In his rebuttal/reply to his critics, I think Harris 'comes clean' to some extent on what his argument is. He writes in response to Russell Blackford (Blackford's text is highlighted, Harris' reply is not)
If we presuppose the well-being of conscious creatures as a fundamental value, much else may fall into place, but that initial presupposition does not come from science. It is not an empirical finding... Harris is highly critical of the claim, associated with Hume, that we cannot derive an "ought" solely from an "is" - without starting with people's actual values and desires. He is, however, no more successful in deriving "ought" from "is" than anyone else has ever been. The whole intellectual system of The Moral Landscape depends on an "ought" being built into its foundations.Again, the same can be said about medicine, or science as a whole. As I point out in my book, science in based on values that must be presupposed -- like the desire to understand the universe, a respect for evidence and logical coherence, etc. One who doesn't share these values cannot do science. But nor can he attack the presuppositions of science in a way that anyone should find compelling. Scientists need not apologize for presupposing the value of evidence, nor does this presupposition render science unscientific. In my book, I argue that the value of well-being -- specifically the value of avoiding the worst possible misery for everyone -- is on the same footing. There is no problem in presupposing that the worst possible misery for everyone is bad and worth avoiding and that normative morality consists, at an absolute minimum, in acting so as to avoid it. To say that the worst possible misery for everyone is "bad" is, on my account, like saying that an argument that contradicts itself is "illogical." Our spade is turned. Anyone who says it isn't simply isn't making sense. The fatal flaw that Blackford claims to have found in my view of morality could just as well be located in science as a whole -- or reason generally. Our "oughts" are built right into the foundations. We need not apologize for pulling ourselves up by our bootstraps in this way. It is far better than pulling ourselves down by them.
I applaud Harris for conceding that his concept of 'wellbeing' being the foundation of morality is a presupposition, yet he does not seem to address all the implications this has for his argument. If you note, he does not refute Russell Blackford's argument and in fact it still stands. What Harris says about it is that, '
There is no problem in presupposing that the worst possible misery for everyone is bad and worth avoiding and that normative morality consists, at an absolute minimum, in acting so as to avoid it. To say that the worst possible misery for everyone is "bad" is, on my account, like saying that an argument that contradicts itself is "illogical."'
So for Harris there is 'no problem' in presupposing wellbeing as the basis for moral values and he justifies this by saying that there is an equivalence between this presupposition and the principle of contradiction. Well, there is a lot that can be said about this. Firstly, there is no equivalence between Harris' presupposition and the principle of contradiction. Presumably he means that both his presupposition and the principle of contradiction are self-evident? Well, try and do logic without the principle of contradiction and compare that with trying to talk about morality without Harris' presupposition. It is obviously not self-evident for Nihilists, or Non-Cognitivists or Moral Skeptics, that there are any moral truths, even before we get to a discussion of what they might be. So here we have actually weeded out another Harris presupposition:
1. There are moral truths
If we agree with him on this, then perhaps we can agree with him that his other presupposition of 'wellbeing' is a good starting point for working out what those moral truths are, but then we have come rather a long way on the power of presuppositions alone and none of the way on logic or evidence (i.e. Science).
So where does this leave us? Science cannot determine moral values in the strong sense that moral values (their existence and content) are already presupposed up to the point that science has anything to do with them. Harris has surely conceded this point; at least he has not argued against it.
This is a problem for Harris and it is a 'fatal flaw', inasmuch as Harris seems to allude to a stronger claim, especially in the subtitle of his book, 'How Science can Determine Human Values'. Well in the stronger sense of this claim, this is not possible for the reasons Blackford gives, and Harris concedes as much. If Harris is not alluding to the stronger claim in the first place (which is still not clear) it is still a problem for him as he has chosen to use some misleading and ambiguous language in both his TED talk and his book and, as others have pointed out, the weaker argument that, 'if we are agreed that moral truths exist and that well being is a good basis for determining what those moral truths are then science can help us in better informing our moral decisions', is nothing new under the sun.
This passage from Harris encapsulates what I believe to be his tendency to equivocate on this matter:
However, my view of moral truth demands a little more than this -- not because I am bent upon reducing morality to "physical" facts in any crude sense, but because I can't see how we can keep the notion of moral truth within a walled garden, forever set apart from the truths of science. In my view, morality must be viewed in the context of our growing scientific understanding of the mind. If there are truths to be known about the mind, there will be truths to be known about how minds flourish; consequently, there will be truths to be known about good and evil.
So Harris writes he's 'not bent on reducing morality to physical facts in any crude sense', yet at the same time he ends up saying, 'If there are truths to be known about the mind, there will be truths to be known about how minds flourish; consequently, there will be truths to be known about good and evil.' Presumably these 'truths' about the mind are physical facts? Therefore
he is bent on reducing morality to physical facts (in whatever sense 'physical facts' can mean) Of course Harris inserts the weaker claim in between this contradiction: 'In my view, morality must be viewed in the context of our growing scientific understanding of the mind.'