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The classic formulation of the teleportation paradox goes something like: you have a machine that scans, disassembles, and reassembles you somewhere else instantaneously (modulo details of different explications). The problem which arises is usually: is the new you the "same" in some relevant sense, generally invoking continuity of consciousness.

My question is, pretty straightforwardly: what literature summarizes the present state of the debate, if any? Are there different schools claiming to have "settled" the problem, is there general consensus, or are people mostly still uncertain?

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    I'm sorry - is this too broad a question? I'm trying to understand the downvote...
    – commando
    Oct 18, 2015 at 18:39
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    Not my down vote: Parfitt starts his book Reasons and Persons with exactly that - but I take it as a rhetorical device to use a trope common to SF to explore what constitutes the nature of consciousness or mind; still it's worth noting that questions on AI, teleportation and the like tends to attract cranks of one kind or another - don't get me wrong I'm not claiming you are one ;). Oct 18, 2015 at 18:47
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    The no-cloning theorem in QI shows that quantum states aren't copyable - I'd doubt if Parfitts is interested in such details - I could be wrong: I just looked at the first few pages. Oct 18, 2015 at 19:04
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    Thank you, your comments alone are extremely helpful! Fortunately enough our library has that book on hand.
    – commando
    Oct 18, 2015 at 19:33

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Just a few. For continuous identity, "Ship of Theseus" paradox; for consciousness and identity, Donald Davidson's "Swamp Man Argument;" for scientific perspective on teleporting, Vlatko Vedral "Decoding Reality" and related papers. There is undoubtedly much, much more and there is just as undoubtedly no settled agreement on any of it.

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    I think the OP would be best assisted in his inquiries by reading over all that has been said in regard to the Swamp Man Argument. After reading up on the Ship of Theseus thought experiment, it seems to me that it leans more towards the metasphysical side of things. Correct me if I'm wrong. Oct 19, 2015 at 1:20
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    Yes, Ship of Theseus is an old chestnut, but historically basic to arguments of continuous identity, of whatever sort. Just sprang to mind. Oct 19, 2015 at 3:04

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