If L:ob’s theorem is true, then surely we can use it without any reference to the details of its proof? Isn’t the point of a proof to obtain a black box, so that we do not have to worry about all the various intermediate steps? And in this case, wouldn’t it defeat the purpose of having a proof if, to explain how the proof was misapplied, we had to delve deep into the guts of the proof, rather than just pointing to the relevant features of its interface?
If L:ob’s theorem is true, then surely we can use it without any reference to the details of its proof? Isn’t the point of a proof to obtain a black box, so that we do not have to worry about all the various intermediate steps? And in this case, wouldn’t it defeat the purpose of having a proof if, to explain how the proof was misapplied, we had to delve deep into the guts of the proof, rather than just pointing to the relevant features of its interface?