Martin,
If human morality truly has this wonderful theme I have to tell you that the human heart is ruled by something very opposite. As evidence I give you the world and our history. Humans by nature are not so good and all our history proves this out. For us to be good is a struggle, to follow our nature is easy.
I agree to an extent. Humans do not necessarily do what they inwardly recognise to be good. But the recognition of what is good and right is there in humanity. You should believe that, even with your faith-based restrictions, after all, what tree did Adam and Eve eat from?
I also agree with what JJ has posted above. In the main, and most fundamentally, the human heart is prepared to respond to Love.