I always assumed that there could be no contradictions -- that the principle of non-contradiction was absolute, so to say. Recently, however, I read about dialetheism and paraconsistent logic and realized that some philosophers disagreed. It seems all of logic falls apart if contradictions are permitted. I fail to understand how their position makes any sense (which could admittedly be just a failure on my part). So is it possible someone could better explain their viewpoint? Surely none of them believe that, say, one could simultaneously open and close a book, right?