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PlaidX comments on The Presumptuous Philosopher's Presumptuous Friend - Less Wrong
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You can do both this experiment and newcomb without omega, or at least, you can start with a similar, but messier setup and bridge it to the tidy omega version using reasonable steps. But the process is very tedious.
Past discussions indicate quite conclusively that Newcomb is completely unmathematizable as a paradox. Every mathematization becomes trivial one was or the other, and resolves causality loop caused by Omega.
If problems with Omega can be pathological like that, it's a good argument to avoid using Omega unless absolutely necessary (in which case you can rethink if problem is even well stated).
I would be shocked if it didn't. It's a trivial problem.
Trivial how? Depending on mathematization it collapses to either one-boxing, or two-boxing, depending on how we break the causality loop.
If you decide first, trivially one-box. If Omega decides first, trivially two-box. If you have causality loop, your problem doesn't make any sense.