"1. Moral truths are anthropocentric truths":
On our account, moral facts exist, but not as objective facts which would be true for any rational creature anywhere in the universe. Moral facts are facts only with respect to a community of human beings that have created them...
Most people aren't philosophers, therefore moral realism is false? I'm not seeing the connection here. The core of the paper was talking about moral judgments or beliefs. Now they're suddenly drawing conclusions about the objects of those beliefs -- the "moral facts", not just our thoughts about them. Isn't this a whopping non-sequitur? Is it yet another instance of the lazy conflation of belief and truth (as suggested by their subsequent reference to the "moral truths held by members of [a] society") or is there some more charitable interpretation that I'm missing?
"2. The naturalistic imperative: all ought statements must be grounded, eventually, in an is statement" They offer as an example of a good is-to-ought inference:
Sheila is the mother of a 4-year-old boy, so Sheila ought to keep her guns out of his reach.
But of course even non-naturalists can endorse this (enthymatic) inference. That's because there are further moral premises implicit in the background, e.g. that mothers ought to keep their children safe from harm. This is not an example of empirical grounding of a moral claim, but of the empirical application of a more general moral principle.
This raises a more general worry I have about naturalistically inclined philosophers. When they claim that ethics must be "empirically informed", they could mean one of two things. If they simply mean that empirical contingencies affect how moral principles apply to our actual situation, then that's utterly uncontroversial. (A consequentialist will be interested to learn what would actually bring about the best consequences, for example.) But if they mean something stronger, that empirical findings should influence our first principles -- not just which conditional claims turn out to apply, but what should be conditionally claimed in the first place -- I don't see the faintest reason to believe this.
"3. Monistic theories are likely to be wrong"
If there are many independent sources of moral value [Haidt classifies humans moral intuitions under 5 categories: harm, fairness, authority, purity, and ingroup/outgroup] then moral theories that value only one source and set to zero all others are likely to produce psychologically unrealistic systems that most people will reject.
Note, again, the sloppy conflation of descriptive and normative "value" (belief and truth). Haidt likes to accuse liberals of failing to "understand" anti-gay sentiment, for denouncing it as immoral 'homophobia' rather than "appreciating" that it's a moral judgment which derives from our evolved 'purity' module. We parochial liberals limit ourselves to the first two "sources of value", and "neglect" the latter three. But here's the thing: just because there's a mental module which inclines people to judge yucky things as immoral, doesn't mean they're right. (Duh.) Sloppy, sloppy, sloppy.
4. Haidt and Bjorklund's fourth "implication" is that a moderate relativism is true:
If relativism is taken as the claim that no one code can be proven superior to all others, then it is correct, for given the variation in human minds and cultures, there can be no one moral code that is right for all people, places, and times.
Says who? Again, nothing in the descriptive theory of SIM implies any such thing; these guys are just making stuff up. (Aside: we should also take care to distinguish situation-sensitivity vs. relativism proper.)
They go on to reject radical relativism, understood as they claim that "no one code can be judged superior to any other code". Apparently a code that "radically violate[s] the values and wants of a large proportion of the people involved" fails to qualify as "well formed". It's nice that they don't want to endorse slavery and the like, but this ad hoc principle reinforces my sense that they're just making stuff up as they go along.
"5. The methods of philosophical inquiry may be tainted":
If the SIM is right and moral reasoning is usually post hoc rationalization, then moral philosophers who think they are reasoning their way impartially to conclusions may often be incorrect. Even if philosophers are better than most people at reasoning, a moment's reflection by practicing philosophers should bring to mind many cases where another philosopher was clearly motivated to reach a conclusion and was just being clever in making up reasons to support hear already-made-up mind... The practice of moral philosophy may be improved by an explicit acknowledgment of the difficulties and biases involved in moral reasoning. As Greene has shown, flashes of emotion followed by post hoc reasoning about rights may be the unrecognized basis of deontological approaches to moral philosophy.
This raises interesting issues about the genetic fallacy, and the extent to which explanatory reasons can debunk normative reasons. In assessing "clever" arguments, I don't usually care what "motivated" the author. Whether deontology is the most rational and systematically defensible approach to ethics seems logically independent from the question of its psychological "basis" in human proponents. I guess a spectator might draw on genetic considerations as a kind of Bayesian meta-evidence. But from within the practice of philosophy itself, I'm not sure these considerations are really all that relevant.
So, there you have it. Five alleged "philosophical implications", of which the first four are blatant non-sequiturs, and the fifth is at least dubious. Whether SIM is true or not doesn't really affect any of these questions. (Would the truth or falsity of SIM really influence your beliefs here, or even shift your credence in the slightest?) We need to do a priori philosophy to determine (1) whether there's a uniquely rational moral system, (2) which empirical contingencies have moral relevance, (3) whether disgust - as well as harm - can ground moral facts, (4) whether some moral codes are better than some or all others, and (5) in what conditions 'genetic' considerations are philosophically relevant.
Those are the fundamental philosophical questions here, and (so far as I can see) empirical psychology in general - and SIM in particular - doesn't have any implications for any of them. Certainly Haidt and Bjorklund haven't shown any. Perhaps other readers might have more luck?