Without Aristotle or Saadia, or Aquinas mentioning it in those particular passages that deal with specific sins, I believe they are all fitting natural law with their larger system of things having a goal or purpose. So what would not be natural law would be what does not go towards that purpose of being human. [They explain that as being basically what we would say is attachment with God.]
So natural law is not the same thing as according to natural desire.
[I am mentioning this because it is the source of John Locke's "Natural rights" which is a different way of stating the Ten Commandments. That is Thou Shalt Not Steal is the same thing stated in a different way of the fact that people have a right to their own property.
