That's only true for systems where the principle of explosion actually holds though, isn't it? So it wouldn't apply to paraconsistent systems. In the end, Göde

That's only true for systems where the principle of explosion actually holds though, isn't it? So it wouldn't apply to paraconsistent systems. In the end, Gödel is actually giving us a choice: Either accept incompleteness or accept inconsistency. Of course it's true that historically incompleteness has been perceived as the only viable choice, but at least a few paraconsistent logicians like Graham Priest have argued for (non-explosive) inconsistency instead.