p>

<p>Why does a chair or a photon or empty space or concepts or the Dharma (teachings) or Nirvana have no svabhāva?</p>

<p>From <a href="https://en.wikipedia.org/wiki/Madhyamaka#Svabhava_-_essence" rel="nofollow noreferrer">the Wikipedia article</a> on Madhyamaka, it sounds like something that is unconditioned has svabhāva. But that's not right according to Madhyamaka.</p>

<blockquote>
  <p>Nagarjuna's critique of the notion of own-nature
  argues that <strong>anything which arises according to conditions, as all
  phenomena do, can have no inherent nature, for what is depends on what
  conditions it.</strong> Moreover, if there is nothing with own-nature, there
  can be nothing with 'other-nature' (para-bhava), i.e. something which
  is dependent for its existence and nature on something else which has
  own-nature. Furthermore, if there is neither own-nature nor
  other-nature, there cannot be anything with a true, substantial
  existent nature (bhava). If there is no true existent, then there can
  be no non-existent (abhava).</p>
</blockquote>
 10100: <p><strong>In abhidhamma</strong>:</p>

<p>Sabhāva =  saka-bhava = own saṇkhāra = saṅkhata = sappaccaya = sahetuka = <strong>an effect of causes</strong>.</p>

<p>So, the answer is "<strong>an effect of causes</strong>".</p>

<p><strong>Note:</strong> This is the same reason that why saṅkhāra equal to kamma-bhava.</p>
 43: <p>An analogy I always give is that of a bush that looks like a dog. You see the dog from afar, but once you come closer the illusion falls apart and you see the individual branches and leaves. There is no dog. </p>

<p>Everything is like that: not only difficult things like "self" or "USA" or "love" but literally every single thing, as simple as a "chair". They seem solid and well-defined until you examine them carefully, and then they turn out to be simplifications that depend on observer defining context, scale of observation, and criteria for their delineation. </p>

<p>Coming back to the bush, the dog was observer's projection. There was no dog. Or was there? The experience of the dog existed in observer's subjective space. The dog was observer's interpretation. </p>

<p>When we look at things conventionally, from far away, without examining them carefully, it seems like they exist apart from our interpretation. That existence is called svabhava. Sva means own and bhava means individual being or individual existence. It seems that individual things have their own individual existence, apart from observers. But that is an extremely naive simplification that only holds because we look at things from inside a very limited subset of all possible observation modes.</p>

<p>The question ancient thinkers asked, is there any dharma that has svabhava. In other words, is there any phenomenon that under careful scrutiny will not fall apart like the dog and turn out to be a bunch of unrelated phenomena assembled and delineated by the observing mind.</p>

<p>It's not just the parts and the name as Tenzin explained. That's a simplification. It's not that things are made from parts (like the dog was made from branches) and rely on observer for a name (the dog). It is that we picked a certain area of observation (part of the mountain covered in bushes) we chose certain scale, we picked criteria for delineation (in this case color), and most importantly we ignored lots of details that were there, that did not fit with our idea of dog! </p>

<p>A very good non-Buddhist explanation of this process can be found in book called 'Hierarchy Theory' by Valerie Ahl. And of course the best Buddhist explanation is Nagarjuna's Mulamadhyamikakarika, translated as 'The Fundamental Wisdom Of The Middle Way' by Jay Garfield. </p>

<p>You are also right about equating sankhara with (absence of) svabhava. Sankhara means "assembly", not just an assembly of parts though, but rather a bundle of causal chains. Causal chains on both the object side and the observer side. When you see every thing in its temporal aspect, as opposed to statically, when you see causal chains bundling together for a while and then breaking apart, you will see that our notion of "identity" only made sense in a static view of the world.</p>

