Bugmaster comments on First, they must be convinced to play the game - Less Wrong Discussion
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I've never been a Christian, so I could be wrong about this, but many Christians I'd met would disagree with you. They believe that if they die -- permanently, without hope of revival -- while being "right with God" (the precise meaning of which varies by sect), then they get to go to Heaven. Going to Heaven has infinite positive utility.
Desecration issues aside, if what the cryonics companies are selling is the real deal, then signing up for cryonics involves being bound to your physical body for a long time, potentially forever. Sure, you might be awakened at some distant point in the future, and there is some positive utility to living more days on this Earth, but this utility is finite.
Thus, the Christian has a choice between going to Heaven ASAP, and attaining an infinite positive utility; or signing up for cryonics and either attaining a finite positive utility (if it works), or keeping his utility unchanged for a long time (if it doesn't). Therefore, it would be irrational for the Christian to sign up for cryonics.
I don't see where the "permanently" part comes from. It may be the layman's interpretation, but I don't think it's Biblically motivated.