I understand the principle, yes. But it means if your friend is a liar, no argument he gives needs to be examined on its own merits. But what if he is a liar and he saw a UFO? What if P(he is a liar) and P(there’s a UFO) are not independent? I think if they are independent, your argument works. If they are not, it doesn’t. If UFOs appear mostly to liars, you can’t ignore his evidence. Do you agree? In my case, they are not independent: it’s easier to argue for a true proposition, even for a very intelligent AI. Here I assume that P must be strictly less than 1 always.
I understand the principle, yes. But it means if your friend is a liar, no argument he gives needs to be examined on its own merits. But what if he is a liar and he saw a UFO? What if P(he is a liar) and P(there’s a UFO) are not independent? I think if they are independent, your argument works. If they are not, it doesn’t. If UFOs appear mostly to liars, you can’t ignore his evidence. Do you agree? In my case, they are not independent: it’s easier to argue for a true proposition, even for a very intelligent AI. Here I assume that P must be strictly less than 1 always.