Is Moral Nihilism a Morality?

[SenseMaker007]

So, okay. Error theory is cognitivist. We're on the same page there. But I don't get why nihilists must be noncognitivists in your conception. It seems arbitrary really.

Error Theory says all statements about morality are wrong but according to Wikipedia:

Moral nihilism (also known as ethical nihilism) is the meta-ethical view that nothing is morally right or wrong.

(my emphasis)

You see, I agree with Wikipedia's definition of moral nihilism and that's exactly why I don't think Error Theory is a form of nihilism.

Now, a response would be if you were to say something like "Error Theory doesn't deem all statements to be morally wrong, so it can still be nihilistic, it just says that they are logically wrong from a metaethical standpoint." But then I'd just respond with "That's exactly why it isn't expressing anything normative." This is where I think the confusion resides.

Error theorists think that

1) moral statements express beliefs (cognitivism)

and

2) all such beliefs are necessarily false (nihilism)

Well, I've explained why I don't think evaluating something to be false, rather than meaningless, is nihilistic. But I think it would be helpful if we got past this purely semantic disagreement, do you agree?

Instead, I have two follow-up questions:

(1) How exactly can a noncognitivist metaethical theory express normative function?
(2) How exactly does saying that all statements about morality are false (Error Theory) express normative function?

I don't see how saying X is meaningless implies that you ought to do or not do X and I don't see how saying that all statements about morality are false means that you ought to do or not do anything at all. Whether everything is permissible because nothing is objectionable, in the case of Error Theory, or whether nothing can be deemed to be permissible or not because the whole thing is meaningless, in the case of noncognitivism, I don't see how either implies that we should or ought to do anything, or should or ought to avoid doing anything, from a normative standpoint.