Woo, been a while since a post. Okay. Consider the following argument, contra moral nihilism, i.e. the view that nothing is moral or immoral:
(1) If a belief is true, then we ought to believe it.
(2) Nihilism is a belief.
So, (3) If nihilism is true, then we ought to believe it.
(4) It is not the case that we ought to believe nihilism.
Therefore, (5) Nihilism is not true.
Is there something to 1 such that, if a nihilist were to deny it, he would be leading himself to irrationality? It would seem so. The denial of 1 is, after all, "It is not the case that if a belief is true, we ought to believe it." This seems to almost undercut the entire idea of rational argument. Denying 1 would also mean that it's not the case that, if nihilism were true, then we ought to believe it. Maybe they're fine with that, but I'm sure as heck not becoming a moral nihilist if I don't have any obligation to.
The nihilist seems to be committed to 4, since any "oughts" related to things like intellectual virtue or intellectual honesty are false on nihilism; these are, after all, ethical ideas (honesty is a virtue).
Maybe the nihilist could find some way of understanding "ought" which is entirely unrelated to ethics, making it possible to affirm that if a belief is true, then we ought to believe it, along with an obligation to believe nihilism. All of this without committing to the truth of any moral theses. This already seems implausible as such. Questions of epistemic justification, intellectual responsibility, and warrant are probably inseparable from ethics in some way. Nevertheless, suppose the nihilists pull it off. This leads to there being at least some normativity and responsibility, and the possibility of normativity and obligation in one sphere makes it harder to see why the nihilist would deny normativity and obligation in the sphere of ethics.
The situation looks grim for the nihilist then. They can (A) deny 1, implying that we're free to believe whatever we please (including the falsity of nihilism), as well as making the whole project of rational argumentation dubitable, or (B) deny 4 and accept that there is some normativity and obligation, putting them at odds with their claims about ethics. Or maybe they'll come to terms and accept all our premises. :-)
That's all a little sloppy I think, but I hope it makes sense. If not, please tell me.
P.S., birthday in two days! Would be a nice birthday present if I could figure out the soundness of this argument.