Ugh. Where to start...
One might well ask: why does any of this indicate that moral propositions have no rational justification? The arguments presented here show fairly conclusively that our moral judgements are instinctive, subconscious, evolved features. Evolution gave them to us.
Yes, because evolution gave us the instincts that solved the prisoner's dilemma and made social life possible. Which is why Jonathan Haidt finds it more helpful to define morality as, rather than being about harm and fairness, something like:
Moral systems are interlocking sets of values, practices, institutions, and evolved psychological mechanisms that work together to suppress or regulate selfishness and make social life possible.
Green is basically screaming bloody murder at how people stupidly conclude that incest is wrong in a case where some bad attributes of incest don't apply, and how this is part of a more general flaw involving people doing an end-run around the usual need to find rational reasons for their moral judgments.
His view is in complete ignorance of recent ground-breaking research on the nature of human morality (see above link). Basically, most secular academics think of morality only in terms of harms and fairness, but, worldwide, people judge morality on three other dimensions as well: ingroup/loyalty (do we maintain a cohesive group?), authority/respect, and purity/sancity (the last one being the intuition challenged by Greene's example).
While political discourse in the West has focused on harm and fairness, human nature in general is judging from all five. This narrow focus has resulted in Westerners, not surprisingly, being unable to justify from the three others unless they come from a ... religious background!
Or, more succinctly, morality is a meme that enables solutions to the prisoner's dilemma. All five dimensions, to some extent, work toward that end.
What Greene has discovered is better described as "Westerners do not have the educational background to justify and express their moral intuitions that go beyond harm and fairness." Congratulations: when you force people to talk about morality purely in terms of harms, you can get them to voice moral opinions they can't justify.
Had the participants gotten such grounding, they could have answered the incest dilemma like this:
"As stipulated, there is no harm from what the siblings did. However, that's just disgusting [sanctity], and is disruptive to the social order [authority]. Within your artificial scenario, you have assumed these difficulties away. If I and others did not find such acts disgusting, they would inevitably become more common, and social life would break down: first, from genetic disease, and second, from destabilized family units, where parents are forced to take sides between their own kids. Over time, this hurts society's ability to solve the prisoner's dilemma."
The fact that people cannot connect their moral intuitions to the evolutionary/historical reason that such intuitions evolved is not a reason to come to the conclusion Greene does.
I should also add that it starts off with a very questionable claim:
As a simple example, consider the use of the words in any standard ethical debate - "abortion is murder", "animal suffering is just as bad as human suffering" - these terms seem to refer to objective facts; "abortion is murder" sounds rather like "water is a solvent!".
If you're correctly paraphrasing Greene, this is misleading at best. Yes, those statements are syntactically similar, but most people are capable of recognizing when a statement starts to make a moral claim (or, upon further questioning, some concept they hold that is isomorphic to morality). They recognize that when you get into talk about something being "just as bad" as something else, you're talking about morality.
It's like saying, hey, "Jews are murderworthy" sounds rather like "apples are red", OBVIOUSLY we are ill-equipped to discuss morality!
FWIW, I don't even necessarily disagree with Greene that people approach morality from a flawed framework. But his arguments aren't very good, they ignore the literature, and don't present the right framework. Thumbs down.
Greene and Haidt have coauthored papers together, so I would guess they are aware of each other's work!
Joshua Greene has a PhD thesis called The Terrible, Horrible, No Good, Very Bad Truth About Morality and What To Do About It. What is this terrible truth? The essence of this truth is that many, many people (probably most people) believe that their particular moral (and axiological) views on the world are objectively true - for example that anyone who disagrees with the statement "black people have the same value as any other human beings" has committed either an error of logic or has got some empirical fact wrong, in the same way that people who claim that the earth was created 6000 years ago are objectively wrong.
To put it another way, Greene's contention is that our entire way of talking about ethics - the very words that we use - force us into talking complete nonsense (often in a very angry way) about ethics. As a simple example, consider the use of the words in any standard ethical debate - "abortion is murder", "animal suffering is just as bad as human suffering" - these terms seem to refer to objective facts; "abortion is murder" sounds rather like "water is a solvent!". I urge readers of Less Wrong to put in the effort of reading a significant part of Greene's long thesis starting at chapter 3: Moral Psychology and Projective Error, considering the massively important repercussions he claims his ideas could have:
As an accessible entry point, I have decided to summarize what I consider to be Greene's most important points in this post. I hope he doesn't mind - I feel that spreading this message is sufficiently urgent to justify reproducing large chunks of his dissertation - Starting at page 142:
One might well ask: why does any of this indicate that moral propositions have no rational justification? The arguments presented here show fairly conclusively that our moral judgements are instinctive, subconscious, evolved features. Evolution gave them to us. But readers of Eliezer's material on Overcoming Bias will be well aware of the character of evolved solutions: they're guaranteed to be a mess. Why should evolution have happened to have given us exactly those moral instincts that give the same conclusions as would have been produced by (say) great moral principle X? (X = the golden rule, or X = hedonistic utilitarianism, or X = negative utilitarianism, etc).
Expecting evolved moral instincts to conform exactly to some simple unifying principle is like expecting the orbits of the planets to be in the same proportion as the first 9 prime numbers or something. That which is produced by a complex, messy, random process is unlikely to have some low complexity description.
Now I can imagine a "from first principles" argument producing an objective morality that has some simple description - I can imagine starting from only simple facts about agenthood and deriving Kant's Golden Rule as the one objective moral truth. But I cannot seriosuly entertain the prospect of a "from first principles" argument producing the human moral mess. No way. It was this observation that finally convinced me to abandon my various attempts at objective ethics.