This conversation, while fascinating to watch, will obviously go nowhere fast because of the apparent vast differences in morals/perceptions that each one of the speakers has.
Though I suppose that's the most stimulating conversation to have?
I suppose I'll weigh in (Considering that this is a subject which is very fascinating to me)
I'm mostly concerned with continuation of consciousness rather than life or death, especially in this situation. This does raise a point that shakes me too the very core:
Several months ago, I had a bone marrow biopsy. They administered me anesthesia to keep me happy through the procedure. I thought I handled it extremely well, apparently remembering the whole procedure and requiring no recovery time afterward. From what I recall, I was walked out of the operating room (Having not remembered feeling a thing) into my recovery room, where I presently took to eating a cracker and quietly drinking some water. However, all of those in attendance at the time say that I lucidly described the entire procedure in great detail. Still to this day I can't believe that this is the case. I remember everything except about the operation itself, and anything pertaining to it afterward.
ANYWAY. How does this relate to transporters? Well, during the entire time that I was in the operation, presumably, I was awake and realizing what was going on, and even then, my subconscious continued to function (extremely poorly mind you) But my brain did not go on pause during this experience. I continued thoughts and whatnots all throughout, and so I am the same mind.
That's really the concerning thing about the use of transporters, not whether one's body is preserved during transport or not (As it certainly seems to be,) nor whether one remains the same person with the same thoughts, memories, etc. etc. etc. And indeed, this person is functionally identical to the first. However, what the people who WOULDN'T use the transporter (Myself included) are concerned about is if the same mind continues to work through the process, or if it is merely a copy. We probably could never know for certain.
However, it seems that to be absolutely sure, it would be wise to gradually shift someone from one place to another, not to pop someone out of existence in one place and into existence in another. If someone were to be functioning in both places at once, then SURELY every bit of them is the same life, not only the same structure. Then one can be destroyed because its perception was shared with the one on the other side (If destruction is even necessary.)
I like to think of it this way: You have a choice of being teleported to far away lands using one of two methods: One way is to get shot in the head with a transportation-gun; it kills you, but makes a duplicate in the location of your choice.
Alternately, you could be taken there piece by piece (Each piece still remaining connected some way, of course) including your brain, with parts transported working with parts still remaining, until all of the parts are transported.
I don't know about anyone else, but the second option seems to preserve the SPECIFIC INSTANCE of the person, rater than just their form and function.
(PS. I suppose the whole thing does relate to the ship of Theseus to me. I would be inclined to think that a a dynamic system, such as a brain or a computer, would have to be preserved this way, and to a static system like a ship, it wouldn't really matter.
PPS: I also hate to think about the idea of completely suspending someone in time: I.E. freezing them. Does this count as death? Or at least the same conscious person? I don't think we could definitively ever say. But anyway, I'd take a transporer, but only if it goes *fade!* rather than *pop!*)