Is there a particular theory against the philosophical possibility of eternal life? I ask this because it seems to me that if eternal life were possible, men may lose the incentive to philosophize, hence the demise of philosophy.

I don't understand the comment that follows the question. I can't think of any philosophical questions in which I'm reguarly interested that would look terribly different if I knew I was going to live forever. Indeed, as Wittgenstein writes in the Tractatus , it's quite unclear how much the fact of eternal life would do much even to solve philosophical questions about the "meaning" of life. As Wittgenstein notes, an eternal life would in many ways be as much of a puzzle as a mortal one.

Is it possible for one to possibly know what exists after death? As humans, with a mind that exists solely as physical matter (and a soul, if religion is counted), when we die, how is it possible for this purely physical mind to keep on functioning, and allow us to realize that we are dead? As well, if we have souls, how can an entity created purely of energy (or whatever you think a soul is made of) have senses and detect that it exists, or even think?

Some people think they do know what exists after death. As Alex notes, "Nothing" is one option, and some people believe they have strong enough evidence for this view to make it a reasonable belief, and perhaps even to count as knowledge. On the other side, there are people who would claim to know, on the basis of divine revelation, that they will survive the deaths of their bodies. Presumably, not both camps can be right, and both camps might be wrong about their claims to know . But I don't see any general reason, absent consideration of the details, for supposing neither of them could know. Perhaps one wants to say that neither camp can really know, on the ground that truly conclusive evidence isn't available. But truly conclusive evidence is rarely available for anything, and yet we claim to know lots of things. That is to say: The claim that it is not possible to know what exists after death seems to be based upon a general sort of skeptical challenge that, allowed to run free, would...

If people did not fear death, is it likely that religion as we know it would not exist?

That question can be taken in many different ways. One way is historical. I'm in no position to answer that question. Another would be sociological. I'm not in a position to answer that question, either. Part of the problem here is that I'm not an historian or sociologist. Another is that there's substantial vagueness in the phrase "religion as we know it". Here's a different question I can answer: Does relgious faith have to be bound up with or somehow a consequence of one's fear of death? The answer to that question seems to me obviously to be "No". I suppose there are particular forms of religious faith that are so bound up with a fear of death, and perhaps these are the most visible in American public life or the most salient to non-believers, but there are plenty of forms of religious faith that are not.