I still believe the idea of immortality is silliness, and I just thought of a good reason why:

Assuming the universe is trillions of years old, life at least as complicated as ours should have come around before us. If that is true, and inconsequential immortality was a possible venture, they would have discovered it by now. If that is true, the universe should be teeming with life, since the rate of reproduction would be ever expanding with no limit in sight. And if that is true, we should've made contact by now.

But we haven't made contact, thus all of our hypothetical precursors didn't reproduce indefinitely, thus they didn't achieve immortality, and so I highly doubt we will either. In fact I'd say it's downright arrogant to think we ever would, regardless of your point of view, since it's quite obvious nobody else has done it yet.

EDIT: Just found the right term for "inconsequential immortality," which is actually called biological immortality (which means that you never age, but you can still be harmed and even killed).

As it happens, there is a certain type of jellyfish that is potentially biologically immortal, as it can reverse its life cycle by transforming back into a polyp, thus escaping death. These jellyfish are not much more common than any other creature on earth, however, as they are extremely vulnerable to predators in the polyp stage and they are still vulnerable to disease as well.

But, if we somehow able to create a biologically immortal human mutant by stealing genes from this jellyfish, we would have, for all intents and purposes, a biologically immortal man.