Hi, thanks for replying. Harris's work isn't as clear as it should be. But having read him a couple of times, I think he deserves a little more credit.
First, his thesis is actually a lot weaker than it would appear. He's arguing that natural (scientific) facts can account for moral facts. To do this, he asks us to assume the universality of the well-being of conscious creatures. It's an argument appealing to intuition. This is also an argument for value. What is good is maximising the well-being of conscious creatures.
He denies to be a utilitarian, but his arguments push him towards this.
Second, if we accept this, then what we ought to do is just to do good. So, his argument would look more like this:
1. If you punch John, a conscious creature, then his well-being is diminished.
2. Intuitively, you ought not unnecessarily diminish the well-being of conscious creatures.
3. Thus, you ought not punch John.
Harris will deny you last syllogism because he wouldn't agree with P2.