"The unexamined life is not worth living" is a famous phrase apparently spoken by Socrates at his trial. He chose death rather than exile. Exile from Athens would mean he could no longer continue his investigation of life's important and interesting questions.
Many philosophers take this quote as justification for their own choice to spend their lives philosophizing. They would argue that the life of a philosopher is valuable because the philosopher is examining the important questions of life.
However, it seems to be implied in Socrates' statement that not only are there people who are living an "unexamined life", but that those people's lives are worthless. I question that implication because I believe that when a person encounters the concept of their own mortality they necessarily will examine their life. The degree and extent to which they carry out that examination varies greatly, but I think it does happen.
I choose to examine those interesting and important questions of life regardless of whether those questions have answers or not. However, that has no bearing on the value of my life. The lives of those who do not choose to "examine" their lives, if indeed such people do exist, are no more nor less valuable than my own.
Socrates choice of death over exile was the decision he felt was right, for himself. However, that does not extrapolate to others. We all make our own choices and try to live the lives that are best for us.
