Hume thinks moral properties are “not derived from reason” (are not facts in the world or abstract relations). Give his argument for this claim. What ARE moral properties in Hume’s view? What are they like? Name a strength and a weakness in this view of moral properties.
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That's right. In his terminology, they cannot be derived from "relations of ideas".
This means that they cannot be discovered a priori, or through pure reason, like Kant thought. Nor can they be found in "matters of fact" (a posteriori reasoning).
He says several things arguing that morality does not derive from reason. For one, he first argues that things that come from reason alone, cannot motivate our actions. Then he states that morality IS supposed to motivate our actions. Thus, morality cannot come from pure reason alone.
Here's a direct quote: "Since morals, therefore, have an influence on the actions and affections, it follows that they cannot be derived from reason; and that because reason alone, as we have already proved, can never have any such influence. Morals excite passions, and produce or prevent actions. Reason of itself is utterly impotent in this particular. The rules of morality , therefore, are not conclusions of our reason."
Hume is an emotivist. So he believes that moral statements and judgments are really just expressions of our emotions. So for example, the proposition "killing is wrong" is like another way of saying "boo for killing!" It's just an expression of emotion, and emotions are cannot be either true or false. It's like if you walk by someone and see them crying, or see someone make a disgusted face. Those are emotions, but you cannot point at them and go "false!". It doesn't make any sense. It is the same with moral properties.
An advantage would be that it allows other cultures to have their own set of morality, which is not any more justified with our set of morals, and thus, not any better or worse.
A disadvantage would be that, well, the statements "murder is wrong" and "stealing is bad" cannot be true or false. This would really bother people. Many people believe these statements are true regardless of the culture or setting you're in. To make it even more interesting "torturing infants only for fun is wrong" cannot be true nor false.
I would suggest that you read Hume, he seems to be involved in this conversation.
And then purge that crack pot from your mind.