So what about if you're aware of general socially agreed morals, and can appear to adhere to them, but this is more out of your own sense of what's rational/useful/constructive and what isn't, as opposed to any firm sense of things being right/wrong, good/bad?
What are you then? Is it just that your moral centre is staked around the concept of utility, a valuing of constructiveness and efficiency/efficacy, rather than around the concept of what's good for people, makes them happy, avoids harm to others etc.?
The two can overlap... at least in appearance. A person who never really thinks or cares about what's "right" or "good" might still appear to be doing right, doing good. Does this mean they're moral?