To me the scenario seems to be as simple as: If Omega predicts X, X will happen. If X wouldn’t have happened, Omega wouldn’t predict X.
Sounds like you might be having confusion resulting from circular mental causal models. You’ve got an arrow from Omega to X. Wrong direction. You want to reason, “If X is likely to happen, Omega will predict X.”
Sure. So, X implies that Omega will predict X. The four possible states of the universe:
Where X is “You will give Omega $5 if Y happens” and Y is “Omega appears, tells you it predicted X, and asks you for $5″:
1) X is true; Omega does Y 2) X is false; Omega does Y 3) X is true; Omega does not do Y 4) X is false; Omega does not do Y
Number two will not happen because Omega will not predict X when X is false. Omega doesn’t even appear in options 3 and 4, so they aren’t relevant. The last remaining option is:
X is true; Omega does Y. Filling it out:
X is “You will give Omega $5 if Omega appears, tells you it predicted X, and asks you for $5.”
Hmm… that is interesting. X includes a reference to X, which isn’t a problem in language, but could be a problem with the math. The problem is not as simple as putting “you will give Omega $5” in for X because that isn’t strictly what Omega is asking.
The easiest simplification is to take out the part about Omega telling you it predicted X… but that is a significant change that I consider it a different puzzle entirely.
X is “You will give Omega $5 if Omega appears, tells you it predicted X, and asks you for $5.”
That is an interesting math problem. And the math problem has an solution, which is called a quine). So the self-referentialness of the prediction is not by itself a sufficient objection to your scenario.
Sounds like you might be having confusion resulting from circular mental causal models. You’ve got an arrow from Omega to X. Wrong direction. You want to reason, “If X is likely to happen, Omega will predict X.”
I believe the text you quote is intended to be interpreted as material implication, not causal arrows.
Sure. So, X implies that Omega will predict X. The four possible states of the universe:
Where
X is “You will give Omega $5 if Y happens” and
Y is “Omega appears, tells you it predicted X, and asks you for $5″:
1) X is true; Omega does Y
2) X is false; Omega does Y
3) X is true; Omega does not do Y
4) X is false; Omega does not do Y
Number two will not happen because Omega will not predict X when X is false. Omega doesn’t even appear in options 3 and 4, so they aren’t relevant. The last remaining option is:
X is true; Omega does Y. Filling it out:
X is “You will give Omega $5 if Omega appears, tells you it predicted X, and asks you for $5.”
Hmm… that is interesting. X includes a reference to X, which isn’t a problem in language, but could be a problem with the math. The problem is not as simple as putting “you will give Omega $5” in for X because that isn’t strictly what Omega is asking.
The easiest simplification is to take out the part about Omega telling you it predicted X… but that is a significant change that I consider it a different puzzle entirely.
Is this your objection?
That is an interesting math problem. And the math problem has an solution, which is called a quine). So the self-referentialness of the prediction is not by itself a sufficient objection to your scenario.
Nice, thanks.