I think I agree. But I would formulate it otherwise:
i) Omega’s prediction are true.
ii) Omega predicts that carrot-choosers have heart attacks.
c) Therefore, carrot-choosers have heart attacks.
As soon as you accept i), c) follows if we add ii). I don’t know how you define “causal mechanism”. But I can imagine a possible world where no biological mechanism connects carrot-choosing with heart attacks but where “accidentally” all the carrot-choosers have heart-attacks (Let’s imagine running worlds on a computer countless times. One day we might observe such a freak world). Then c) would be true without there being some sort of “causal mechanism” (as you might define it I suppose?). If you say that in such a freak world carrot-choosing and heart attacks are causally connected, then I would agree that c) can only be true if there is a underlying causal mechanism.
But in that case, when Omega tells me that if I choose carrots I’ll have a heart attack, then almost certainly I’m not in a freak world, and actually Omega is wrong.
Assuming i), I would rather say that when Omega tells me that if I choose carrots I’ll have a heart attack, then almost certainly I’m not in a freak world, but in a “normal” world where there is a causal mechanism (as common sense would call it). But the point stands that there is no necessity for a causal mechanism so that c) can be true and the game can be coherent. (Again, this point only stands as long as one’s definition of causal mechanism excludes the freak case.)
Seems like there are two possible cases. Either:
a) There is a causal mechanism
b) None of the reasoning you might sensibly make actually works.
Since the reasoning only works in the causal mechanism case, the existence of the freak world case doesn’t actually make any difference, so we’re back to the case where we have a causal mechanism and where RichardKennaway has explained everything far better than I have.
I think I agree. But I would formulate it otherwise:
i) Omega’s prediction are true. ii) Omega predicts that carrot-choosers have heart attacks.
c) Therefore, carrot-choosers have heart attacks.
As soon as you accept i), c) follows if we add ii). I don’t know how you define “causal mechanism”. But I can imagine a possible world where no biological mechanism connects carrot-choosing with heart attacks but where “accidentally” all the carrot-choosers have heart-attacks (Let’s imagine running worlds on a computer countless times. One day we might observe such a freak world). Then c) would be true without there being some sort of “causal mechanism” (as you might define it I suppose?). If you say that in such a freak world carrot-choosing and heart attacks are causally connected, then I would agree that c) can only be true if there is a underlying causal mechanism.
But in that case, when Omega tells me that if I choose carrots I’ll have a heart attack, then almost certainly I’m not in a freak world, and actually Omega is wrong.
Assuming i), I would rather say that when Omega tells me that if I choose carrots I’ll have a heart attack, then almost certainly I’m not in a freak world, but in a “normal” world where there is a causal mechanism (as common sense would call it). But the point stands that there is no necessity for a causal mechanism so that c) can be true and the game can be coherent. (Again, this point only stands as long as one’s definition of causal mechanism excludes the freak case.)
Seems like there are two possible cases. Either: a) There is a causal mechanism b) None of the reasoning you might sensibly make actually works.
Since the reasoning only works in the causal mechanism case, the existence of the freak world case doesn’t actually make any difference, so we’re back to the case where we have a causal mechanism and where RichardKennaway has explained everything far better than I have.