In his philosophy, Nagarjuna uses the Pratityasamutpada to prove, that everything is empty and without reality. In the end, however he proves not only the emptiness of that very Pratityasamutpada but he also somehow leaves the law (of dependent arising) intact and working. Does anyone understand his point, especially in what concerns Pratityasamutpada?
I took a university course in Asian Philosophy and my professor explained emptiness this way:
Nagarjuna makes the claim that an essence (a list of essential qualities that make a thing what it is) can only be stated in reference to other things. This is a way of saying that all things are defined in relation to other things, including samsara and nirvana.
The point of doing this, supposedly, is to help us realize that this means enlightenment and samsara are defined in terms of each other: Without samsara we can't define enlightenment, and without enlightenment we can't define samsara.
Basically according to this professor, Nagarjuna makes the argument that "We're all in this together" and we should be helping each other reach enlightenment and not strive for it by ourselves.
He also stated that Emptiness is a flashy re-packaging of the teaching of dependent origination.
In my opinion, the concept of Emptiness makes sense, but I don't really see how it's useful above and beyond the teachings in Early Buddhism. If anything, an enlightened person is more able to help others, so there shouldn't be a problem in striving towards enlightenment.
Nagarjuna uses Pratityasamutpada as a proof for emptiness by means of his many arguments found in chapter 1 of the Mulamadhyamakakarika. Basically he lays out a series of reductio ad absurdum arguments that show that if you posit real phenomena, it absurdly follows that change and arising cannon occur. But because Pratityasamutpada does occur, the initial assumption that phenomena are real is refuted.
Later in the work (i.e. Chapter 24) he says basically the same thing but the other way around. He addresses the possible criticism that emptiness negates core Buddhist teachings, and Nagarjuna argues that because of the fact that if emptiness were false, change could not occur, emptiness doesn't negate core Buddhist teachings, but is in fact the only thing that makes them possible in the first place.
Putting these together we conclude that Pratityasamutpada proves emptiness, and emptiness makes Pratityasamutpada possible. Pratityasamutpada explains the conventional level of things, and emptiness explains them on the ultimate level, and these two fit together in the union of appearance and emptiness, and Nagarjuna famously declares:
Whatever is dependently co-arisen
That is explained to be emptiness.
That, being a dependent designation
Is itself the middle way.