If I were in some sort of situation where I was sick from a terminal illness, then I would, because if I didn't know, the anticipation and... well... unknown would drive me crazy.
Now, if some mystical seer walked up to me on the street and asked if I would like to know the date of my death, I would give him a stern "No, thank you" and walk away. It's like the exact opposite of the terminally ill example. If I knew the date of my own death and I was perfectly healthy at the time, then the knowledge would drive me crazy.
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