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gRR comments on An example of self-fulfilling spurious proofs in UDT - Less Wrong Discussion

20 Post author: cousin_it 25 March 2012 11:47AM

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Comment author: gRR 26 March 2012 01:57:52AM *  0 points [-]

I thought it couldn't find any other proofs of length < N, because it would imply there was no proof of S. But this is not a problem if S is false... Ok, modification:

def U(): Enumerate proofs by length up to a very large N
if found a proof that "A()==1 implies U()==5, and A()!=1 implies U()<=5"
then if(A()==1) return 5 if found any other proof of the same form
then whatever A() return 0
if(A()==2) return 10
return 0

EDIT: Wait, this is not good, now if(A()==2) is unreachable...
EDIT2: No, not actually unreachable, but any proof for a statement of the form "A()==2 => U()==10..." must be of length > N, which is what was needed, I suppose. Still feels like cheating, but I'm not sure why...

Comment author: cousin_it 26 March 2012 07:56:48AM *  1 point [-]

What's the intended consequence of A()==2 in your implementation of U? Is it U()==0 or U()==10? And which of those would actually happen?

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