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Dentin comments on I need a protocol for dangerous or disconcerting ideas. - Less Wrong Discussion
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I suspect part of the issue here is that your concept of subjective self isn't constructed to be compatible with these kinds of thought experiments, or with the idea that reality may be forking and terminating all the time. I can say that because mine -is- compatible with such things, and as a result pretty much all of this category of problem doesn't even show up on my radar.
Assuming I had a magical copying device that could copy my body at a sufficient accuracy, I could:
use the copier to create a copy of myself, and as the copy I could do the household chores then self destruct to free up resources without worrying about my 'self' dying.
use the copier to create a copy of myself, then as the original go do the chores/self destruct without worrying about my 'self' dying.
if there was a resource conflict which required the destruction of a copy, I could decide that I was the 'least important' copy and self terminate without worrying about my 'self' dying.
When a person's sense of identity can do the above things, concerns about your dust scenario really don't even show up as relevant - it doesn't matter which timeline or state you end up in, so long as your self is active somewhere, you're good.
How would you treat the above situations?
I wouldn't do it in the first place, since there's a fifty percent chance of me winding up doomed. But if the copy is already created than no, it would not be me dying.
That is absolutely dying.
Same thing for this.
That's what I figured. If anything, I'd say that this is your core issue, not dust theory. Your sense of subjective self just doesn't map well onto what it's actually possible to do, so of course you're going to get garbage results from time to time.