The term means that I believe deeply that God exists and cares about all life, including human beings; that "God" is a term we use to describe a universal force bigger than ourselves and vastly greater than we can imagine; that any doctrine promulgated by a particular religion is inherently self-limiting and has only partial truth; that no one has the best or only truth, and anyone who thinks so is deluding themselves and possibly others around them. Science has everything to do with it, since it is the area of human thought that most dares to grapple with the scale of the universe and our place in it. Most religions are too concerned with their own survival to face the inadequacy of their theologies. As JB Phillips said, "Your God is too small." I admire religious organizations for what they do to better the human condition -- up to the point where their theology gets in the way. As one of your guests said recently, "[Christianity] answers questions I didn't ask." And it, and others, are silent on the questions most important to me. I have fond memories of my tradition (Episcopalian) but their theological language is alienating to me. The best I can say is "I don't know;" I wish I could say more about what I know but that would not be completely honest.
More information about text formats