<p>There is no "identity" carried through from one moment of time to another. Instead, things constantly morph, rather like clouds. We see individual things in the clouds, but those things don't have fixed identities, they don't have svabhava. Instead, there's humidity and temperature and areas of low and high pressure, and the observer at a certain point on the ground with something on their mind, projecting things on the clouds. This observer itself and the observer's mind does not have separate individual existence either, does not have svabhava. Observer and observer's mind is also a bundle of causal chains, not something solid, static, and separate from the rest of the world. </p>
 10304: <p>Svabhāva, traditional Chinese Buddhist text translated as "自性", i.e., Self-nature. A Svabhava is a Thing-of-itself, it exists on it's own, cannot be deconstructed by the <em>Eight Conditions</em> quested by Nagarjuna; it is not caused by <em>Causal-correlations</em> (因緣), nor <em>Compounded</em> (和合). However, the world is made by (1)Causal-correlations and (2)Compounding, of every phenomena that the intellectual mind able to conceive. Therefore, it is empty. Because anything that's coming from Causal-correlations or Compounding, when investigating by the intellectual examination incisively with a superior mind, the result is - unobtainable. For nothing is obtainable therefore, the term to address it: "Emptiness". </p>

<p>My elaboration is, Causal-correlations and Compounding shorted as Correlative-arising (緣起). In my investigation, "<em>dependent-arising</em>", or most of the English translated terms I came across are, questionable; creating unnecessary hindrances to understand what precisely it meant. </p>

<p><strong>(1) Causal-correlations</strong></p>

<p>There are four types of Causal-correlations, Sanskrit: Catvārah-pratyayāh (四緣). Nagarjuna listed and deconstructed each as:</p>

<p><sub>(the translated terms are my designations)</sub></p>

<p>a) <em>Correlative-cause</em> (因緣): Cause and effect. Deconstructed as: an effect not appeared the cause can't be defined; if the effect not in the cause, the cause cannot cause the effect, but if the effect already in the cause the effect doesn't need the cause for it existed already... etc.  </p>

<p>b) <em>Consecutive-cause</em> (次第緣): A temporal cause, i.e., with the factor of time. Deconstructed as: if the effect not appeared, the cause can't disappear; however if the cause not disappeared how could the effect appear... etc.? </p>

<p>c) <em>Causative-cause</em> (緣緣): A spatial cause, i.e., with the factor of another object. Deconstructed as: for due to a) the cause and effect cannot be established therefore not a "thing" there, there's no object to give as a cause.  </p>

<p>d) <em>Superlative-cause</em>(增上緣): All the above causes multiplied. Deconstructed as: since the above three can't be established this also null. </p>

<p>I'm afraid Jay Garfield's understanding of the Catvārah-pratyayāh which a very basic Abhidharma concept so questionable in his <em>The Fundamental Wisdom of The Middle Way</em>; I read his chapter 10, then 1 and 2, put aside.   </p>

<p><strong>(2) Compounding</strong> Compounding is unobtainable. For if things are different, they can't be compounded to be one thing; yet if they are the same, can't be compounded either, for same thing doesn't compound :). (I was laughing all the way when reading Madhyamaka (Classical Chinese translated by Kumarajiva) the 1st time, now I can't help laughing again when writing at here :))... difference due to differing therefore differences, different object unobtainable... etc.  </p>

<p>Since all phenomena of the world are made by Causal-correlations and compounding, none is having Svabhava. Since all phenomena none is with Self-nature therefore it is empty, i.e., unobtainable (不可得). It is impermanent, conditioned. However, Nagarjuna didn't stop at here, not stopping at deconstructing, what he pointed to is, what beyond this Emptiness that given rise to all phenomena, the world and sentient... etc. Here is most of the scholastic Buddhist Masters/teachers fell. Such as, Tibetan Tsongkhapa by holding onto Madhyamika-Prasangika (wrong) viewpoint constructed his two Chenmo(s) misleading many Buddhists, bolting on the Intellect-mind (意識心), the 6th Vijñāna as permanent [which needed maintenance of each day 16 hours of xxx Tantric O<sub>gs</sub>M, all months, all years... well maybe good news for some, who knows!? ;] .   </p>

