> I think the next step is to demand that proofs either be human-scale or they prove that a human-scale proof is impossible and the machine proof is as good as it gets.
> I suspect that's possible without tripping over the halting problem. (But I can't prove it.)
I doubt that it is. For the language of proofs to be powerful enough to be able to
express an arbitrary proof it would have be Turing Complete. Proving that a proof
is the smallest proof of a given concept (i.e. there is no smaller human understandable proof)
would then be proving the minimality of a program in a Turing Complete language.
> I suspect that's possible without tripping over the halting problem. (But I can't prove it.)
I doubt that it is. For the language of proofs to be powerful enough to be able to express an arbitrary proof it would have be Turing Complete. Proving that a proof is the smallest proof of a given concept (i.e. there is no smaller human understandable proof) would then be proving the minimality of a program in a Turing Complete language.