I am diving into meta-ethics for the first time to ground my normative ethical thinking. I was trying to classify meta-ethical positions succinctly and came up with the following:

• Cognitivism: Moral expressions are truth-apt.
  • Realism: There are mind-independent moral facts (objective).
    • Naturalism: Moral facts are reducible to non-moral facts.
    • Non-naturalism: Moral facts are not reducible to non-moral facts.
  • Anti-Realism: There are no mind-independent moral facts.
    • Non-objectivism: Moral facts exist, but they are all mind-dependent (subjective).
    • Error Theory: Moral facts do not exist.
• Non-Cognitivism: Moral expressions are not truth-apt.
  • Emotivism: Moral statements express emotional attitudes. (A.J. Ayer)
  • Universal Prescriptivism: Moral statements prescribe behaviors which are universalizable. (R.M. Hare)
  • Quasi-Realism: Moral statements project emotional attitudes as though they were real properties. (Simon Blackburn)
  • Many others...

First, is this characterization of the various views in meta-ethics generally correct or am I making any big errors or leaving anything out?

Second, does having a normative ethical theory presuppose moral cognitivism? The reasoning would be that to argue what is right/wrong, good/bad, virtuous/vicious, etc. (as normative ethical theories do) we need to agree first that these concepts can be expressed as truth-apt propositions.

Finally, do any of the major normative ethical theories (consequentialism, deontology, virtue ethics, divine command theory, etc.) entail one or more of these views, or can they all be realized independent of a person's meta-ethical views? (If the answer to question 2 is yes, then I am referring only to the varieties of cognitivism expressed above for this question.)

EDIT: I have changed my scheme above to include error theory as a form of anti-realism. Also, by "fact" I simply mean "true proposition".

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