Metaethics Part 1: Cognitivism/Non-cognitivism

[DLJ]

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cognitivism, In metaethics, the thesis that the function of moral sentences (e.g., sentences in which moral terms such as “right,” “wrong,” and “ought” are used) is to describe a domain of moral facts existing independently of our subjective thoughts and feelings, and that moral statements can accordingly be thought of as objectively true or false.

https://www.britannica.com/science/cognitivism

Contrast this with noncognitivists who think "Murder is wrong" is not a fact or opinion. It is a "gut reaction" .... "Murder, bleh!" or "Murder, yuck!"
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Based on previously discussed / corrected definitions and that flow diagram, are you ok with Ethical Cognitivism and Moral Non-cognitivism as both being accounted for?