The way that you phrase this, “suppose the plausibility of A jumps to 80,” has no rigor. Depending on the way you choose to calculate this, it could lead to change in B or not.
if we consider them independent, we could imagine 100 different worlds, and we would expect in 40 of these worlds A to be true, etc., which would leave us with:
10 worlds where AB is true
30 worlds where A(!B) is true
15 worlds where (!A)B is true
45 worlds where (!A)(!B) is true
In general I would expect evidence to come in the form of determining that we are not in a certain world. If we determine that the probability of A rises, because we know ourselves not to be in any world where (!A)(!B) is true, then we would have to adjust the probability of B.
Your given reason, “because it’s looking very cloudy this afternoon.” Would probably indicate that we are uniformly less likely to be in any given world where A is false. In this case, the plausibility of A should jump without effecting the plausibility of B.
So what I’m really saying is that there is no sense in which statements are independent, only a sense in which evidence is independent of statements.
However, a lot of this is speculation since it really isn’t addressed directly in the first chapter, as Christian points out.
The way that you phrase this, “suppose the plausibility of A jumps to 80,” has no rigor. Depending on the way you choose to calculate this, it could lead to change in B or not.
if we consider them independent, we could imagine 100 different worlds, and we would expect in 40 of these worlds A to be true, etc., which would leave us with:
10 worlds where AB is true 30 worlds where A(!B) is true 15 worlds where (!A)B is true 45 worlds where (!A)(!B) is true
In general I would expect evidence to come in the form of determining that we are not in a certain world. If we determine that the probability of A rises, because we know ourselves not to be in any world where (!A)(!B) is true, then we would have to adjust the probability of B.
Your given reason, “because it’s looking very cloudy this afternoon.” Would probably indicate that we are uniformly less likely to be in any given world where A is false. In this case, the plausibility of A should jump without effecting the plausibility of B.
So what I’m really saying is that there is no sense in which statements are independent, only a sense in which evidence is independent of statements.
However, a lot of this is speculation since it really isn’t addressed directly in the first chapter, as Christian points out.