There are several modern philosophies that posit man's final mortality (when you die, your existence ends). There is even an aberrant branch of modern evangelicalism that is arguing for annihilation for the confirmed wicked. Secularism and aberrant religion are giving us a very limited perspective: time. We are being told that time is all we have. This raises some interesting problems.
The first problem is that the erasure of eternity is an inadvertent erasure of everything that makes life meaningful. What do I mean? This: eternity is the only phenomenon that gives meaning to time. Let me see if I can explain. Suppose that when your life is over on this planet, your existence is also over. That means that nothing you did will ever count for anything as far as you are concerned. It is true that the things that you did will have enduring impact upon those that are down line from you in the flow of the law of cause and effect, but it is not true that it will make any difference to you that that is true. "Being" is required for meaning. If you do not exist, there is no meaning for you. There are those who think that while they exist, it is meaningful to them for them to think of the down line impact of their behavior, but the fleeting ego investment of a brief existence is really an illusion. There was no meaning for you before you existed and there will be no meaning for you if you cease to exist. Therefore, though there is an illusory "meaningfulness" in time, it is an illusion if time is all there is. Thus, the erasure of eternity is also the erasure of any meaningful meaning.
The second problem is that the erasure of eternity is an inadvertent erasure of everything that gives life any boundaries. What do I mean by this? This: eternity is all there is that gives life any sense of right and wrong. If a person lives only in time, there is no sense in him limiting himself in any of his desires or pursuits. If, when our physical lives are over, we cease to exist, the only thing that makes sense is to attempt to make our brief time in time as satisfying as we can. That means pushing the limits of satisfaction -- no matter who gets hurt in the process. There are those who would say that we must limit ourselves because we are also subject to our choices and they may lead us to a lot of pain. Excuse me? It seems to me that we are subject to pain no matter what choices we make. Pain is inescapable. And death is inescapable. Therefore, since we cannot escape either, what sense does it make to limit our pursuit of pleasure just to try to put off the inevitable? Paul was right when he said that if the dead do not rise, let us eat, drink, and be merry for tomorrow we die. But, the real problem here is this: if everyone gives up a sense of boundaries, the world will rapidly become the worst possible experience of everyone scrambling to get what they want at everyone else's expense. In other words, eternity is the only reality that lays a foundation for men to curb their innate meanness and allow others to experience good. In other words, eternity is the only thing that keeps time from becoming Hell.
The third problem with the erasure of eternity is an inadvertent erasure of personal value. If you are only a time-bound being that had no value before you existed and will have no value after your existence is over, what makes you think you have any value now? When eternity is erased, the only value a person has is the value he has in his own eyes, and that is nothing more or less than ego mania. Dispensable "being" creates dispensable people, and dispensable people are without enduring value. Enduring value. There is no such thing without eternity. Without eternity, we are worth nothing. It does not matter what happens to us any more than what happens to the hog that is sent to the slaughter to satisfy the appetites of those who enjoy cured ham. If we only exist in time, our existence is worthless.
It is no accident that our world is rapidly becoming more hopeless, mean, and despairing. It is rapidly accepting the notion of time-bound existence, and meaninglessness, meanness, and valuelessness are a part of that parcel.