Are there moral truths?

Against the relativism of Protagoras, for whom "man is the measure of all things", Plato grounds values in objective Forms, the Just itself and the Good itself, which depend on neither convention nor opinion. Good and justice are universal and real, knowable by reason.

Theaetetus, 152a, 170a-172b · Republic, VI, 504e-509b

Platonic ethics is an ethics of virtue: a person's good lies in the state of the soul, and justice is defined as the harmony of its three parts, each performing its own function under the rule of reason. The good life is not a matter of rules or of calculating consequences but of an ordered, virtuous character.

Republic, IV, 441c-444e · Gorgias, 506c-508c

Truth is the soul's correspondence with what really is, the Forms: true discourse "says of things that they are as they are", whereas the false says them otherwise than they are. This conception, close to correspondence with intelligible being, carries a coherentist component, true knowledge forming a dialectical system bound to the principle of the Good.

Sophist, 262e-263d · Cratylus, 385b-c

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

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 distinguishes two objects of inquiry: relations of ideas (mathematical, certain and demonstrable) and matters of fact, whose truth lies in their conformity to what experience reveals of the real. Factual truth is thus a matter of correspondence with experience, while the truth of relations of ideas is a matter of internal coherence, hence the split weights.

Enquiry Concerning Human Understanding, sect. IV, part I (relations of ideas and matters of fact)