That proves that A can’t cooperate, but it doesn’t prove that it defects, since there remains the possibility that the program doesn’t output anything.
The program is guaranteed to finish because there’s a finite number of proofs to check, and checking every proof takes finite time (a proof checker cannot loop forever on a given proof).
That proves that A can’t cooperate, but it doesn’t prove that it defects, since there remains the possibility that the program doesn’t output anything.
The program is guaranteed to finish because there’s a finite number of proofs to check, and checking every proof takes finite time (a proof checker cannot loop forever on a given proof).
So with an argument like the one that A defects, I can prove that your mind is inconsistent:
“Cousin_it will never prove this statement to be true.”
I know that this is true, and presumably you know it too… which is a contradiction.
I don’t know that it’s true.
And I don’t see how this makes the proof wrong.
It doesn’t make the proof wrong.
Oh, sorry then :-)
“Lucas cannot consistently assert this sentence” is an old philosophers’ joke, actually.
Yes, I can.