Sva-bhava translated as "own being". This is a direct translation, not an interpretation. Interpretations such as "openness" for "sunyata" (emptiness) say too much.

"Inherent existence" for svabhava introduces an interpretation, though this expresses well what Nagajuna meant. Nāgārjuna takes this term over from somewhere else. A thing's own-being is what ever belongs properly to what that thing is, whatever is essential to that thing (so that svabhava corresponds to the Western term "essence"). Svabhava also "identifying feature" or "identifying characteristic". As far as Nāgārjuna is concerned, svabhava is the same as svalaksana (="own characteristic"). The svabhava/svalaksana of fire is heat. In their view, if something is hot, fire is involved (even when water is hot--hot water borrows fire from somewhere else). Heat was to them a tactile sensation, something that can transform the environment; they didn't have our kinetic theory of heat. Svalaksana is the "necessary feature of a thing" by which it is what it is, not a "necessary condition" of the thing. Svalaksana and svabhava are the same in reference, but belong in different discussions. Svabhava contrasts with parabhava (other being) and prajnapti (concept), while svalaksana contrasts with samanyalaksana--general characteristics that all samskrta (created, dependently arisen) dharmas share. Nirvana was not thought by most schools to be samskrta (it was "asamskrta"), and the Sarvastivadins thought space was also "asamskrta". The svalaksana of a thing is particular of that thing; no other dharma in addition to fire has heat as its svalaksana (or as its svabhava). Popular example: elephant. Many characteristics define it as an elephant--long prehensile nose, ears like winnowing fans. Tail like a rope, etc. When you know those characteristics, you can identify the elephant, but the characteristics are not all of what an elephant is. Some features are uniquely elephantine, but other features are shared with other creatures. Example of fire: heat is a characteristic of fire, but there isn't really any fire aside from the heat. Heat is fire (remember that fire is a dharma, whereas an elephant is not a dharma). The own being of fire is the fire/heat itself. So fire's own being is equivalent to the thing itself. When a particular dharma is said to be a condition for all other dharmas except for itself, the term for itself with frequently be svabhava, meaning not "except for its own-nature/own-being" but instead "except for itself".

Own-being connected with the idea of identity. "Self-being" also OK as a translation. Sva cognate with the sui in suicide. The own being is what the dharma really is, the dharma-in-itself, the dharma itself: it is something like the "selfhood" of a dharma. In fact, in one of the major Abhidharma works of the Sarvastivada (a commentary), there is little discussion about why it is incorrect to think that the selves of persons exist and why it is OK to say that the selves of dharmas exist (people have selves (svabhavas)--not OK; dharmas have selves--OK). The term, reconstructed from the Chinese, is dharma-atman. Nāgārjuna interested in something definable as the self of a dharma. Why do the Sarvastivadins talk about it in this way? They're not stupid. They use atman there in the sense of "nature". This usage was normal in Sanskrit and seemed innocuous to these people. Some works on Buddhism make you think that atma(n) was taboo, but even the buddha used the word a lot. "Monks, rely on yourselves." There's a story where the Buddha is sitting in the forest and a wealthy young man who'd been having a picnic with "courtesans/hookers" came running over, looking for the courtesan who'd presumably stolen something from him. He said, "Have you seen a woman?" The Buddha said, "No, wouldn't it be better to search for the self instead of searching for a woman?" Then the Buddha instructs them in the Dharma. This story comes from the Theravadin vinaya. Here the Buddha uses a supposedly taboo term in an interesting way. People who think the Buddha was really Vedantan like this story (in Vedanta, the "self" that carries on lifetime after lifetime, exchanging bodies like taking off and putting on clothing, is a key idea, as is the "supreme self" (rendered in English as the capital S "Self"). But if the Buddha had Vedanta philosophy in mind, then the discussion that followed (instruction in the Dharma) should have something to do with the self (atman) that one is supposed to be seeking, but it doesn't--it's the usual stuff about dependent arising. The Pudgalavadin Buddhists liked this passage, because they believed the Buddha actually did teach the reality of the self. The Buddha likely meant that the disciples should look within themselves to see the transitory and composite nature of the self. In Vedanta, the atman is indivisible, as in Jainism, where the jiva is a unitary being (though there is no "supreme" jiva as there is a supreme atman). The Buddhists believed that the atman was not atomic but instead changing and divisible. In Buddhism, the "self" is not atomic, not definite, so it is not a real basis for attachment, which produces suffering. Svabhava not exclusively Sarvastivadin, as the Pali equivalent is used in the Theravada in a Sutra commentary. It's not in the Sutras themselves. It is in some of the Sarvastivadin Abhidharma texts, but not in the Theravada Abhidharma. Maybe Sarvastivadins started using this term and were followed by others, but we just don't know. We know most about Theravada and Sarvastivada, so we tend to assume that these two were "what was going on in early Buddhism. But there were all those other schools.

