Some people want badly to live forever.
This has long been the case, but until recently it was an unrealistic goal -- unless interpreted very broadly, as in living forever through one's children, one's artworks, one's connectedness with the world, etc.
These "looser" ways of living forever are deeply meaningful -- they do, in a strong sense, involve one's mind living on after one's body's death. Each mind is a set of patterns, and in these ways many of the core patterns of one's mind can live on independently of the body that previously carried them.
But one thing that these looser forms of immortality don't give you is immortality of the self.
Advanced technology, however, may soon make this stronger form of immortality possible -- maybe through pharmacology or other biological means like stem cell infusions, maybe through nanotech bio-repair bots, or maybe via more controversial mechanisms like uploading.
However the technological details work out, for many of us, this prospect is tremendously exciting. For Cosmists who want to keep growing, choosing and enjoying, the prospect of not dying is often an appealing one.
Is Immortality Desirable?
But, although some people want badly to live forever, others badly want not to: they consider death intrinsic to the meaning of their lives.
Neither of these desires is intrinsically unhealthy or foolish: they just reflect different self-models, different ways of interpreting the relationship between the self and the world, and the relationships between selves that exist at different times.
Imposing immortality on those who don't want it, is nearly as bad as imposing death on those who don't want it.
Of course, either death-avoidance or death-seeking can be carried to unhealthy extremes.
Obsession with danger sports or dangerous drugs or outright suicidalness -- i.e. the Freudian "death-wish" -- are the obvious examples of unhealthy death-seeking.
Unhealthy death-avoidance could manifest itself as a reluctance to do anything even slightly dangerous, for fear of sacrificing one's potentially infinite future life -- and I have actually met some radical futurists who suffer from this sort of issue!
As Ben Franklin said: "Moderation in all things, moderation included."
Is Immortality of the Individual Good or Bad for Society?
It's not clear what mix of death and immortality (or extreme longevity) is optimal on a society-wide basis, in terms of maximizing joy and growth.
Clearly the death of brilliant, productive individuals with brains full of knowledge and experience is a waste.
On the other hand, there's some truth behind the bon mot that "Science advances one funeral at a time" -- old minds can get hide-bound with habit; new perspectives can lead to accelerated advancement.
It seems rather clear, though, that whatever the optimal balance is, currently human existence is tipped way too far toward the death side of things ... due to brute biological necessity.
Helping with life extension research is one of the most important things any person can do today.
Continuity of Self
Perhaps the deepest issue regarding immortality is "continuity of self."
If I live a billion years, and change by 1% each year, then before long I may become something that has no resemblance or commonality at all with what I am today. In what sense will that be "me"?
One way to think about this is: If a mind is changing smoothly and incrementally (maybe quickly, maybe slowly), and at each stage the phenomenal self of that mind feels like it's preserving itself as it changes -- then one has meaningful mental continuity. Perceived continuity of self, combined with empirical continuity of mind-stuff, is continuity enough.
This kind of "continuity of self" probably places limits on how fast a mind can evolve ... if you evolve too fast, the self can't feel itself evolving, and the subjective experience will basically be that of one mind dying and another getting born in the same vehicle.
One can imagine a future in which a certain group of minds abandons continuity and evolves super-fast into something amazingly advanced, whereas another group maintains continuity and as a result transcends more slowly.
Continuity and Growth
Continuity emerges in Cosmism as part of the value of Growth. Growth is not just about new patterns forming as time unfolds -- it's about old patterns growing into new and richer ones.
Without continuity of self, selves don't grow, they vanish and are replaced!
On the other hand, if continuity of self slows down the evolution of mind, then it may be a bad thing to the extent that it restrains the growth of minds.
The Choice principle suggests that each mind be allowed to judge this tradeoff for itself, inasmuch as this is possible.
One hopes there are ways of obsoleting this dilemma, which are not yet apparent!