Why do you call anything the natural purpose of anything?
Why do we call steering the purpose of your car's steering wheel? Because in the first place it does steer the car, and in the second place that fact is necessary to the explanation of why the car has one.
Yes, but you're talking about human nature, not a car.
Yes, but we can identify purpose in the same way in human nature. New life is the chief purpose of our sexual powers, because in the first place they do cause new life, and in the second place that fact is necessary to the explanation of why we have them.
But you're assuming that our nature has a design just like a car has a design.
I'm not assuming anything. A forensic pathologist concludes that the wounds on the victim's body were intended. An archaeologist concludes that the object he has dug up is an artifact. An intelligence analyst concludes that the radio blips he is picking up express a coded message. Watson concludes that the symbols cut into the bark of the tree were made by Holmes to point out the trail. In each case, the investigator finds that an intelligent cause is the most reasonable inference from the pattern of the evidence.
Well, I'm not a forensic pathologist. But that leads me to another problem. You say that natural law expresses the common moral sense of plain people, but plain people don't even understand these theories.
Saying that plain people don't know the natural law because they don't understand natural law theory is like saying that they don't know bodies fall because they don't understand the relativistic theory of gravitation. The phenomenon is one thing; the theory which describes and explains it is another.
So when you say plain people know the natural law, what exactly do you mean?
That there are moral basics they can't not know, like "Play fair," "Don't murder," and "Take care of your family." I don't mean that they know theoretical propositions like "There are moral basics we can't not know" or that they could explain to you about deep conscience and design inferences.
What good are the theoretical propositions, then?
They guard us from certain confusions, help out in a few difficult cases, and guide moral educators. And they help to answer people like you, who don't think folk do have real knowledge of the basics of right and wrong.
But they don't. There aren't any moral basics that everyone knows.
Of course there are. I just mentioned three of them: "Play fair," "Don't murder," and "Take care of your family."
Those are just platitudes. Everyone has his own idea of "playing fair."
Does he? Try making up your own idea of what's fair -- say, "giving the greatest rewards to the laziest workers" -- and see how seriously people take you. I mean outside of government.