This is one of those topics that I find extremely interesting. I have just got to put my two cents on this whole matter here. But firstly...
agiri_goshiki wrote...
When you die, you die twice.
Once when you're heart stops beating.
And once more when your name is muttered for the last time.
Yes! Although I could either be over-thinking this "phrase" too much or perhaps the other way around, I definitely agree with it. Also, what I'm about to say/think is probably completely irrelevant to the big picture anyway, so why bother being reserved about expressing it.
Thinking about this question, I cannot help but think about the keywords here: "Death" and "End". Personally, I believe that we as well as pretty much everything else are immortal in a sense. I say "in a sense", but what I really mean is that there's just another side to everything that is. It's common knowledge that when one dies, they aren't and cannot be aware that they died. Instead, earlier in their life, they most likely had the knowledge and image of death "persistently" weighing down on their existence. Usually, this knowledge is gained either by being told, or if not so, then from natural instincts of ours over the course of our own development in nature.
This now leads to an interesting train of thought I had: "What if our world as it is now sort of 'reset' to a new 'beginning'? Where everyone suddenly had to start over from scratch with functions like language, thoughts, and speech." With this example, there would be no one to inform us of the concept of death nor to tell us that we were going to die in the future. If not a single human knew about death this way and continued living their "repetitive" day-to-day life... that would make them eternal beings even if their body were to die... in a sense.
Though "death is the result of time". And time is a result of the concept of a beginning and an end to all things. That being said, we humans haven't been able to absolutely prove that there's a definitive beginning to everything. "There could be an event that comes even before this 'beginning'". How could we perform the same absolute proof-work for the end to everything? And not only that, is time itself even an absolute thing to begin with?
Building upon my train of thought above... those reset humans in that reset world would most likely begin their new existence living a simple, daily life in an absolute present-sense. It's the only knowledge they'd have "at the time". But as they experience the repetitiveness of that life, it'd feel as if it could be infinite. Their knowledge of the world would be that it's limitless and infinite, rather than our knowledge of it being that it's influenced by time. In these special circumstances, wouldn't death be a non-existent thing for those people? Their world would seemingly "repeat" itself eternally... and they wouldn't know that they died when/if they did.
Comical thought experiments aside... I can pretty much conclude: "yes" and "no", to the question. Based on my own beliefs, we are a rare and complex existence of a rather subjective nature. Whether we die or not... and whether it's the end or not, is entirely up to us and our control over knowledge/words/language. If, through those powers, we birthed the concept of time, and stayed true to it, then we probably shall die. I believe that there's always two sides to the world... everything that "which is", and everything that "which isn't". One cannot exist without the other. This power we own is merely just the ability to actively place the limits on to that "which is".
Actually, I'd consider true "death" to be when you feel as if you're not moving forward in life. It takes place in the present, so it exists absolutely. Because of that stagnating feeling, it's the "end", as nothing shall move forward from that point. See how it could potentially warp ones' perspective so much to view it as death (or a form of it). Who's to say that person is incorrect? This exact thinking is a specialty of the human existence (particularly, the tool we use: language).
The death we commonly know could be interpreted in so many different and diverse ways. One way I look at it is, common death is the same and/or has the same sensation of deep sleep. With our common knowledge of time, that dream we'd be having as we "sleep" would always be moving forward. And we'd always have the buried feeling that: "At some point, this dream will be over." To me, that rather doesn't seem like the end.
The world can be objective and finite, but then it MOST definitely has to be subjective and infinite in return.
TL;DR: Quote from one of my favorite philosophers... "Death is not an event in life: we do not live to experience death. If we take eternity to mean not infinite temporal duration but timelessness, then eternal life belongs to those who live in the present. Our life has no end in just the way in which our visual field has no limits." -- Ludwig Wittgenstein
That concludes my exact thoughts on this specific topic. I apologize if I went in circles with it, but I just couldn't help myself when it comes to this sort of thing. It's just too much fun.