Godel's Incompleteness Theorems and the Limits of Formal Systems

Anonymous

A clean piece — I particularly liked the way you framed the move from {X} to {Y}.

Anonymous

I think there's an interesting tension between your argument in §1 and the conclusion in §3 that I'd like to draw out. If we accept your characterisation of {X} as you describe it, it seems to commit us to a position on {Y} that some readers would find harder to defend than your headline claim. That said, I think this is a feature not a bug — it's exactly the kind of unargued commitment we should be making explicit in this debate, and you've put it on the table cleanly.

Anonymous

Worth flagging that Lucas-style readings of this (mind exceeds Turing-machine capability) routinely conflate semantic and syntactic completeness — your §2 handles the distinction well.