The caveman think: "Today, I will go kill the giant cave-bear because I've seen in my dream that I could do it...Or he could simply misconstrue this dreamy reminiscence as a divine command or mystical experience:
"I'll go kill the giant cave-bear because God told me so in my dream"We all know what would probably be the (terrible) outcome of such situation, so maybe it is really for the best if we don't remember those hypothetical situations cooked up by our brain, thus avoiding getting stupid ideas...
However, our brain is not very good at erasing those simulations and we often have partial, dreamy and vague memories of them. This could probably have given our primitive ancestors the feeling that, beyond sleep, our mind (or soul) was accessing a fantastic, greater than nature world where everything was possible, where we could live forever and never get hurt. The paradise.
And, if in our everyday sleep we can reach paradise (or hell when we're stuck in an ever repeating bad nightmare) then, perhaps, when we enter the Big Sleep, the Eternal Slumber, we can live forever in it, once and for all.
Yes, perhaps the concept of life after death was simply inspired by dreams.
That's a thought that would have certainly pleased Shakespeare...