The Inadequacy of Relativism
Moral relativists claim that our moral intuitions are a product of our biological evolution, and hence they possess no metaphysical objectivity. All morality is therefore merely a human construct and nothing more.
However, by the same naturalist account of the world, rationality is also a product of our biological evolution. If we have no reason to ascribe any objectivity to our moral intuitions, we have no reason to ascribe any objectivity to our rational intuitions either. If we have no reason to believe that the intuition "one should not inflict cruelty" has any objective value, we also have no reason to believe that our rational intuition of a deductive inference being correct or a logical axiom being self-evident has any objective value.
A stubborn naturalist can even concede to this, I believe. But then he would try to squeeze his way out by suggesting a pragmatic account of rationality. He might say: okay, I accept that there is no reason to suppose rational intuitions have any objectivity validity, but we can accept rationality on the account that it 'works'.
But how can this pragmatist view explain how do we know they work? How do we know a deductive argument "works"? This becomes a problem of circularity. In order for us to know a rational intuition works, we must already possess that knowledge!
This is a genuine problem; rational pragmatism is therefore at a serious loss of explanation. A moral relativist has no choice but to accept rational relativism as well. Relativism simply collapses on itself. A relativist is thrown into the worst epistemological crises in philosophy, the hyperbolic doubt of Descartes. When you cannot even trust your own reason, what can you trust?
Conclusion: A belief in moral relativism on account of naturalism also necessitates a belief in rational relativism, and therefore it dies its own death.
[My thanks to Komal for helping me develop this argument.]