> 1. I don't think human reasoning is consistent in the technical sense, which makes the incompleteness theorem inapplicable regardless of what you think about

> 1. I don't think human reasoning is consistent in the technical sense, which makes the incompleteness theorem inapplicable regardless of what you think about us and Turing machines. Human reasoning is certainly limited. I mean, imagine the kinds of formulas one would get applying GT to the brain. They would be so enormous they'd be entirely impenetrable to human reasoning. We couldn't even read them in a single lifetime. As for proving GT itself, this proof has been formalized. There's no reason a computer couldn't prove GT by itself.