Moral realism holds that there are moral facts and that at least some moral claims are true. There really is a fact of the matter whether it’s bad to be a racist. It really is bad to rape someone.
The truth of moral realism is difficult to show. This really isn’t as problematic as it may seem at first blush. Almost everything in philosophy is difficult or impossible to show. It’s (probably) impossible to demonstrate the reliability of sense-perception. People usually just come ready-made with their moral intuitions and accept their beliefs in a basic way, that is, without argument. I’ve argued before that such belief is not problematic so long as there are no overriding defeaters. But many defeaters for the truth of moral realism have been offered, ranging from arguments that moral judgements are subjective and thus not reflective of an external reality, to the idea that evolution would fail to produce true moral beliefs, to the idea that morality and naturalism are incompatible.
I don’t think that moral realism can be deduced from some more fundamental truth. I think it must be defended in a dialectical manner.
Here’s one example of such a dialectical strategy: We can show that any alleged defeaters for moral realism can also be levied against the reliability of sense perception, and yet we still hold that beliefs based on sense perception are rational, so we should also believe that beliefs based on moral intuition are also justified. Here’s how this works: There’s conflict between different sense-observers of some event E, in which the different observers disagree over what they saw. Yet this does not offer a strong enough defeater to undermine the whole-web of sense perception. A similar story can be told for moral realism. We can even (in many cases) explain why such disagreement arose in the case of the different sense observers as well as the different moral observers. Maybe the sun blinded a quarter of the sense observers, thus explaining their divergent experience. Maybe the Nazis failed to take into account all the moral data, thus explaining their divergent experience.
Here’s another example of such a strategy:
We can attack the alternative positions and show that they’re incoherent. This is known as the (non-fallacious) ad-hominem strategy. This strategy functions as an argument by elimination. This isn’t the same as establishing the truth of moral realism, it’s merely showing the inadequacy of the alternatives. So, what's the moral realism's alternative? Moral nihilism, which breaks into two: (a) Error-theory and (b) non-cognitivism. Error-theory holds that all moral claims are false. Non-cognitivism holds that all moral claims are just disguised emotions or attitudes and thus not subject to truth evaluation. Both suffer problems and have strong objections that can be levied against them (see here for an argument against error-theory). If we succeed in showing that the alternatives are inadequate, this goes some way towards showing that moral realism is rational.
Another:
We can reduce the cost of accepting moral realism by accepting a reductionary account of moral claims. Moral naturalism would be one example of this approach (check out Peter Railton). Parfit's approach of having moral truth being based on normative reasons that lack an ontology is another.
And another;
If it can be shown that God exists, many of the defeaters that are levied against moral realism are weakened. A theistic universe just seems prima facie more compatible with moral facts than a naturalistic one--some theists even argue that God’s existence is required for certain categories of moral truths, such as obligations and duties. A theistic universe can offer a very plausible story about how we come to have reliable moral beliefs in a way that evolution struggles to do. And, a theistic universe allows God to eventually punish and reward moral agents in a just manner.
Again:
Companion-in-Guilt arguments for moral realism seem quite potent to me. They rely on a parity between moral reasons and epistemic normative reasons; the idea being that everyone should accept epistemic normative reasons, and in doing so, are committing themselves to the same sort of entity as moral reasons. I'm thinking this move depends on Moral Rationalism, or the idea that morality reduces to rationality.
And the final dialectical method available for the moral realists:
Jolt the intuitions of the moral nihilist. Is it really not wrong for a person to torture and murder a 10 year old child? Was MLK’s life really wasted--the world really did not improve because of the work that he did? Was Hitler really no worse than Jesus? Our intuitions here are as strong as our intuitions that the external world exists. This experience of moral intuitions counts at least as some sort of justification for believing them. Phenomenal Conservatives seem to have at least some point to their arguments.