Where does morality get its authority?

The distinction of good and evil arises from a sentiment of approval or disapproval, not from a deduction of reason: morality is felt more than judged. This sentiment is rooted in sympathy, the capacity to share others' affects, which makes us approve qualities useful and agreeable to oneself and to others. Hence an ethics of care and sentiment, with a virtue component (qualities of character) and a consequentialist concern for utility.

Morality is more properly felt than judg'd of.A Treatise of Human Nature, III, I, 2

Enquiry Concerning the Principles of Morals, sect. I and IX (moral sentiment, utility) · A Treatise of Human Nature, III, part I, sect. 1-2 (morals not derived from reason)

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

In the Dialogues Concerning Natural Religion, Hume dismantles the argument from design: the order of the world warrants no secure inference to an infinite, wise and good creator, above all given evil. Without professing firm atheism (he allows a vague cause or causes of order), he empties theism of any determinate content: the position leans clearly toward agnosticism and atheism.

Dialogues Concerning Natural Religion (esp. parts V, VIII and XI) · The Natural History of Religion

Nothing is good without qualification except a good will: neither talents nor happiness, which can serve evil. If moral worth lies neither in the object willed nor in the consequences, it can lie only in the form of the maxim, its fitness to hold as a law for all. From this the categorical imperative is derived: act only on a maxim I can will to be universal. This is a deontology that refuses, against utilitarianism, to measure duty by outcome; the Doctrine of Virtue reintroduces the virtues, but as derived from duty, hence a small residual weight on that pole.

Act only according to that maxim whereby you can at the same time will that it should become a universal law.Groundwork of the Metaphysics of Morals, section II

Groundwork of the Metaphysics of Morals, sections I and II · Metaphysics of Morals, Doctrine of Virtue

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

Since all knowledge is bounded to phenomena, God, who is not one, escapes proof: Kant dismantles the proofs of God's existence one by one (ontological, cosmological, physico-theological), the first failing in its leap from concept to existence. Yet what is barred to knowledge is required by morality: without God and immortality, the accord of virtue and happiness (the highest good) would stay unthinkable. God thus returns as a postulate of practical reason, an object of rational faith and not of knowledge, which warrants a moderate rather than an assertive theism.

Critique of Pure Reason, "Transcendental Ideal" · Critique of Practical Reason, Dialectic