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I’m working on a writing question and need an explanation to help me learn.

Two species of reason
In order to think about the place of reason in ethics, we need to make a distinction. A Holy Grail in practical philosophy would be a reason that everyone must acknowledge to be a reason, independently of their sympathies and inclinations. I shall call that a Reason, with a capital letter. It would armlock everyone. You could not ignore it or discount it just because you feel differently. It would have a necessary influence, or what philosophers sometimes call ‘apodictic’ force. It would bind all rational agents, insofar as they are rational. If you offer someone a reason (no capital letter) and they shrug it off, you might say they are insensitive or inhuman, callous or selfish, obsessive or weird, imprudent or sentimental. These are defects of the heart. You may regret them, but if the audience feels differently you may not be able to prove to them that they are defects at all. But if you offer someone a capital-letter Reason and they shrug it off, then something different is wrong. Their very rationality is in jeopardy. There is something wrong with their heads.
Philosophers, of course, are professionally wedded to reasoning, so it is natural to them to hope that we can find Reasons.
Before the 18th century, many moral philosophers thought that we could. They thought that fundamental principles of ethics could be seen to be true by the ‘natural light of reason’. They were ‘a priori’, having the same kind of certainty as logic, arithmetic, or geometry; you could see from your armchair that they had to be true. If you couldn’t see it, then your understanding must be at fault, just as if you can’t understand that there is no biggest natural number, or no such thing as a round square. For many such principles were innate, inscribed for us by a benevolent deity, so that ignoring them would be a kind of impiety.
By the end of the 17th century, this theory had lost a lot of ground, especially among philosophers more ready to trust empirical sense experience as a source of knowledge, rather than allegedly divine revelations. If we want provability, it began to be felt, we cannot rely on God to have put it there. But even the great empiricist John Locke (1632–1704) subscribed to a rational foundation for the basic principles of morals:
…The idea of a supreme Being, infinite in power, goodness, and wisdom, whose workmanship we are, and on whom we depend; and the idea of ourselves, as understanding, rational creatures, being such as are clear in us, would, I suppose, if duly considered and pursued, afford such foundations of our duty and rules of action as might place morality amongst the sciences capable of demonstration: wherein I doubt not but from self-evident propositions, by necessary consequences, as incontestable as those in mathematics, the measures of right and wrong might be made out, to any one that will apply himself with the same indifferency and attention to the one as he does to the other of these sciences.
As this shows however, Locke thought this was something that could in principle be done, rather than something that had already been done. And he thought it had to be done with an excursus through theology, which scarcely inspires confidence.
This view was first challenged in the 18th century by the ‘sentimentalists’ the Earl of Shaftesbury and Frances Hutcheson, but then with much greater force by David Hume (1711–76), who took a dim view about the power of reason anywhere, but especially here. For Hume, reason’s proper sphere is confined to mathematics and logic, while knowledge about the way things are is due solely to sense experience. Neither affords us any substantive principles of conduct. Hence there are no Reasons. Hume drives the message home flamboyantly:
Reason is and ought only to be the slave of the passions, and can never pretend to any other office than to serve and obey them…Tis not contrary to reason to prefer the destruction of the whole world to the scratching of my finger. ’Tis not contrary to reason for me to choose my total ruin, to prevent the least uneasiness of an Indian or person wholly unknown to me. ’Tis as little contrary to reason to prefer even my own acknowledged lesser good to my greater…
There is evidence that Hume came to regret the rhetoric in such passages, and he plays it down when he returns to the issue in later works that he came to prefer, notably his Enquiry Concerning the Principles of Morals. But he continued to think that human reason has a limited reach. It includes mathematics and logic, for if we try to disobey their laws, understanding gives out and thought itself becomes impossible. We are left with no ideas at all. And we can talk of the reasonable, or scientific, approach to understanding the world, which often speaks with one voice, leaving no room for dissent. But when it comes to ethics we are in the domain of what Hume called passion or sentiment, general terms covering desires, attitudes, emotions, and preferences: the practical dispositions that direct our wills. And it sounds as though in this domain the heart rules everything.
That might be misleading. Our passions and sentiments need to operate in the world that we learn about. Mistakes about where we are and what is what is a prelude to acting disastrously, both for ourselves and others. As we shall see in Part 3, an inability to reason properly is as great a recipe for human disasters as actual vice and malevolence. Stupidity is at least as dangerous as sin. But what we incline towards and are motivated to pursue, after reason and experience have done their work, is another thing. Even basic, unambitious concerns, such as self-interest or sympathy, are not mandated by reason alone. If we choose to neglect our own interests we may be feckless and imprudent, but we are not contradicting ourselves. The plight of others gives us reasons to act, certainly, but not Reasons. There may indeed be some formal limits on our preferences: there is something ‘irrational’ about preferring A to B, and also at the same time preferring B to A. But there are no substantive restrictions on our passions imposed by reason alone.
This could be put in terms of a contrast between description and prescription. Calculation and basic consistency is involved in getting our descriptions of the world right. What we then prescribe is beyond their jurisdiction. This is what Hume meant by saying that reason is in fact wholly at the service of the passions. The passions, preferences, desires, and attitudes that we have are supremely important, for it is only in order to direct them towards effective action that we need to know anything about the world in the first place.

Summarize in your own words.