Well, the current me right now is entirely different matter than the Phil Lynch of 10 years ago, right? Ship of Theseus paradox and all that. So what's the dif if it happens much quicker?
In one case, that of biological aging, Phil has worked as a continuous system (cells being replaced in a continuously functioning system, just as the "working" ship of Theseus continues to function as a system as one plank is replaced at a time) over time. In another case, that of teleportation, there is a discontinuity. You cease to exist, however briefly, as a system. Your matter is converted into energy (all the planks shattered into sawdust) and then rearranged in a different space. A system, indistinguishably similar to your own, appears in a different space.
Consider that, by your logic, one might murder you in five minutes without harming you. This would NOT do you (present you, pre-five-minutes-from-now-you) any harm. Or perhaps let's make it five days or five years. I think you would object that future you is still you - at least in any case where this was a real-world situation removed from the cozy confines of philosophical reasoning.
The
Ship of Theseus line of reasoning pushes us to accept a purely functionalist reading of identity. Under this view, we would view "you" as a sort of computer program or computer file like an MP3. So long as the information is conserved and reinstantiated in a functioning system, there is no loss. And if the only thing that causes us to resist this line is a lingering superstition about "souls," then it would seem that we have no good reason to object to stepping on the transporter pad. But identity might not lie in any soul or in mere functionality.
I think prudential reasoning would
or should stop you from hopping in the transporter.
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I might allow for a replicator transporter to make a copy of me somewhere else. Perhaps my copy would materialize on a starship and observe great adventures. But would I (the original) really feel like I was one with my copy who warped away from Earth and never returned? No. I would feel cheated. I would wish that "I" were the one on the starship and NOT my copy. A conventional transporter, however, would not put me on the starship either! "I" would be destroyed and a perfect copy would enjoy all those adventures. In neither case (duplicator or destroyer) would I (as I understand myself as a conscious creature) be able to get to the ship by using the transporter. Without benefit of a shuttle craft, I would have to resign myself to accepting that I would never really know (first hand) what it is like to be on a starship (if Tapestry and Below Decks are any indicator, however, perhaps it's not all it's all that great!).