They figure that there is a 50% chance of being on Vulcan.
They then look at the following statement: “If you are on Vulcan, then you are on the mountain” and redistribute all of the Vulcan probability to the Vulcan Mountain. The mistake is not realising that the constraint of 50% chance of being on Vulcan only applies at the start and isn’t necessarily maintained. But this feels weird because the statement seems to be limiting its scope to Vulcan; or at least until you start looking at the counterfactual.
This. The phrasing “if you are on Vulcan, then you are on the mountain” *sounds* like it should be orthogonal to, and therefore gives no new information on and cannot affect the probability of, your being on Vulcan.
This is quite false, as can be shown easily by the statement “if you are on Vulcan, then false”. But it is a line of reasoning I can see being tempting.
I think people reason as follows:
They figure that there is a 50% chance of being on Vulcan.
They then look at the following statement: “If you are on Vulcan, then you are on the mountain” and redistribute all of the Vulcan probability to the Vulcan Mountain. The mistake is not realising that the constraint of 50% chance of being on Vulcan only applies at the start and isn’t necessarily maintained. But this feels weird because the statement seems to be limiting its scope to Vulcan; or at least until you start looking at the counterfactual.
This. The phrasing “if you are on Vulcan, then you are on the mountain” *sounds* like it should be orthogonal to, and therefore gives no new information on and cannot affect the probability of, your being on Vulcan.
This is quite false, as can be shown easily by the statement “if you are on Vulcan, then false”. But it is a line of reasoning I can see being tempting.