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MrHen comments on My Fundamental Question About Omega - Less Wrong
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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.