Good point! Lewis’ notation P_+(HEADS) does indeed refer to the conditional credence upon learning that it’s Monday, and he sets it to 2⁄3 by reasoning backward from P(HEADS) = 1⁄2 and using my (1).
So yes, there are indeed people who believe that if Beauty is told that it’s Monday, then she should update to believing that the coin was more likely heads than not. Which seems weird to me—I have a great deal more suspicion that (1) is unjustifiable than that (2) is.
If you half and don’t think that your credence should be 2⁄3 in heads after finding out it’s Monday you violate the conservation of evidence. If you’re going to be told what time it is, your credence might go up but has no chance of going down—if it’s day 2 your credence will spike to 100, if it’s day 1 it wont’ change.
Is conversation of expected evidence a reasonably maintainable proposition across epistemically hazardous situations such as memory wipes (or false memories, self-duplicates and so on)? Arguably, in such situation it is impossible to be perfectly rational since the thing you do your reasoning with is being externally manipulated.
Yes—Lewis held this, for instance, in the most famous paper on the topic.
Good point! Lewis’ notation P_+(HEADS) does indeed refer to the conditional credence upon learning that it’s Monday, and he sets it to 2⁄3 by reasoning backward from P(HEADS) = 1⁄2 and using my (1).
So yes, there are indeed people who believe that if Beauty is told that it’s Monday, then she should update to believing that the coin was more likely heads than not. Which seems weird to me—I have a great deal more suspicion that (1) is unjustifiable than that (2) is.
If you half and don’t think that your credence should be 2⁄3 in heads after finding out it’s Monday you violate the conservation of evidence. If you’re going to be told what time it is, your credence might go up but has no chance of going down—if it’s day 2 your credence will spike to 100, if it’s day 1 it wont’ change.
Is conversation of expected evidence a reasonably maintainable proposition across epistemically hazardous situations such as memory wipes (or false memories, self-duplicates and so on)? Arguably, in such situation it is impossible to be perfectly rational since the thing you do your reasoning with is being externally manipulated.
You would violate conservation of expected evidence if
P(Monday) + P(Tuesday) = 1
However this is not the case because P(Monday) = 1 and P(Tuesday) = 1⁄2