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The ghost of Parnell is Far, the presentation to the Queen is Near?
Perhaps. I had thought of the quote in the context of a distinction between epistemic/Bayesian probability and physical possibility or probability. For us (though perhaps not for Father Brown) the ghost story is physically impossible, it contradicts the basic laws of reality, while the presentation story does not. (In terms of the MWI we might say that there is a branch of the wavefunction where Gladstone offered the Queen a cigar, but none where a ghost appeared to him.) However, we might very well be justified in assigning the ghost story a higher epistemic probability, because we have more underlying uncertainty about (to use your words) Far concepts like the possibility of ghosts than about Near ones like how Gladstone would have behaved in front of the Queen.
I seem to instinctively assign the ghost story a lower probability. The lesson of the quote might still be valid, can you come up with an example that would work for me?
Sure. Take one mathematical fact which the mathematical community accepts as true, but which has a complicated proof only recently published and checked. Surely your epistemic probability that there is a mistake in the proof and the theorem is false should be larger than the epistemic probability of the Gladstone story (if you are not convinced, add more outrageous details to it, like Gladstone telling the Queen "What's up, Vic?"). But according to your current beliefs, in the actual world the theorem is necessarily true and its negation impossible, while the Gladstone story is possible in the MWI sense.
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