And the point you're trying to make here ignores what I said. It is certainly the case that if you permit every violation of non-contradiction, whether or not it violates any other rule, you wind up with nonsense. In no way does that establish that nonsense follows from any violation of non-contradiction even in the face of other rules. I don't have deep enough knowledge to say one way or the other, but some mathematicians seem to think there are things of interest there and your superficial rejection does nothing to prove them wrong.