- #1
Jamma
- 432
- 0
Hi all. I'm sure a lot of you will have seen this (possibly a few will be sick of seeing it, I don't know) but I've only just seen it.
http://en.wikipedia.org/wiki/Unexpected_hanging_paradox
Is it not a bit embarrassing/degrading for philosophy to state that: "...have even led to it being called a "significant problem" for philosophy." ?
As far as I can make out, this isn't too difficult of a paradox to unravel.
If we look at the prisoner's logic (say by the point he has ruled out Thursday and Friday):
"I have ruled out Thursday and Friday, so if it is Wednesday and I haven't been hung yet, then I must be hung on Wednesday. But then I know I'll be hung on Wednesday, so I can't be hung then either."
or, more revealingly:
"By MY logic, I can't be hung on Thursday or Friday, so by MY logic, if it's Wednesday, I will definitely be hung, which wouldn't be surprising, so I won't be hung on Wednesday."
Is it not obvious where this paradox is coming from? We have a logical system but where we impose another rule which says that "if we conclude logically [I will not be hung on x-day] then [it is possible I will be hung on x-day]" (since it will then be a surprise).
It seems to me that the paradox is coming about from the fact that our logical system refers to its own conclusions in a non-trivial way, making it obviously non consistent. We have effectively set as a rule "any conclusion which we can make logically about when the prisoner cannot be hung must also be false".
It's be nice to get some other views on this paradox from people who have a better way with words than me! :D
http://en.wikipedia.org/wiki/Unexpected_hanging_paradox
Is it not a bit embarrassing/degrading for philosophy to state that: "...have even led to it being called a "significant problem" for philosophy." ?
As far as I can make out, this isn't too difficult of a paradox to unravel.
If we look at the prisoner's logic (say by the point he has ruled out Thursday and Friday):
"I have ruled out Thursday and Friday, so if it is Wednesday and I haven't been hung yet, then I must be hung on Wednesday. But then I know I'll be hung on Wednesday, so I can't be hung then either."
or, more revealingly:
"By MY logic, I can't be hung on Thursday or Friday, so by MY logic, if it's Wednesday, I will definitely be hung, which wouldn't be surprising, so I won't be hung on Wednesday."
Is it not obvious where this paradox is coming from? We have a logical system but where we impose another rule which says that "if we conclude logically [I will not be hung on x-day] then [it is possible I will be hung on x-day]" (since it will then be a surprise).
It seems to me that the paradox is coming about from the fact that our logical system refers to its own conclusions in a non-trivial way, making it obviously non consistent. We have effectively set as a rule "any conclusion which we can make logically about when the prisoner cannot be hung must also be false".
It's be nice to get some other views on this paradox from people who have a better way with words than me! :D