Rolan, Arx: Exactly. The meat computer is in and of itself, not that special. It suffers the "Grandfather's Axe" problem over the course of a single human's life span. If you replace both the handle, and the blade, is it the same axe?
obligatory wikipediaIn this case, replacing the parts over time has no net negative effect on the person, because the "person" is not the physical body per se-- but is instead the process being hosted by that physical body.
The issue gets further complicated however. Let us look at a more easily examined system of similar ontological nature: A personal computer.
Over the years, a person builds a home-built computer from modular parts. As parts fail, they replace them. One of the parts to fail is the hard disk. Prior to cycling it out, they copy all the data off of it. The ontological question now is, did the old data get discarded with the dead HDD, or was the data salvaged from it?
I hold that the question is moot, because in the case of the human body, such copying happens anyway, as the physical atoms are replaced one by one over the person's lifetime.
To continue the computer analogy, we could say that the process supporting human conciousness may operate like a RAID array. As a part of normal operation, parts are swapped out with new ones, and old discarded, and data is recovered internally automatically. That way the organization of the "RAID array" remains constant, even though the data inside, and the drives that make it up, are both "lost" under some notions of ontological origin, and are just replacement parts and copies. Now, we can "fail" drives on the raid array sequentially, and drop in new drives to replace them, and rebuild the array from the parity data. The Raid array will do what it does naturally, and repair the array with the new parts, and continue to serve data as long as you stay under the threshold of replaced parts before parity is unable to reconstitute the array's contents. You can then have drives from each bay in the array that you have swapped out and rebuilt. You can take all those "failed" disks, and pop them into another raid controller, and tell it to resynchronize. You now have a complete copy of the array, on another controller.
There is nothing magically special about a human's conciousness, any more than the data on the raid array. There is nothing special about the physical body of a human, any more than the drives that make up the raid array. Both can be replaced and duplicated within the realm of reasonable justification.
I exist as the currently instantiated process that gives rise to my conciousness. That process can be seamlessly transferred to another substrate through incremental replacement, just as the data on a raid array can be. That process can likewise also be copied onto a new substrate directly while retaining the original, just like with the raid array. I am not magical.