[FOM] RV: Is Godel's Theorem surprising?

[Ignacio Nattochdag]

Charles Silver wrote:

"	Both Panu and Harvey expressed doubts about this remark I made: "I  
believe this [the Kripke] proof also shows--please correct me if I'm  
wrong--that a specifically *mathematical* proposition (though an  
unusual one) cannot be proved nor can its negation.    (I.e., Godel's  
first theorem.)
	After they read the proof carefully, do Panu and/or Harvey think the

proposition *is* in a sense mathematical (though as I said,  
"unusual"), or do they think it is *not*, and why?   Similarly, what  
do others think?
	
	(Hmmm, what now occurs to me is to find out what Putnam thinks.)"

The proposition in Putnam's proof is Pi2 and he states it using a Sigma1
notion that he calls "n-fulfillability": an argument that I think could be
raised against its "mathematicality" is the fact that it can not be treated
as a problem of computation, because the non-standard model can't be coded
recursively in an interesting way (any coding would trivialize beyond
recognition all that is significant in Putnam's proposition). Personally, I
do not think this is reason enough to discard it dogmatically as
non-mathematical; also, we all know that the question: what really is a
"mathematical" proposition? has not an universally agreed on answer and will
still be discussed when we are all long dead,   

Regards,

I. Nattochdag.   




 

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