I don't see how. Even if I am "split in two", "I" certainly still exist, if even in two different instantiations. I simply do not see how this special case is any kind of argument against the notion that a person can live on after their body dies. If, in the case you describe, there are two "Freds", so what?
This is of course hypothetical, as no one has ever experienced that in any way... but I don't think that you would be "split in two".
As I see it - and this is not irrelevant philosophical, but based on cognitive research - the consciousness is based on the physical reality of the brain. That means that even a brain that is identical as much as you can get it does not produce the same consciousness.
So in this case, it would not be "you" in two different instantiations. It would be "you" and "someone else" who might share the same personality, the same memories, the same way of thinking. But not "you".
FrumiousBandersnatch used the StarTrek teleporter as an example in his post. This is indeed a good way of showing both perspectives... outside and inside.
When Commander Riker gets teleported, for all regards, nothing has changed. It was "Commander Riker" before, and it is "Commander Riker" after. He looks the same, acts the same.
But there was this instance where Riker was "split" in a transporter accident. Suddenly, there are two Rikers. And while both of them believe to be the "real" Riker, they both are distinct persons. They are not a single consciousness within two bodies... they are seperate conscious entities.
Fiction, of course. But based on what we know about how consciousness works.
I politely suggest that you may be letting irrelevant - irrelevant in a sense I am about to qualify - philosophical questions obscure the issue.
Here is the point: When Fred says "I would like to live on beyond death", he is simply saying that he as a subject who experiences things wants to continue to experience those things. Fred could probably care less that there is another "copy" of him walking around. In fact "Fred 1" and "Fred 2", while initially identical, will certainly "diverge" as time progresses and, for all intents and purposes, become two distinct individuals.
Yes. Exactly what I am saying. But this is the problem: "he as a subject who experiences things"
does not continue to experience those things. Someone else, who is very very similar to him, almost identical to him, continues to experience these things... Fred does not.
While it is an interesting philosophical question "Which one is really Fred", it is not relevant to what really matters - the original Fred persists as a "being that experiences", even if there are two of them.
Or, put another way, if someone were to create an identical copy of me right now, would that in any sense diminish my experience of living life? Of course not.
No. Making a copy of you would not diminish you. Making a copy of you
and then killing the original you... that would diminish you.