Why do so many people insist so strongly, even aggressively, that without death, nothing would have any value? What's the big deal?

That's a great question! I suppose the idea is that without death, there would be urgency or boundary to our lives. Perhaps people think that part of what makes relationships important is that they will end. Maybe, too, there is a general, biological point, it would be hard for anything to live without death even a vegetarian needs to live on plants that are no longer alive. But the question might be adjusted somewhat: granted there is (perhaps inevitably there has to be death, but is it inevitable or necessary that that there can be no afterlife (at least for persons)? Is an afterlife possible (as is believed by billions of people historically and today, certainly in some of the great world religions) and what impact would an afterlife have on our values in this life? There is a fascinating literature on this. Bernard Williams has a famous essay to the effect that an afterlife would be (ultimately boring and so it would be irrelevant to the values of this life. I have a less famous essay "Why we need immortality" to the effect that if we love this life and people we should hope for more life. You can track both down by just doing a google (mine is in two anthologies and originally appeared in Modern Theology. You can find Williams' through the entry on his in the online Stanford Encydlopedia of Philosophy. Perhaps the truth lies inbetween, though I still commend the more up-beat view on an afterlife.

Your question is most often discussed under the topic The Meaning of Life. Stewart Goetz has a terrific book under that title with Continuum you might find helpful and illuminating!

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