By “Upsilon couldn’t exist”, I mean that Upsilon doesn’t live in any of the possible worlds (or only in insignificantly few of them), not that it couldn’t appear in the possible world where you are speaking with Omega.
The convention is that the possible worlds don’t logically contradict each other, so two different outcomes of coin tosses exist in two slightly different worlds, both of which you care about (this situation is not logically inconsistent). If Upsilon lives on such a different possible world, and not on the world with Omega, it doesn’t make Upsilon impossible, and so you care what it does. In order to replicate Counterfactual Mugging, you need the possible worlds with Upsilons to be irrelevant, and it doesn’t matter that Upsilons are not in the same world as the Omega you are talking to.
(How to correctly perform counterfactual reasoning on conditions that are logically inconsistent (such as the possible actions you could make that are not your actual action), or rather how to mathematically understand that reasoning is the septillion dollar question.)
Ah, I see. You’re saying Omega must prove to you that your prior made Upsilon less likely than Omega all along. (By the way, this is an interesting way to look at modal logic, I wonder if it’s published anywhere.) This is a very tall order for Omega, but it does make the two scenarios logically inconsistent. Unless they involve “deception”—e.g. Omega tweaking the mind of counterfactual-you to believe a false proof. I wonder if the problem still makes sense if this is allowed.
By “Upsilon couldn’t exist”, I mean that Upsilon doesn’t live in any of the possible worlds (or only in insignificantly few of them), not that it couldn’t appear in the possible world where you are speaking with Omega.
The convention is that the possible worlds don’t logically contradict each other, so two different outcomes of coin tosses exist in two slightly different worlds, both of which you care about (this situation is not logically inconsistent). If Upsilon lives on such a different possible world, and not on the world with Omega, it doesn’t make Upsilon impossible, and so you care what it does. In order to replicate Counterfactual Mugging, you need the possible worlds with Upsilons to be irrelevant, and it doesn’t matter that Upsilons are not in the same world as the Omega you are talking to.
(How to correctly perform counterfactual reasoning on conditions that are logically inconsistent (such as the possible actions you could make that are not your actual action), or rather how to mathematically understand that reasoning is the septillion dollar question.)
Ah, I see. You’re saying Omega must prove to you that your prior made Upsilon less likely than Omega all along. (By the way, this is an interesting way to look at modal logic, I wonder if it’s published anywhere.) This is a very tall order for Omega, but it does make the two scenarios logically inconsistent. Unless they involve “deception”—e.g. Omega tweaking the mind of counterfactual-you to believe a false proof. I wonder if the problem still makes sense if this is allowed.