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
"Morality is more properly felt than judg'd of": reason, which compares ideas or establishes facts, cannot by itself produce moral distinctions. These rest on sentiments of approval and disapproval, which sympathy extends and which the adoption of a general point of view corrects for partiality; reason clarifies the relevant facts, relations and consequences, without itself producing approval or disapproval. The rules of justice and property do arise from a convention of mutual interest, with no original contract or promise, but that origin does not replace the sentimental ground of their moral approval.
A Treatise of Human Nature, III, I, 1-2; III, II, 2; III, III, 1 · An Enquiry Concerning the Principles of Morals, Appendix I
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
Morality rests neither on God's will nor on feeling, but on the autonomy of practical reason, which gives itself its own law. Any ground other than reason's self-legislation, whether happiness, perfection or a divine command, would make morality heteronomous: one would obey for the sake of something other than duty. God is postulated only to make possible, in the highest good, the union of virtue with proportionate happiness, never to ground moral obligation.
Groundwork of the Metaphysics of Morals, II (autonomy and heteronomy) · Critique of Practical Reason, Dialectic
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?)