In Madhyamaka.Matt J wrote: In Buddhism, the central principle is "emptiness" or sunyata.
Otherwise, the unifying principle would probably be "dependent origination". Even dependently arising things may acquire intrinsic features, that distinguish them from other things. Think of emergent properties that are more than the sum of the parts. Or souls that creep into bodies at birth. Nagarjuna's argument would now be that whatever experientially arises, it has no unique nature of its own. The need for that is sometimes difficult to imagine for minds that have been raised with particle models. In pre-atomic thinking, things were seen as opaque. Water became air when it evaporated. "How can a tree form" was not a question of water molecules, photons, carbon dioxide that floats in the air and kalium and other ions in the ground. Up to a certain level, a tree was basically opaque. Our modern standard model of "quarks" is not far from what Nagarjuna argues. Today he would probably say a tree arises from the conditions named above, but there's no spiritual entity housing it that magically makes it different from other things. It's "uninhabited", it can be experienced, end of story. And by the way, the same goes for human beings. So stop searching for souls, there are none. Shunyata.
It is an attempt to abolish mysticism, that was prevailing in pre-Buddhist times and produced Shamanic and Vedic ritual. Even in Ionia it can be found in the stories of Homeros. The era from 500 BCE to 0 BCE was one that tried to break away from animistic models, but could only do so in bursts. Apparently, at the time of Nagarjuna, the argument was still present. And today it still is. It is a consequence of the development of human thinking. Animistic thinking is the first ontologic explanation that is available when the human mind develops, and we all run through these stages as a child. Dependent on education, we develop more advanced explanations, until at some point, thinking is ripe enough to get beyond itself and drop back out of the illusion, while staying aware of that, which is the difference between liberation and the state of a child. A child does not pose certain questions, but is not aware of it, and is thus drawn back into confusion once these questions arise.
Consequently, by equalling identity and causal independence via "svabhava", identity comes from the illusion of causal independence. As there is no causal independence, and everything is causally dependent, there also is no identity. Thus nothing has a permanent "nature", where "soul" would be the concept of a permanent nature for human beings, and "spirits" the concepts of a permanent nature of things experienced. So his message is nature just happens, and everything is unspirited.
Not all schools of Buddhism will share that. If the goal is to get beyond the realm of desires, existential questions do not necessarily need to be dealt with. Only once the ontological and soteriological questions have been raised, they too need to be pacified.
Vedanta would now say: Yes, but everything expresses itself as consciousness, which appears to be the common denominator of it. As plant-consciousness cannot be argued, because the questions are arising in human-consciusness as subject, only the question of "what is human consciousness?" has to be dealt with. The Vedic answer would be "part of a bigger consciousness called Brahman that encompasses everything. The Universe as one living being where some parts of it are fallen to the illusion that they are really separate entities. So try to merge with that Brahman, or god nature. Advaita would then say "But they're not different anyway. There's nothing to merge, just rest in consciousness."
In the end, both land in the same state. However, in my opinion, Nagarjuna's philosophy does not have to deal with "internal phenomena", as was the basis of Samkhya, or the five skandhas, as they're only required when discussing internal, mental phenomena, which apparently was where Yogas started from.