nagarjuna's point is not that contradiction or many-valued logic can be tolerated. nagarjuna, who is addressing a specific set of buddhist logicians, is finding paradoxes in logic in an attempt to break those logicians clinging to logic, and (somewhat presciently in the history of buddhism) suddenly enlighten them. he, like most buddhists, is not making any ontological or metaphysical claims whatsoever.
it's similar to kant's antimonies. he is not trying to assert contradiction exists, he is trying to point out why we need to countenance ideas like a distinction between noumina and phenomena. or like zeno's paradoxes, which have a rhetorical purpose: to confirm zeno's teacher parmenides's claim that the universe is one undifferentiated whole. see also plotinus, who does roughly the same thing (any real ontological difficulty posed by the paradox of plurality is uninteresting to them; they have a thesis and their statement of the paradox is for a purpose).
incidentally, i don't mean to slag graham priest too much. after all, j.c. beall was my logic professor, and i'll always fondly remember how he introduces every new step in a proof by saying, slowly, "now holllld on, what about (etc)." the dialetheists will always hold a place in my heart. that said, i think godel did about all that need be done with the liar's paradox, and we ought to be wittgensteinians regarding language in the first place (words mean what they do in virtue of their being used by agents for a purpose; you cannot fully enumerate representational content of an utterance solely in virtue of its shape. all utterances are context sensitive. for more, see the almost unreadable but spot on work of charles travis, e.g. unshadowed thought).
it's similar to kant's antimonies. he is not trying to assert contradiction exists, he is trying to point out why we need to countenance ideas like a distinction between noumina and phenomena. or like zeno's paradoxes, which have a rhetorical purpose: to confirm zeno's teacher parmenides's claim that the universe is one undifferentiated whole. see also plotinus, who does roughly the same thing (any real ontological difficulty posed by the paradox of plurality is uninteresting to them; they have a thesis and their statement of the paradox is for a purpose).
incidentally, i don't mean to slag graham priest too much. after all, j.c. beall was my logic professor, and i'll always fondly remember how he introduces every new step in a proof by saying, slowly, "now holllld on, what about (etc)." the dialetheists will always hold a place in my heart. that said, i think godel did about all that need be done with the liar's paradox, and we ought to be wittgensteinians regarding language in the first place (words mean what they do in virtue of their being used by agents for a purpose; you cannot fully enumerate representational content of an utterance solely in virtue of its shape. all utterances are context sensitive. for more, see the almost unreadable but spot on work of charles travis, e.g. unshadowed thought).
http://www.thezensite.com/ZenEssays/Nagarjuna/Nagarjuna_and_...
http://homepages.uconn.edu/~jcb02005/
http://www.amazon.com/Unshadowed-Thought-Representation-Lang...