This is an interesting question because as-is, I don't think anyone can really understand what it means to be someone else. For this purpose, I can say my consciousness is something that exists currently and has memories from before, but there is no way to verify that the memories were recorded by the same consciousness. There could have been a different person that no longer exists.
Perhaps a good alternate angle is to consider the “copy” (rather than “replacement”) proposition someone else mentioned: let's say a perfect copy of you could be made (i.e. the entirety of a consciousness is somehow material). Are the two consciousnesses linked somehow? Or are they completely separate despite thinking exactly alike, having the same memories &c.? If they are separate, what happens if the original is killed? Then, the next logical step is to ask how that is different from a consciousness transplant.
It's wild stuff. Or seems like it to a thus-far (presumed) single consciousness.
If you make an exact copy of me at time t, then until the original and the copy part ways and have distinct thoughts and experiences, they're both just me_t, one no more so than the other. At t+1, me_t doesn't exist any more; this is true regardless of how many copies of me_t once existed.
Perhaps a good alternate angle is to consider the “copy” (rather than “replacement”) proposition someone else mentioned: let's say a perfect copy of you could be made (i.e. the entirety of a consciousness is somehow material). Are the two consciousnesses linked somehow? Or are they completely separate despite thinking exactly alike, having the same memories &c.? If they are separate, what happens if the original is killed? Then, the next logical step is to ask how that is different from a consciousness transplant.
It's wild stuff. Or seems like it to a thus-far (presumed) single consciousness.