Is Moral Nihilism a Morality?

[Alan V]

Well, let's say someone just became and atheist and wanted to investigate alternative ethical systems to get away from theistic morality.  Per Wikipedia, he has a range of choices including nihilism:

Ethical theories that can be naturalistic

• Altruism
  
• Consequentialism
  
• Consequentialist libertarianism
  
• Cornell realism
  
• Ethical egoism
  
• Evolutionary ethics
  
• Hedonism
  
• Humanistic ethics
  
• Moral skepticism
  
• Natural-rights libertarianism
  
• Objectivism
  
• Utilitarianism
  
• Virtue ethics
  

Cultural relativism and nihilism posit that each one of those systems is a farce.  I was wondering where a person who thinks that all morality is arbitrary looks to get their moral propositions.  I know they have them, lol.

(all ethical theories are "naturalistic")

Actually, nihilism falls under the category of moral skepticism. So if nihilism says each one of these systems is a farce, then it is self-refuting.

That opens the door for nihilists to consider alternative perspectives.