I would have to agree with SP. And I also would like to say that death is an end. Your body becomes what it was all along, a batch of chemicals which enrich the circle of living creatures --- little ones at first then plants and animals. So in that sense yeah we do go on. And its in a really beautiful unselfish useful way.
Once we start to view our lives as finite maybe the human race will focus more on making things better right here right now. Because really you may not have a tomorrow. So stress and stretch your humanity today. Learn today. Experience today. That may mean spending more time with friends or kids (or cats) whatever. I always appreciated John Lennon's song IMAGINE. "Imagine theres no country it isn't hard to do. nothing to kill or die for. and no religion too. Imagine all the people living life in peace youuuuu you may sayayayayayay I'm a dreamer, but I'm not the only one. I hope some day you'll join us and the world will be as one."
See my faith is in the human race. We won't be the destroyers for the patriarchal gods of the holy books. We'll find a way because we must. And knowing that gives me hope. More hope than a promised fairytale conclusion to my life. Dead is dead. Today I'm still alive so lets see what I do with that.
Immortality implies no beginning, no end, wich is what the Greeks taught.
I don't think so: imo this would suit the concept of eternity (aiƓn), at least in Platonism, better than immortality (athanasia). One can become immortal (athanatizomai), which implies a beginning.
Once we start to view our lives as finite maybe the human race will focus more on making things better right here right now. Because really you may not have a tomorrow. So stress and stretch your humanity today.
I hope for that kind of a realization too among those who fail to do something now and just say it'll all be fixed in the afterlife. Whatever the case, why shouldn't we do our best for a just humane world now? I think there'll always be those though that see a finite existence as an excuse for indulging in their nihilistic bents, wrecking havoc on the rest of us. So for the unfortunate people that don't see justice in this world, or have suffered horribly, I really do wish they can get some comfort somehow upon death.
Editted to add: here's a link to a prosaic explanation on NDEs.