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cousin_it comments on Reflection in Probabilistic Logic - Less Wrong
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Congrats to MIRI! Just some comments that I already made to Mihaly and Paul:
1) Agree with Abram that unidirectional implication is disappointing and the paper should mention the other direction.
2) The statement "But this leads directly to a contradiction" at the top of page 4 seems to be wrong, because the sentence P(G)<1 isn't of the form P(phi)=p required for the reflection principle.
3) It's not clear whether we could have bidirectional implication if we used closed intervals instead of open, maybe worth investigating further.
We tried closed intervals a fair bit, no luck so far.
Posted an edited version in response to some of these issues. Thanks again for the remarks!
(I feel less strongly about the bidirectional implication than you; as math I can see why you would definitely want it, but in practice I am nearly as happy to eat the epsilon of error.)
My concern is more about "leaving money on the table" so to speak. The result with epsilon error would be satisfying if we knew it was impossible to do better.
I consider Paul's response to be sufficient.