Answer:
Life after death is a contradiction by definition, since death is where life ends. However, many things are contradictions of themselves by definition (eg atheism is a religion by definition, yet atheism is the lack of belief in a supernatural power and therefore in any religion). In nature obviously the death of one entity always means life for others. Life in general profits from the finitude of individual life.
Since our ancestor primates started to become self conscious it became more and more hard to accept that our existence is finite. Being hard to accept unfortunately doesn't make it untrue. There is no scientific clue that there is anything like a soul or spirit that is not a part of our body, so there is also no reason to suggest that after we die some conscious part of us will live on.
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There is, of course, no scientific proof to say that there isn't a part of us that lives on; science is inconclusive on many of the big religious and moral questions, and so cannot be used as an argument.
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On the other hand there is a lot of scientific proof that most (or even all) of the human traits that are/were considered to be part of a soul or spirit can be changed by something as simple as brain surgery. This by most people is considered evidence that these traits are in fact part of the living (and dying) body.