When you’ve eliminated the impossible, if whatever’s left is sufficiently improbable, you probable haven’t considered a wide enough space of candidate possibilities.
Seems fair. The Holmes saying seems a bit funny to me now that I think about it, because the probability of an unlikely event changes to become more likely when you’ve shown that reality appears constrained from the alternatives. I mean, I guess that’s what he’s trying to convey in his own way. But, by the definition of probability, the likelihood of the improbable event increases as constraints appear preventing the other possibilities. You’re going from P(A) to P(A|B) to P(A|(B&C)) to.. etc. You shouldn’t be simultaneously aware that an event is improbable and seeing that no other alternative is true at the same time, unless you’re being informed of the probability, given the constraints, by someone else, which means that yes, they appear to be considering more candidate possibilities (or their estimate was incorrect. Or something I haven’t thought of...).
When you’ve eliminated the impossible, if whatever’s left is sufficiently improbable, you probable haven’t considered a wide enough space of candidate possibilities.
Seems fair. The Holmes saying seems a bit funny to me now that I think about it, because the probability of an unlikely event changes to become more likely when you’ve shown that reality appears constrained from the alternatives. I mean, I guess that’s what he’s trying to convey in his own way. But, by the definition of probability, the likelihood of the improbable event increases as constraints appear preventing the other possibilities. You’re going from P(A) to P(A|B) to P(A|(B&C)) to.. etc. You shouldn’t be simultaneously aware that an event is improbable and seeing that no other alternative is true at the same time, unless you’re being informed of the probability, given the constraints, by someone else, which means that yes, they appear to be considering more candidate possibilities (or their estimate was incorrect. Or something I haven’t thought of...).
Maybe he meant how a priori improbable it is?
That sounds right.