Be assured that I am not prone to having mystical experiences, but I do it must be said seem to spend an inordinate amount of time in that twilight zone between sleep and waking (either going into or coming out of sleep). And in such a state for some hours very early one morning I wrestled with the question of death and came to a conclusion.
At the end of it all I felt absolutely sure that I (and presumably you too) would never could never be totally snuffed out.
There are two basic ways of responding to such an 'insight', as I see it: to take it at face value (as I did at the time), or to take it merely as evidence for how our brains work.
On the second (and more plausible) interpretation, all I did on that sleepless morning was to demonstrate to myself that my conscious self (due to the limitations of my brain and presumably all human brains) was incapable of conceiving of its own future nonexistence.
I know some people claim to be able to conceive of their future nonexistence (and to be quite happy about the prospect), but I would argue (like Matthew Hutson) that such people are still imagining themselves as a faint presence in their own post-death future.
Of course, nothing concerning the reality or non-reality of survival can be inferred from the fact (if it is a fact) that we cannot conceive of our own individual deaths.
Just getting clear what (if anything) personal identity is and making sense of the notion of such an entity surviving the death of the body with which it had been associated is a very difficult task. Sometimes I think it is a futile one.
I may have more to say about these and related questions in the future, but, just to give an indication of the sort of thinking which I think touches on the nub of the problem, I want to mention a classic thought experiment devised by Derek Parfit.
Briefly, it is about a choice of means of transport. It is some time in the future and you need to visit Mars on a regular basis. You have the slow option of a space ship; or the speed-of-light option which involves a Star Trek-like scanner which records your body's exact physical state and sends the information to Mars where you are reconstructed, memories intact. The scanning process is fatal, but it doesn't matter as you will be aware only of having arrived on Mars.
Parfit thinks that people would get over their initial reluctance to use the new system very quickly, and that we wouldn't feel as though the reconstructed people were just copies of defunct originals.
But what if a number of copies were made? And, most importantly, how do I know that if I was scanned etc., I would, from a subjective point of view, 'wake up' on Mars (or anywhere), rather than just die, pure and simple, copy or no copy?*
Now, all this may sound very hypothetical and irrelevant to whether you or I will survive (in some sense) our respective deaths. But new developments in cosmology, notably the theory of eternal inflation, make it very relevant. For it appears likely that exact (and not so exact) copies of us do in fact exist in distant and forever inaccessible reaches of an unimaginably large and expanding complex of universes (variously called the multiverse or the megaverse).
I know it sounds fanciful, but leading physicists have put forward such views; and, though I remain personally skeptical about particular theories, the notion that the cosmos is (infinitely) more than what we can observe or even potentially have access to is very plausible and generally accepted in the physics community.
In the end, the (possible) existence of duplicate and similar worlds probably has no bearing on whether my subjective sense of self will be extinguished at my death. It is, however, a comfort to know that the cosmos may not be as boringly bounded as mid-20th century science suggested.
It may be going too far to say that anything is possible, but the vista of possibilities has certainly expanded.
*Parfit doesn't believe we relate to the future (or the future relates to us) in the way we think we do (or in the way we think it does). As I recall, he even suggests that the future should not concern us any more than the past.
When I first read Parfit's book Reasons and Persons I struggled with this idea for a while, but finally gave it up as being inconsistent with the fact that, as individuals, we plan (or fail to plan) for the future and enjoy or suffer the consequences. (Parfit's view would be, I presume, that these experiences were not being had by a self-entity that moved from the past to the future or perhaps by any entity at all.)