[FOM] Is Godel's Theorem surprising?
A. Mani
a_mani_sc_gs at yahoo.co.in
Sat Dec 9 19:57:52 EST 2006
On Friday 08 Dec 2006 16:28, Harvey Friedman wrote:
> ALSO: There are two senses of surprise for a theorem. One is that one is
> surprised by the fact that the theorem is true. The other is that one is
> surprised by the fact that anyone was able to prove that the theorem is
> true. There were probably many people who weren't too surprised that it is
> true, but who were shocked that anyone was able to prove such a thing.
>
The generalization is unjustified, though for the context it is OK.
There are many possible ways of defining Surprise(Thm).
The correspondence theory of truth is difficult to use here... coherence
performs better. A correspondence way of seeing it may be written like
Surprise(Thm) iff [v(Thm) = True & v(Thm) \neq Almost True] or [v(Thm) =
Almost True & \nvdash Thm ] or [v(Thm) = Almost True & \vdash Thm] or [v(Thm)
= False & v(Thm) = Amost True] or .......
For the coherence way
Surprise(Thm) iff [v(Thm) = True & Warrant(\vdash Thm) = low] or .....
looks better.
There are many more possibilities either way.
A. Mani
Member, Cal. Math. Soc
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