It kills the Lobian argument, I believe, since this implication “if there’s a proof that you cooperate, then cooperate ” is no longer true. Instead, here’s a Lobian argument for defection:
Suppose there is a proof that you defect. Then either there is a proof of contradiction, or there is no proof that your move is the same as your opponent’s. Either way, you defect.
It kills the Lobian argument, I believe, since this implication “if there’s a proof that you cooperate, then cooperate ” is no longer true. Instead, here’s a Lobian argument for defection:
Suppose there is a proof that you defect. Then either there is a proof of contradiction, or there is no proof that your move is the same as your opponent’s. Either way, you defect.