Re: “I can write a program P that iterates through all possible proofs in S of length < 3^^^3 bits, and create a list of all TMs provable to terminate in less than 3^^^3 bits in S.”
An unspecified halting analysis on 2^3^^^3 programs?!?
Not within the universe’s expected lifespan, you can’t!
Apart from that, this looks rather like an intractable rearrangement of:
Re: “I can write a program P that iterates through all possible proofs in S of length < 3^^^3 bits, and create a list of all TMs provable to terminate in less than 3^^^3 bits in S.”
An unspecified halting analysis on 2^3^^^3 programs?!?
Not within the universe’s expected lifespan, you can’t!
Apart from that, this looks rather like an intractable rearrangement of:
http://en.wikipedia.org/wiki/Berry_paradox