There are two ways in which the subject of morals may be treated. One begins from inquiring into the abstract relations of things; the other, from a matter of fact, namely, what the particular nature of man is, its several parts, their economy or constitution; from whence it proceeds to determine what course of life it is, which is correspondent to this whole nature. In the former method the conclusion is expressed thus, that vice is contrary to the nature and reasons of things; in the latter, that it is a violation or breaking in upon our own nature. Thus they both lead us to the same thing, our obligations to the practice of virtue; and thus they exceedingly strengthen and enforce each other. The first seems the most direct formal proof, and in some respects the least liable to cavil and dispute: the latter is in a peculiar manner adapted to satisfy a fair mind, and is more easily applicable to the several particular relations and circumstances in life.
Joseph Butler, Fifteen Sermons Preached at the Rolls Chapel, Preface. Hume's arguments at the beginning of Treatise, Book III, can be seen as a rejection of this idea. Hume has a sharp dualism about abstract relations and matters of fact; they just cover different things and so can't converge on anything. In the Treatise he argues precisely this for moral matters: morality cannot be based on abstract relations at all, and therefore must be based on matters of fact (namely, a kind of moral sentiment). Butler's convergentism -- that you can start at different places and get to the same place if you just take a large enough view -- is a general feature of his thought, and plays a significant role in how he himself applies his famous idea that probability is the guide of life.
