Hard time understanding what exactly Hume and Prinz argue for sentimentalism.

Thanks for your response. Focussing on Hume, I have been reading "Moral distinctions are not derived from reason" and "Of the other virtues and vices". These are the passages form Treatise I have a hard time grasping. I realise my question is a bit broad, so I'll include some notes I took off a website explaining Hume.

"In Treatise Hume argues against the epistemic thesis (that we discover good and evil by reasoning). -Does this by arguing that neither demonstrative nor probable/causal reasoning has vice and virtue as its proper objects. -Demonstrative reasoning discovers relations of ideas, and vice and virtue are not identical with any of the four philosophical relations. (Resemblance, contrariety, degrees in quality, or proportions in quantity and number) whose presence can be demonstrated. -These could also not be identical with any other abstract relation; for such relations can also obtain between items such as trees that are incapable of moral good or evil. Furthermore, were moral vice and virtue discerned by demonstrative reasoning, such reasoning would have to reveal their inherent power to produce motives in all who discern them; but no causal connection can be discovered.

-Causal reasoning does infer matters of fact pertaining to actions, in particular their causes and effect; but the vice of an action (its wickedness) is not found in its causes or effect, but is only apparent when we consult the sentiments of the observer."

Reading back these notes I can't grasp what exactly they're saying. I think it's mostly the way in which it's written and I need someone to explain it to me in lay-man's terms or examples like "What process would Hume say happens when you judge a murderer to be morally in the wrong".

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