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M*W: Interesting question, and there seems to be a competition, but not in the minds of atheists (and I cannot speak for all of them). Having been a christian, and knowing what they think and believe, there is a feeling an atheist might have as a sense of completion. We don't rely on something that is not there. The environment is there. We are here, and we're all going straight back into the environment. We won't come back in anyone else's body. We won't come back as a ghost. We simply become worm food, and the life cycle continues....
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M*W: I don't feel that at all. I feel I owe them everything, even though I'll be worm food long gone. In due time, I don't expect to even be remembered at all. Not to get into a discussion about genetic memory at this time. I also don't believe all atheists have a defeatist attitude of it all coming to an end. Essentially, I won't care then, but I still do now. Now is all I've got. Now is all you've got. We have to live our lives in the now. That is the most important concept.
As an atheist, I know that is all there is, but I don't have any fears of dying. When I became atheist, I realized I had nothing to fear at all.