To understand what is meant by "Buddha Nature," we can look at the story of the three turnings of the wheel of Dharma taught by Shakyamuni Buddha. The first turning of the Dharma wheel is the four noble truths: that discontent arises from grasping the ever-changing phenomena of body and mind as "me," and that freedom from this discontent is revealed through the path of not grasping anything as truly me. The four noble truths is a kind of deconstruction method. However, in this first turning, all the different elements that we can deconstruct this person into really do exist. Earth, wind, fire and water, for example: those kind of physical elements, when you break them down into their smallest bits, are indestructible elemental energies or physical matter, atoms. Early Buddhists, who were first turning exponents, had this kind of theory—that the world is made up of atoms—several centuries B.C., long before modern scientists discovered atoms. We don’t really exist as independent “persons”; we are a conglomeration of all this stuff that we think is a real “me,” but if we look closely, we only find atoms. This turning of the Dharma wheel was only the first.
The second turning of the Dharma wheel was fearlessly proclaimed in the Perfection of Wisdom Sutras, in which the deconstruction project goes even further. Here, not only is there no real "me," but there are also no four noble truths, and, sorry to say, there are not even any atoms. There aren’t any particles or elements of mind, not even eyes, ears, nose, tongue or body, or colors, sounds, smells, tastes, touch, or objects of mind; all the things that were such wonderful elements to deconstruct the person into in the first turning can no longer be grasped as existent, because to do so would get in the way of our complete freedom. Sometimes this second turning is said to be the relinquishment, or letting go, of all fixed reference points. Anything can be a reference point: atoms, earth, fire, wind, earth, all the different mental elements of mind; in the end there’s nothing that can be found in an essentially existent state. All that appears is merely a construction of mind; mental imputations build on previous mental imputations, and in the end nothing whatsoever can actually be found. Ultimately, when we actually try to find an atom or anything else, we can see something there, we can feel and taste lots of things, but at the very essence of it, we can’t find anything truly existing.
The second turning of the Dharma wheel traditionally involves concentrated analysis and logical reasoning to convince our very confident mind that actually nothing can really be found; this is the amazing but challenging project of Nagarjuna. Such reasoning takes a lot of effort, applied again and again, to really undermine our beliefs, because we go about our day quite confidently thinking that things can be found. We believe that the road we walk on is really made up of little asphalt molecules, but the second turning is about breaking down that confidence so that actually the road that seems to be supporting us can't be found, and even the asphalt molecules can’t be found. That might sound kind of disturbing; why would we want to undermine our confidence that we can walk on the road? It is somewhat painful to hold the unconscious belief that the road will support us, even though such pain is rarely noticed. But the point is that much greater forms of pain are based on exactly the same principle: that we believe what appears to us is truly existent and therefore we can’t help but grasp onto it or try to get away from it.
Finally, the third turning of the Dharma wheel is the way mind is originally free from all fixed reference points and at the same time is luminously clear and aware; this is also called Buddha Nature. Not only does Buddha Nature not require analytical reasoning to prove, but it can't really be proved by analytical reasoning. We might think that's a relief, since maybe then we can skip the difficult second turning work of studying Nagarjuna's deconstructive logic and so on, and just enter the third turning of Buddha Nature, immanent and already complete. That may be possible, since anything is possible, especially from the point of view of the third turning. But generally it's said that to approach the realization of this naturally present, already perfect Buddha Nature, it's very helpful to first wholeheartedly engage in the step of deconstructing everything into vast unfindability, to relinquish all reference points. Otherwise we may not be able to appreciate the full extent of Buddha Nature, or even more problematic, we might consciously or unconsciously make Buddha Nature into a reference point and get at least a little hold on it and use that to maintain our sense of security that "at least there’s this!" If nothing else, we can at least have this thing called Buddha Nature. But Buddha Nature is not a thing, and especially not a thing we can have. When the ancient Zen teacher Zhaozhou was asked if a dog has Buddha Nature, he said, "no."
Traditionally what we mean by "Buddha," fully realized Buddha, is when Buddha Nature is fully revealed, free from all obscurations. It's hard to say anything about what Buddha is without limiting it, but Buddha is free from this consciousness with which we're aware of everything right now, this consciousness that's seeing appearances of phenomena and aware of what's happening as events outside of itself. This dualistic consciousness that appears to be split into subject and object cannot fully realize Buddha. So Buddha is already unimaginable, right? However, in the Zen tradition, it is said that this very mind is Buddha. This is not the dualistic mind as we know it, but the uncontrived true nature of mind, also called "ordinary mind." This consciousness right now, that appears as subject and object, is actually completely empty of any fixed reference points. If we look for this mind itself, when we turn the light of awareness around to shine back on mind itself . . . Ah! It’s hard to find anything there.
So the fruition of the path in the third turning is not just nothingness, but a Buddha that is infinite compassion. It is the inconceivable inseparability of emptiness and compassionate awareness, complete openness to all. That is not mere negation—it's infinite compassion with infinite skillful means to help beings in an infinite variety of ways, beings that are not objects outside of this awareness. Buddha, without moving a particle or going anywhere, without any effort or even intention, can immediately and completely liberate countless beings in infinite realms simultaneously. That’s not nothing! But it's also not something; it’s completely inconceivable.
One great benefit of trusting in Buddha Nature, is that it's a cure for discouragement in our practice. Nagarjuna, who is mostly a second turning teacher, wrote a few short third turning treatises as well, and one says something like, "Since Buddha Nature is present, one can work hard and find pure gold hidden in rock. But if Buddha Nature is not here, even if one were to work hard, one would only get tired." Buddha Nature is always here, but just obscured. Our normal dualistic thought is like clouds obscuring the vast clear sky of Buddha Nature, but occasionally there's a little hole in the cloud, a glimpse of a small spot of clear sky. From that glimpse we can infer that there's a huge unobstructed clear sky behind the clouds. From the point of view of the sky, the clouds don’t even obstruct it in any way; the sky has no problem with clouds floating through it.
Another benefit in trusting in Buddha Nature is that it can undermine our tendency to praise self and belittle others, since all beings, even cockroaches, are equally inseparable from Buddha Nature. It’s quite humbling actually. And of course Buddha Nature is not exclusive to Buddhism. You don’t have to be Buddhist to have it! Obviously, right? Cockroaches aren’t Buddhist! Buddha Nature is not diminished at all when it manifests as a confused living being. It’s not improved in the slightest in its expression of an infinitely compassionate Buddha. Buddha Nature doesn't ever change. A fully realized Buddha seems to be different from us sentient beings, but the Buddha Nature is identical. That’s one of the most miraculous qualities of this nature, that it never changes from beginning to end, and therefore it’s unconstructed, unconditioned, it's not born, it doesn't die, it's not impermanent, it doesn't come and go, but it's not permanent either because it's not some thing. It is simply the inconceivable inseparability of emptiness and compassionate awareness, shining forth right here and now.