Can a feeling bind?
On the axis: The source of morality · the authority of a feeling
Observing that nature made us compassionate states a fact; concluding that we ought to be so crosses the step from is to ought. If morality is only a feeling, what do we say to someone who does not feel it?
Justification
Hume spots an illicit leap in moral treatises: their authors slip without warning from propositions joined by is to propositions joined by ought, though a new ought cannot be deduced from any set of purely descriptive premises (Hume's guillotine). No relation of fact, and so no act of reason alone, can ground an obligation: value is not a quality of things but lies in the spectator's sentiment of approval. Morality thereby loses its realist foundation, against the rationalist moral realism that thought to read the good off being. Yet this sentiment, common to all human beings and regulated by shared utility, lends judgements a near-universal stability: the position is broadly constructivist, with a relativist share, without lapsing into arbitrariness.
A Treatise of Human Nature, III, I, 1 (the is-ought passage) · Enquiry Concerning the Principles of Morals, sect. IX and Appendix I
Justification
The moral law holds universally for every rational being, independently of cultures and inclinations: this is the most assertive universalism in the tradition. A slight constructivist weight is warranted by autonomy: the law is not discovered in the world, reason gives it to itself.
Groundwork of the Metaphysics of Morals, section II · Critique of Practical Reason
leads to: Status of norms (metaethics) (Are there moral truths?)