wedrifid comments on How to Convince Me That 2 + 2 = 3 - Less Wrong
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Exactly. And with slightly different wording a world in which it seems like you have changed from one logical world to another is itself a just a logically possible world.
That would be awkward! It would require an awful lot of reality testing on the question of just how logically impossible things were. Even after that your confidence in just about anything would be fubared.