Re: the two generals, its applicability is limited to the very specific positive confirmation contained in the communication, right? For example, consider the following message:
Confirm attack at dawn, and please respond if you agree. If I receive your confirmation, I will not respond, so take my silence as final agreement on the plan. In any other scenario, I will not assume agreement, and send a message to resume the discussion.”
If the second general sends confirmation, and receives no response, don’t both generals now have complete information? Or am I missing the point of the exercise.
No, this doesn't work, since how can the other general know if the confirmation made it through. If he sent it, then he can't assume it makes it through, but you will be joining the attack only if it does.
Fitch's Paradox reminds me of Lob's theorem: if we can derive (Provability of P implies P) in a sufficiently strong proof system, we can derive P. But I'm not sure what to make of it: provability is a weird notion distinct from knowledge.
Existence of unknowable truths doesn't seems that paradoxical to me, though.
Re: the two generals, its applicability is limited to the very specific positive confirmation contained in the communication, right? For example, consider the following message:
Confirm attack at dawn, and please respond if you agree. If I receive your confirmation, I will not respond, so take my silence as final agreement on the plan. In any other scenario, I will not assume agreement, and send a message to resume the discussion.”
If the second general sends confirmation, and receives no response, don’t both generals now have complete information? Or am I missing the point of the exercise.
No, this doesn't work, since how can the other general know if the confirmation made it through. If he sent it, then he can't assume it makes it through, but you will be joining the attack only if it does.
Short story re: blue eyed islanders: https://slatestarcodex.com/2015/10/15/it-was-you-who-made-my-blue-eyes-blue/
Fitch's Paradox reminds me of Lob's theorem: if we can derive (Provability of P implies P) in a sufficiently strong proof system, we can derive P. But I'm not sure what to make of it: provability is a weird notion distinct from knowledge.
Existence of unknowable truths doesn't seems that paradoxical to me, though.
Very interesting comment! I wonder whether we can find a robust formal connection for the affinity you have mentioned...