Why is #4 above “less than” and not “less than or equal to”?
::thinks a bit::
What this is saying is, if there are logically possible worlds where A is false and B is true, but no logically possible worlds where A is true and B is false, then A is strictly less likely than B—that all logically possible worlds have nonzero probability. This is a pretty strong assumption...
Epistemic probabilities / plausibilities are not properties of the external world; they are properties of the information you have available. Recall that the premise X contains all the information you have available to assess plausibilities. If X does not rule out a possible world, what basis do you have for assigning it 0 probability? Put another way, how do you get to 100% confidence that this possible world is in fact impossible, when you have no information to rule it out?
Why is #4 above “less than” and not “less than or equal to”?
::thinks a bit::
What this is saying is, if there are logically possible worlds where A is false and B is true, but no logically possible worlds where A is true and B is false, then A is strictly less likely than B—that all logically possible worlds have nonzero probability. This is a pretty strong assumption...
Epistemic probabilities / plausibilities are not properties of the external world; they are properties of the information you have available. Recall that the premise X contains all the information you have available to assess plausibilities. If X does not rule out a possible world, what basis do you have for assigning it 0 probability? Put another way, how do you get to 100% confidence that this possible world is in fact impossible, when you have no information to rule it out?