The science of morality is the study of what we “ought” to do (or “should” do) and has the goal of not only of determining/discovering those “prescriptions” but of developing the necessary tools and technologies to rigorously prove their validity. The first step of that process is to define exactly what we mean by ought. Statements which contain ought are prescriptive statements of what should be done or how the world should be.
Unfortunately, many people blindly quote David Hume’s A Treatise of Human Nature in a misguided “appeal to authority” in order to “prove” that rigorously deriving “oughts” is impossible — apparently, not having read it and being entirely unaware that Hume’s treatise is precisely an exercise in the science of morality and that his statements are simply those of a philosopher/scientist criticizing the rigor of the arguments/theories of others while proposing his own. In the passage normally quoted by proponents believing in an insurmountable “is-ought divide“, Hume is merely noting, first, that every moral system author he knows has made claims about what ought to be on the basis of statements about what is and, second, that none of them explain their reasoning as “‘tis necessary that it shou’d be observ’d and explain’d“.
Hume *NEVER* says that such a derivation is impossible, merely that it “seems altogether inconceivable, how this new relation [ought] can be a deduction from others [is, is not], which are entirely different from it.” Hume’s point is merely that there is a significant difference between descriptive statements (about what is) and prescriptive or normative statements (about what ought to be) and he, personally, can’t conceive of how the transition would be rigorously justified (even though he unknowingly brushes by the answer later).
Since ought statements are prescriptive statements of what should be done or how the world should be, the important question and the bridge over the is-ought divide is *WHY*? If one has a goal, there is a clear path from what is to what one “ought” to do in order to fulfill that goal. It is definitional in this simple case that one “ought” to perform those actions that give the best probability of goal success. Or, in mathematical terms, ought is a function of goals and circumstances that describes the actions which lead to the highest probability of success for those goals under those circumstances i.e. Ought = F(Goals, Circumstances). This should make it clear that, if the goal is undefined, ought is undefined.
The primary reason for Hume’s difficulty in conception is the assumption of true universality for moral “oughts” without an equivalent universal goal. If it is true that one has a goal yet it appears that one “ought not” perform the actions that are most likely to lead to goal success, it is because there is a more important goal that is blocked (or violated) by those actions. The problem with universal morality is that, for any action, we can always conceive of circumstances where a fundamental goal/motive would be violated by that action. And, indeed, Hume himself recognizes the primacy of goals/motives in saying that “In short, it may be established as an undoubted maxim, THAT NO ACTION CAN BE VIRTUOUS, OR MORALLY GOOD, UNLESS THERE BE IN HUMAN NATURE SOME MOTIVE TO PRODUCE IT, DISTINCT FROM THE SENSE OF IT’S MORALITY.”
Since there is no truly universal goal that will always trump all others, there can be no truly universal “oughts”. Note, however that, on the other hand, there are certain commonalities of goal and circumstance that humans will always experience — so this does not mean that morality is as relative as many people desire/fear. Indeed, much of the currently perceived variance in moral relativity is due to lack of knowledge and understanding of what is truly optimal for human goals — whatever they are. That these commonalities exist is made evident by the fact that humans have evolved a common sense of morality. In fact, it is worth noting that much of the current state of the science of morality is merely discovering why the actions that the human moral sense suggests us are the best possible “guesses” that could have evolved by this point and when (and why) they aren’t optimal.
Thus, a science of morality *can* start on a firm scientific basis and proceed rigorously from there.