I’d say that this is too optimistic. Omega checks the future and if, in fact, you would eventually win the lottery if you started playing, then deluding you about lotteries might be a good strategy. But for most people that Omega talks to, this wouldn’t work.
It’s possible that the number of falsehoods that have one-in-a-million odds of helping you exceeds a million by far, and then it’s very likely that Omega (being omniscient) can choose one that turns out to be helpful. But it’s more interesting to see if there are falsehoods that have at least a reasonably large probability of helping you.
True; being deluded about lotteries is unlikely to have positive consequences normally, so unless something weird is going to go on in the future (eg: the lottery machine’s random number function is going to predictably malfunction at some expected time, producing a predictable set of numbers; which Omega then imposes on your consciousness as being ‘lucky’), that’s not a belief with positive long-term consequences. That’s not an impossible set of circumstances, but it is an easy-to-specify set, so in terms of discussing ‘a false belief which would be long-term beneficial’, it leaps readily to mind.
I’d say that this is too optimistic. Omega checks the future and if, in fact, you would eventually win the lottery if you started playing, then deluding you about lotteries might be a good strategy. But for most people that Omega talks to, this wouldn’t work.
It’s possible that the number of falsehoods that have one-in-a-million odds of helping you exceeds a million by far, and then it’s very likely that Omega (being omniscient) can choose one that turns out to be helpful. But it’s more interesting to see if there are falsehoods that have at least a reasonably large probability of helping you.
True; being deluded about lotteries is unlikely to have positive consequences normally, so unless something weird is going to go on in the future (eg: the lottery machine’s random number function is going to predictably malfunction at some expected time, producing a predictable set of numbers; which Omega then imposes on your consciousness as being ‘lucky’), that’s not a belief with positive long-term consequences. That’s not an impossible set of circumstances, but it is an easy-to-specify set, so in terms of discussing ‘a false belief which would be long-term beneficial’, it leaps readily to mind.