With our moral convictions, as with our belief in logic, or in the reality of the external world, few of us arrive at our actual conclusions by a rational process. It is not that we discover what the correct rules of inference are and then apply them, and come up with our conclusions. On the contrary, in logic and morals at least we derive our notion of what the correct rules of inference are from our convictions about what is the case. This means that we can no more prove that our moral convictions are valid than we can prove that the rules of logic are valid, just as we cannot prove that there is a reality external to ourselves.
Bryan Magee (from Confessions of a Philosopher, 1997)