Their argument is that quantum gravity can encode undecidable statements, and therefore cannot be completely computed. Of course take it with a grain of salt, since it relies on an incomplete and possibly inaccurate characterization of quantum gravity, something we don’t know anything about. Still, a cool idea.

On the other hand, if it's just me, and everything including you is just simulated for my benefit, it's not too hard.

And again, almost every statement in this paper is wrong, including the main claim

Only if you assume the law of the excluded middle, right?

Statements aren’t just true or false, they can also be malformed or undefined.