I said in the previous post that this is not a valid argument: "The case I make in the book is that morality entirely depends on the existence of conscious minds; minds are natural phenomena; and, therefore, moral truths exist (and can be determined by science in principle, if not always in practice)."
I do agree that the phenomenon of morality would not exist if conscious minds did not exist, if that's what's meant by what comes before the first semi-colon. That's because I think that the concept of the phenomenon of morality involves social regulation of the conduct of creatures that are at least conscious (they probably need to be self-conscious as well, and and maybe have other cognitive characteristics).
We observe societies with various norms of behaviour that are enforced by attitudes of praise, blame, ostracism, etc., and we recognise this phenomenon as "morality", and I expect we would not recognise it as morality if it involved regulation of things that are not conscious. Even when we apply moral standards to the behaviour of business corporations, which are not literally conscious, I doubt that we'd think we were applying moral standards if not for the fact that directors, business executives, shareholders, and so on are conscious.
In all, I accept:
P1. If conscious minds did not exist, the phenomenon of morality would not exist.
Harris may want something stronger than this, but I don't see how he's entitled to help himself to it. I also accept:
P2. All conscious minds are natural phenomena.
From P2. we can conclude that if there were no natural phenomena there would be no conscious minds.
The conclusion that then follows from all this is actually:
C. If no natural phenomena existed the phenomenon of morality would not exist.
That is hardly a surprising conclusion. I'm sure it's true. Note, however, that we are talking about morality as a social phenomenon. It does not follow that "moral truths" exist in the sense that moral realists typically mean. To try to demonstrate that will require a different argument, probably one with far more controversial premises.
Doubtless there are truths about the phenomenon of morality. But one of those truths about the phenomenon may be that human beings and human societies often claim falsely that their moral norms are objectively binding (in the sense discussed in the metaethical literature). It may, indeed, be one of the truths about the phenomenon of morality that moral norms are never objectively binding in the relevant sense. That is, roughly: they are never binding, on pain of irrationality, on the people concerned, irrespective of their actual desires. Whatever bindingness they do have does not transcend the relevant desires and institutions.
Arguments to the effect that the phenomenon of morality would not exist without the existence of natural phenomena, or that it is itself a natural phenomenon, or that it can be studied in some sense that we might call "scientific", go nowhere near establishing moral realism. All of the metaethical issues that divide realists of various kinds from anti-realists of various kinds are left open by all this. We're looking at a very bad argument.