From my naive point of view I'm confused about how this argument can possibly work. Perhaps someone can explain it? 1. It seems to me that if you assume that

From my naive point of view I'm confused about how this argument can possibly work. Perhaps someone can explain it? 1. It seems to me that if you assume that mathematics is inconsistent, you shouldn't then consider an inconsistency in the argument sufficient grounds to throw away the assumption. I suppose that means that I don't accept proof by contradiction in the case that the assumption is the inconsistency of mathematics. 2. Sanity Check: We can create known inconsistent systems, could the same logic prove that such inconsistent systems are consistent too? It seems to me that it could, am I wrong? 3. Supposing that mathematics did prove its own consistency, the fact that inconsistent systems can also prove their own consistency means that you can't take a proof of consistency to be strong evidence that the system is consistent. 4. Gödel didn't say that mathematics couldn't prove its own consistency, he just said that if it could it was unsound, which is a bit of a concern too.