Svabhava is a useful term: helps define the things you're interested in, and it is important in Buddhism to identify phenomena (=dharmas), especially the mental ones that inspire attachment and are in the end productive of suffering. You identify the dharmas so that you can deal with them. Abhidharma complexity makes sense given the emphasis on correct analysis of the mental processes that create suffering.

Svabhava the means by which you identify what's what, the real nature of the phenomena.

Intruiging stuff from the Pudgalavada: the third noble truth is nirodha/nirvana is asamskrta and has no characteristics. Yet they were willing to characterize it in various ways--being of the nature of peace, end of suffering, etc. But it's not clear whether they thought nirvana had a single defining characteristic that was its svalaksana (remember this is a complex field, and different schools and individuals thought differently).

Let's talk about svabhava in relation to "concept". Svabhava indicative of reality. Something is real if it has a svabhava. Self (if you're not a Pudgalavadin) has no own-self and is not real. According to worldly conventions/ordinary discourse, there are selves. All languages have reflexive pronouns (myself, etc.). But there is no ultimate self because what is supposed to be a self does not have any own being. You won't be able to pin down exactly what a thing is if it doesn't have own-self. Prajnapti means two related things: concept and designation (no English word does the same work). So the self exists "in name only". Self is a creation of language, not something that is there in its own right.

The Buddha says you can use words and designations but you should know they're not absolute.

Prajnapti a verbal noun formed from the causative of the verb "to understand"--whence "wisdom" (understanding--prajna). You understand something by its concept and designation, but there are different levels of understanding. Full understanding takes some work. Another point: the self is unreal because it is a system of momentary and changing dharmas. The self is always composite and analyzable into the aggregates--hence it is unreal. We're working towards atomism. The Greeks were materialistic atomists, but here the indivisible units are not necessary material (4/5 of the aggregates of self were mental) and are momentary. They are atomistic in space and time. The atoms (dharmas) were "real" and simple.

What are we doing? Showing that these ideas are not absurd. Abhidharma and Nagarjunian critique of it not useless and can even be a natural way of thinking. Abhidharma very useful, and Nāgārjuna's critique of it illuminating. Nāgārjuna initially seems a minor trouble maker, but his questioning cuts deep. His critique questions the ways in which we use our minds and the way in which we perceive. The difference between Nāgārjuna and Wittgenstein was that for Wittgenstein improper philosophy was the disease, while for Nāgārjuna all people have the disease, not just philosophers. Even animals have this disease. Animals are worse off because they lack the ability to reason, which can be used to bring difficulties to a crisis and allow escape. For a Chinese Daoist, animals and children are close to the Way--different view from modern one and from the Buddhist one.

He we have an ontology where reality consists of particles of being. Is this account of how these people thought too tidy? Yes. For the Sarvastivadins, shape (not a mental or a material atom; it might be called a "formal" atom) was a dharma. If shape is a dharma, it's atomic. This is worrying!

People misunderstand Nāgārjuna when they believe he is offering a countersystem. Does Nāgārjuna have a system. Is his emptiness part of his system. He emphasizes that we shouldn't ontologize emptiness. Nāgārjuna makes statements not because they're the truth but because they're worth making. "Self" not the truth but it's potentially useful on the path to enlightenment.

So: use whatever way of talking and explaining you want, but don't assume a 1 to 1 relationship between your system and reality, and don't assume that your way of talking is "the truth". Use your concepts and designations (prajnaptis) advisedly. Don't let yourself get into trouble with your concepts. Don't imagine that your concepts are what reality is. They're just useful ways of talking in certain situations. Nāgārjuna fundamentally a pragmatist. Does a concept help you get to nirvana? If yes, use it. If not, get rid of it. In the end, whatever works works, and no discourse, no formation of thought is privileged. However, the tricky thing is that you still want to say that the Buddha's thought was better than all the rest, because it works the best. The people Nāgārjuna was talking to believed in the reality of the dharmas but Nāgārjuna did not think the dharmas were the ultimate reality.