[FOM] Is Godel's Theorem surprising?

[Aatu Koskensilta]

ignacio wrote:
> It is possible to prove Gödel's first theorem without using diagonalization,
> that’s right: but any other technique you use to prove it is, from a formal
> mathematical point of view, equivalent to diagonalization

Why? How does Kripke's proof as presented by Putnam, for example, 
involve diagonalization "from a formal mathematical point of view"? And 
even if it does, how do you justify the (staggeringly strong) claim that 
any proof of incompleteness must involve diagonalization?

Aatu Koskensilta (aatu.koskensilta at xortec.fi)

"Wovon man nicht sprechen kann, daruber muss man schweigen"
- Ludwig Wittgenstein, Tractatus Logico-Philosophicus