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TheOtherDave comments on I Will Pay $500 To Anyone Who Can Convince Me To Cancel My Cryonics Subscription - Less Wrong
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By examining the history of interactions which occured between the two states.
Because it is very easy to construct thought experiments which show that thought, behavior, and memory are not sufficient for making a determination. For example, imagine a non-destructive sci-fi teleporter. The version of you I'm talking to right now walks into the machine, sees some flashing lights, and then walks out. Some time later another Dave out of a similar machine on Mars. Now step back a moment in time. Before walking into the machine, what experience do you expect to have after: (1) walking back out or (2) waking up on Mars?
Well, yes, but what are you looking for when you do the examination?
That is, OK, you examine the history, and you think "Well, I observe X, and I don't observe Y, and therefore I conclude identity was preserved." What I'm trying to figure out is what X and Y are.
Both.