“All prescriptive theory” is quite a large field that isn’t even finished. Formal logic and the square of opposition has the A proposition being ‘All are”. One learns to be very careful with that. All are x or None are x can allow zero exceptions to be true. Hume wanted to disprove cause and effect relationships, so he necessarily would have pointed out the looseness of ‘is’ propositions to ‘ought’ or should propositions, quite reasonably.
Prescriptive theories can be applied in fields beside moral philosophy, and in some case the formal logical tests would be applied equally and in others the tests fall outside of simple formal logic and within larger structures for analysis that might best be compared to dead reckon’d sailing judgments. Rather than being logically rigorous propositions formally the use was analytical. One could say for instance that 1 + 3 equals 4 and the answer they provided is 5, and they ought to have written ‘4’. That kind of statement is reasonable.
Moral propositions though, unlike Kant’s categorical imperative that has some logical validity in a dead reckoning sort of way, are descriptive of actually existing human behavior and suggestions to improve that in some cases. In others it could be a simple observational use of the word ‘ought’ for a moral circumstance where variant behavior did not comply with the prevailing idea of the normal correct behavior.
An example for that might be that a baby is crawling across a street amidst heavy traffic, the mother is laying on the sidewalk knocked out from a falling brick, and a passerby walks past the scene and allows the baby to be squished by a truck when he could have easily rescued the tyke from the rode. While not legally responsible to rescue the infant, a police officer that saw the scene from a distance says to his partner the “the rogue ought to have saved that baby”.
Experience of exigent circumstances are rather subjective and conditional, yet descriptive and normative (prescriptive) ethics describe situations in space-time, Situations that are recurrent can be emergent though not unique. Consider the Nurmagomedov vs Porier UFC 242 fight- It was like a martial arts match where each knew various katas or forms. None were unique or original, and there are lots of prescriptive analysis about what ought to have been done to get outcome A, B. or C. Prescriptive ethics about what people think they should do probably never would be over regarding humans. Hume’s Fork (good point) about empiricism and rationalism going separate paths, disregarded by Kant, might be a subject of more modern philosophical research in the developments of 20th century empiricism and Ayer’s book ‘Language, Truth and Logic’ wherein only empirically based statements-more scientific ones, had validity and the remainder were psychological and subjective. W.V.O. Quine broke that paradigm in ‘The Two Dogmas of Empiricism’. Epistemologically speaking the separability of the world and statements about it was renormalized or returned to something closer to a Kantian rather than Humean position. I think a lot of moderns like Dewey’s paradigm of everything being subjective, and so they like Hume’s ideas. He seemed to want to dismiss common ideas about the relation between words and objects-fair enough, yet he went too far in several ways, from a much later point of view in regard to subsequent developments.’
https://en.wikipedia.org/wiki/Normative_ethics Normative ethics are also known as prescriptive ethics, They are usual contrasted to descriptive ethics. Hume created an epistemological battle taken up by Kant. The resolution of the epistemological war was settled by logic and logical analysis of the relation between words and objects. Ethics falls into valleys between the hilltops of epistemology and logic. Subjectivists like Hume later tended to justify moral paradigms with epistemology that broke the ties between rationality and the world itself experienced by individuals. Prescriptive theory is an ethics about what people think they should do in a particular circumstance, descriptive theory is about what people actually do.