<p>Nirvana and the Buddhahood are of the 5th Statement. The Intellect-mind is able to come as far as the <a href="https://buddhism.stackexchange.com/a/22758/10304">Four-statements</a> (Catuskoti) limitation. To go beyond the Intellect-mind, what should be looked for by all practitioners but the Self-nature as in Ch'an <em>(6th Patriarch Huineng: How so the Self-nature, originally is self-sufficient (何期自性, 本自具足))</em>, or the Tathagatagarbha, or the Alaya... the teachings only available in the Mahayana Canon (excluding the later Tantric texts). One of the most important Sutras is Prajna-paramita Sutra, which the related is Heart Sutra. I'm afraid Thich Nhat Hanh though a respectable teacher I respected, his interpretation of Heart Sutra as quoted in <a href="https://buddhism.stackexchange.com/a/25087">this post</a> is questionable. It's only max. to the level of a Śrāvaka, not for the Bodhisattva or Buddha, i.e., not of the Prajna-paramita Heart Sutra the ultimate Emptiness. </p>

<p>The OP asked another question on <a href="https://buddhism.stackexchange.com/questions/25076/usefulness-of-madhyamaka-to-personal-practice">usefulness of Madhyamaka</a>, the key answer is, due to the decline of man's capacity, very rare few able to see directly the Ultimate Reality (still an ignorant claims able to see in meditation and, libeling Nagarjuna :), as stated in the beginning of the Madhyamaka Chinese Text. One of the purposes of Nagarjuna, I think, was enabling a glimpse of Ultimate Reality by pushing the Intellect-mind to the ultimate, by exhausting the Four-statements. If one able to read the original Classical Chinese one will at least sharpen his mind, have a shot of intelligence. Those who incessantly libeling the Mahayana Sutras, pity are they misled by their teachers or traditions. However, this very act is so detrimental to wisdom cultivation even to the worst severed the root of Prajna-paramita rendered these people the Icchantikas <em>warned the Buddha</em>. <em>The Buddha explaint what is Icchantika and why they became the Icchantikas, one of the karmic deeds was they libeled Mahayana teaching due to their ignorance they lack the wisdom to understand the profound deep deep Mahayana doctrines, recorded in Prajna Paramita Sutra</em>. There some so-called "Sutras" inserted, the <em>later Tantric text</em>, unfortunately, in the Tripitaka; but those great Sutras of Prajna-paramita - <a href="https://buddhism.stackexchange.com/a/24325">The 2nd Turning</a>, also Tathagatagarbha - <a href="https://buddhism.stackexchange.com/a/24502">The 3rd Turning</a>, are spoken by Buddha Shakyamuni.                      </p>
 6994: <p>Svabhāva stands for inherent existence.</p>

<p>From an early Madhyamika viewpoint, there are two types of dependent-arising:</p>

<ol>
<li>Causal dependence</li>
<li>Dependence on parts</li>
</ol>

<p>While impermanent phenomena depend on both causes and parts, permanent phenomena do not depend on causes and conditions but they do depend on parts. For instance, a chair is impermanent and depends on causes (if it is made of wood, wood is a substantial cause, etc) and depends on its parts (the legs, etc). Permanent phenomena such as space, emptiness, cessations, etc. depend on parts. For instance, emptiness is emptiness of something on which it depends (not causally, but in terms of part). Therefore, even emptiness, a permanent phenomena, is empty of inherent existence because it is a dependent-arising.</p>

<p>From a Madhyamika-Prasangika viewpoint, there are two types of dependent-arising. The third level is the most subtle:</p>

<ol start="3">
<li>Dependence on name.</li>
</ol>

<p>We say that the meaning of something being empty of svabhāva is that, if you look for it with a mind analyzing the ultimate, you will not find it. Now, if you ask yourself "is the chair its legs... is it the material it's made of... etc" you will find that the chair is merely labeled upon these without being any of these. We say that it is "merely labeled".</p>

<p><br>
This presentation is incomplete and cartoonish because there are various Madhyamika [sub]schools, some for which inherent existence and true existence are synonymous, some not.</p>
