For all the reasons I've outlined, I don't think it's correct to say that Sam Harris has justified his claim that science can in principle give us objective moral values.
However, that doesn't mean that moral values are completely subjective either. Moral systems can be inconsistent, and moral values can be effective or ineffective at achieving more profound moral goals. For those who agree that well-being is of primary concern, various moral decisions can be evaluated objectively with regard to how well they promote it.
Should we value a parent's right to corporally punish a child, or value the child's right to be spared deliberate physical pain? Well, if we wish to promote good character, then an objective decision should be possible given enough data. Unfortunately most of us make these decisions subjectively based on our own upbringing and capacity for empathy.
I suspect that Harris's true position is not that different from my own, and that perhaps our disagreement is more a matter of semantics than incompatible world views.
For the religious among us, Harris's arguments will fall on deaf ears. For them, morality comes from God, so science has no role to play.
For the rest of us, he encourages us to examine our moral values rationally. There are many examples where a scientific approach might give answers to complex questions.
If we agree with him that consciousness is necessary to feel suffering, that the purpose of morality is to prevent unnecessary suffering and that embryos are not conscious, then what is the argument against abortion?
Arguments against euthanasia are only coherent if our concern is the "slippery slope" aspect, where we fear that patients may feel pressured to end their lives. Arguments based on the sanctity of human life are irrelevant.
The legalisation of drugs might prove to be a good idea if we honestly and scientifically weighed the suffering caused by their prohibition against that which might be caused by their legal abuse. Instead, we see politically popular wars on drugs which are largely ineffective and deliver profits into the hands of violent criminals.
And if drugs are legalised, then is it right or wrong to actually use them? This is not a question that should be answered based on inherited moral values but judged on the evidence. Sam Harris himself has advocated for the use of LSD for those who are interested in expanding their mental horizons, and I think he may be right to do so.
Too much of our lawmaking and personal morality consists of knee-jerk, unconsidered responses based on inherited values of irrational shame and pride. I think Harris is entirely right to encourage us to think critically about our morality. I only wish he didn't claim that it could ever be absolute.